The power of focal points

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The Power of Focal Points

A thesis by Mayra van Houts Supervised by dhr. dr. A. Ule Student number: 6057969

MSc Economics

Track: Behavioural Economics and Game Theory 15 ECTS

Abstract

There has been some considerable effort to capture focal points in a variety of

experiments and theories. This paper contributes by further testing characteristics of focal points. The main purpose of this study is to investigate whether people will rely more on saliency of labels in large coordination games compared to small coordination games. The secondary purpose of this study is investigating the power of salient labels in games with asymmetric payoffs. Both hypotheses were tested with experimental data using pure coordination games, Hi-Lo games and coordination games with asymmetric payoffs. No empirical evidence is found for both hypotheses. However, in a survey directly following the experiment, a quarter of the participants did indicate that they switched strategies between the small and large games.

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Statement of Originality

This document is written by Mayra van Houts who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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1. Introduction

Players of games with multiple equilibria are surprisingly more effective in coordinating than standard game theory would predict (Mehta et al., 1994). Even with unrestricted options to choose from, coordination rates can be very high (Hargreaves Heap et al., 2017). Schelling was the first to examine this in some informal experiments and

described the concept in his classic work The Strategy of Conflict (1960). He called such equilibria focal points.

Focal points stand out from the other equilibria by some sort of salience. A strategy is perceived as salient by the players because of some commonly shared features (Leland & Schneider, 2018). Focal points are acknowledged as an important part of decision-making for players in a coordination game, but are also very hard to observe. Due to the psychological and cultural factors of saliency, it is difficult to incorporate in the formal structure of a game (Isoni et al., 2013).

There has been some considerable effort to capture focal points in a variety of experiments and theories. Currently there are two generally accepted explanations for players behaviour in coordination games (Bardsley et al. 2010). The first are cognitive

hierarchy theory (Camerer et al., 2004) and level-k thinking (Crawford et al., 2013;

Crawford et al., 2008). A second approach is team reasoning (Bardsley et al., 2010; Colman & Gold, 2017; Sugden, 1995). In the empirical literature, evidence for both theories has been found and how people coordinate in these games maybe highly dependent on context and the type of game (Bardsley et al., 2010; Bardsley and Ule, 2017; Faillo et al., 2017). It is clear that no unified theory of how people coordinate exists and the concept of focal points remains an interesting area of research. Much is still unclear about the decision making of players.

Hargreaves Heap et al. (2017) find that in some pure coordination games with unrestricted strategies coordination rates are higher than in games where there is a restricted set of strategies. For example, in their experiment they used word games where players either pick from a list of fruits or word games where players could pick any fruit they could think of. Coordination rates were significantly higher in the unrestricted version of this game. Somewhat similar to Hargreaves Heap et al. (2017), this paper will compare focal points in games with small and large strategy sets, but will remain restricted to games with restricted strategy sets.

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5 The primary hypothesis of this paper centres on the saliency of labels in small and large games. It is predicted that in games with a large strategy set, labels with unique elements stand out more and thus players will be more likely to pick a strategy with a salient label.

Another stream of literature focuses on the problems with salient labels in coordination games. Crawford et al. (2008) argue that the power of focal points is strongly reduced in games with payoff asymmetry in their equilibria, such as in the classic Battle of the Sexes game. If the payoffs are asymmetric, players may have a conflict of interest in picking between equilibria. They found sharp decline in

coordination rates in their games when payoffs were asymmetric. Although it can be argued that the labels used by Crawford et al. (2008), are not very salient in the first place.

The second hypothesis of this thesis focuses on games with payoff asymmetry. Contrary to Crawford et al. (2008) the games in this thesis have been designed with labels that are intended to have stronger salient features, with one of the labels being more apparently unique than the others. In this thesis their hypothesis is retested: it is expected that there are no differences in coordination between games with symmetric and asymmetric payoffs, given that the games have labels that have more apparent unique features.

The experiment was conducted online. In total 102 people participated in the experiment. No empirical support is found for either hypothesis, although this was expected for the second hypothesis. Furthermore, I do find qualitative evidence of participants switching strategies between small and large games.

This thesis is organized as follows. In the next section the most important related literature is discussed. In section 3 the games of this thesis are described and

predictions for each game are made. Furthermore it contains a discussion of the hypotheses and a description of the experimental design and procedures. In section 4 the results are reported and analysed. Finally, in section 5 the results and their

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2. Theory

The main purpose of this study is to investigate whether people will rely more on saliency of labels in large coordination games compared to small coordination games. The secondary purpose of this study is investigating the power of salient labels in games with asymmetric payoffs. Several strands of literature are relevant here. First, the

literature that laid the basis for the theory of coordination games and focal points. Second, the studies trying to refine the theory of coordination behaviour (team

reasoning, level-k thinking and cognitive hierarchy theory). Before the literature will be discussed, the concept of a coordination game will be defined. In the last part of this section a brief recap of previous empirical findings will be discussed. Further findings relevant to the specific hypotheses of this study will also be highlighted in section 3.3.

2.1 Coordination games

A coordination game is an interactive decision game in which two or more players have a common interest in coordinating their actions and their expectations of one another’s actions. In playing a simple 2 player pure coordination game, players make assumptions about the possible strategies of the other player and formulate best responses (Bardsley et al., 2010).

The coordination games for this paper are defined as follows: There are two players, each player (P1 or P2) chooses from the same set {s1,…, sm} of pure strategies, where m≥2. If the players choose the same strategy sk, P1’s payoff is π1,k>0 and P2’s payoff is π2,k>0; otherwise, if the players choose different strategies, both payoffs are zero. Hence, there are m pure-strategy equilibria (the main diagonal of the payoff

matrix). All other payoffs are zero. The games include pure coordination games, where all the equilibria have the same payoff, defined by πi,k=πj,l for all i,j ∈ {1,2} and all k,l ∈ {1,…,m}; Hi-Lo games, where some of the equilibria have a lower or higher payoff than the other equilibria, defined by πi,k=πj,k for all i,j ∈ {1,2} and all k ∈ {1,…,m} and πi,k≠πi,l for some i,k,l; and coordination games with asymmetric payoffs, where the players do not have equal payoffs in the equilibria, with strategies j,k such that π1,j>π1,k and π2,j<π2,k for some j,k (Bardsley et al., 2010; Faillo, Smerilli, & Sugden, 2017; Schelling, 1960).

In a pure coordination game there are m symmetrical Nash equilibria. If players are to coordinate on a Nash equilibrium, it has to be differentiated from the other

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7 equilibria in a way that both players recognize. Otherwise a rational solution for a pure coordination game will be choosing the mixed strategy equilibrium with a 1/n

probability for every pure strategy (Bardsley et al., 2010). A solution to make the

equilibria distinguishable in the theoretical analysis is to include assumptions about the labels of strategies.

Every real world interaction that is modelled in game theory has a strategy with a label (Mehta et al., 1994). That label is common knowledge for the players and may be everything that is recognized as so by a player. It can be a colour that stands out, but may also be the first option in a list or a symbol that attracts attention. It is important to know how players are influenced by those labels and how they use those labels in playing games, because those labels can have large consequences for the analysis of games (Mehta et al., 1994). To include the labels in the analysis of coordination games, they are added to the definition of the game. So, completing the definition of a

coordination game, there is a set of L = {l1,…,ln} distinct labels for each strategy, which are common knowledge to both players.

2.2 Focal points

Schelling first introduced the theory of focal points in his famous work The Strategy of

Conflict (1960). About focal points he says: “focal point[s] for each person’s expectation

of what the other expects him to expect to be expected to do” (Schelling, 1960). Say for example, two people have to meet together in Amsterdam, without having the

opportunity to establish a time or place. There will be some place and time that is seen as common to both persons and therefore functions as a focal point, for example

meeting at noon on Dam square. For game theory, a focal point is an equilibrium that is selected by players in response to the salience of its label (Isoni et al., 2013).

Consider the Heads and Tails game, where players have to choose between either ‘Heads’ or ‘Tails’, there are three Nash equilibria: (Head, Head), (Tail, Tail) and the mixed strategy Nash equilibrium (0.5: Head, 0.5: Tail). For a player there is a 0.5 chance of coordinating with the other when choosing between one of those strategies at

random. Therefore one may expect that when this game is played, the outcome would be a 50% division between Heads and Tails. However, experiments show that significantly more players choose Head than Tails, so the actual coordination rates are substantially higher than 50% (Mehta et al., 1994). In this case, the (Head, Head) equilibrium is a focal

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8 point, and the strategy Head is salient for the players. Or one could say that the strategy

Head has a label that stands out for the players of the game.

A combination of characteristics of a strategy may function as focal point if it stands out, because of some unique feature it possesses. This feature may be the label attached to the strategy, but it could also be the possible payoff in the corresponding equilibrium (Colman, 2006). When a label stands out from the others, that label can be called salient or as stated by Gold and Colman (2018): ‘a salient item in a group is one that stands out from the rest by its uniqueness in some conspicuous respect’. This uniqueness is not part of any formal game theoretical analysis of the game, mostly because its features are psychological or culturally defined (Colman, 2006). However, various theories have been developed to capture these features and test them

empirically.

2.3 Theories of Coordination

Several theories have been developed about the nature of focal points. After reviewing the existing literature two main approaches can be distinguished. The first is cognitive hierarchy theory (CHT) and level-k thinking. The second is team reasoning and payoff dominance.

2.3.1 Cognitive hierarchy theory and level-k thinking

As discussed above, it is often assumed that players behave rationally. They form beliefs about the strategy of other players and choose a response accordingly. However, if a player forms incorrect beliefs, and acts on those incorrect beliefs, then players are not in equilibrium. Players may for example be overconfident in their own abilities and

underestimate the other players. Cognitive hierarchy theory (CHT) is a way to describe this individual reasoning, where each player assumes that her strategy is the most refined (Camerer et al.c, 2004).

The model posits different levels of rationality, the lowest level called ‘level 0’ players (L0). The decisions of L0 players are non-strategic and the least rational, they randomize. It is assumed that L1 players know the decisions of L0 players and the way they are distributed over the population, they then act on those beliefs. L2 players go further and use the knowledge about L0 and L1 players to form beliefs. Level-k thinking differs by assuming that players only look at one level below them, instead of all the

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9 levels below. For example a L2 player chooses best responses only for L1 players. This is where CHT differs from level-k thinking, in CHT a L2 players looks at both L0 and L1 players and their relative distribution in the population (Bardsley & Ule, 2017; Camerer et al., 2004; Faillo et al., 2017).

There is some discussion about the assumptions for L0 players (Hargreaves Heap et al., 2014). As mentioned above, one of the possible assumptions is that L0 players play randomly. This can be seen as the default assumption (Faillo et al., 2017). Another

assumption is that L0 players choose the option that stands out to them, being the strategy with the highest possible payoff or the one with the most salient label

(Crawford et al., 2008). Crawford et al. (2008) propose that L0 players focus on payoff salient strategies, that is, payoffs that stand out because they are different or the highest. They further propose that if there are multiple payoff salient strategies, L0 players then use label salience to choose between those strategies. The assumptions on L0 players have been tested, but there is no clear answer to which strategy they use and it might not be consistent across games (Hargreaves Heap et al., 2014). In fact, it might be the case that the relative distribution of L0 players is very low, possibly 0 (Crawford et al., 2013).

2.3.2 Team reasoning and payoff dominance

Between all the theories developed to account for focal points, team reasoning is the most striking. In a way it clashes with the one of the most fundamental axioms of economic theory, that of a rational individual maximizing her own utility. Bacharach (2006) defines team reasoning as follows: “work out the best feasible combination of actions for all the members in the team, and then do your part in it”. With team

reasoning, players begin by asking themselves, independently, if there is a decision rule that would be better for both than individualistic rules, if both players followed the better rule (Crawford et al., 2008). In other words, team reasoning players search for an outcome that benefits the group of players, and then act on that outcome, if it exists (Gold & Colman, 2018).

Team reasoning is also used as an alternative explanation of why payoff

dominant equilibria are chosen in coordination games. Payoff dominance is a principle whereby rational players reject any equilibrium that is strictly Pareto-dominated by another equilibrium (Faillo et al., 2017). For example, in a Hi-Lo game, with payoffs

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10 (10,10), (10,10) and (7,7) on the diagonal, there is no way to coordinate one of the (10,10) equilibria, because the two are isomorphic. A possible strategy for a player is randomizing between those two equilibria. This creates a payoff that is expectedly lower than (7,7). So choosing (7,7) is then payoff dominant (Faillo et al., 2017). It is then team optimal to choose (7,7).

There are also situations in which team reasoning may fail to yield successful coordination. Crawford et al. (2008) point out that when payoffs are asymmetric in the Nash equilibria, a conflict of interest can occur and players may want to coordinate on different equilibria, which influences the feasibility of team reasoning. Another

complicating factor is pointed about by Faillo et al. (2017). There might be ‘naïve team reasoners’ that fail to recognize the salient or payoff dominant strategy, you can still end up in randomizing behaviour.

2.4 Important findings

Bardsley et al. (2010) performed two experiments to test if cognitive hierarchy theory or team reasoning explained focal points better. They found evidence for CHT in one experiment, and team reasoning in the other. They highlight the decision context as an important feature to pay attention to. The specification of the coordination task is acknowledged for having lot of influence on the outcome of the game. So, the framing of a coordination assignment is an important topic to keep in mind when executing this experiment (Bardsley et al., 2010).

Faillo et al. (2017) also found evidence for both team reasoning and level-k thinking. So both modes of reasoning are being used in coordination games. They suggest that there probably is no single theory to explain all coordination and that it depends largely on the formulation of the game being played. Evidence for team reasoning is also found by Bardsley and Ule (2017).

Additional support for team reasoning as rational strategy comes from Gold and Colman (2018). They show for example that under some assumptions team reasoning can explain why it is may be rational to cooperate in a Prisoner’s dilemma, even though the Pareto-dominant outcome is not a Nash equilibrium. This is an important step for economics, as it gives an opportunity to include collective rationality into the standard assumptions.

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11 In coordination games with asymmetric payoffs, such that one player would prefer a different Nash equilibrium than the other player, Crawford et al. (2008) found a sharp decline in coordination. They games are a variations of the classic Battle of the

Sexes game. This is also supported by Parravano and Poulsen (2015) and Faillo et al.

(2017) who executed similar experiments. However, both Crawford et al. and Parravano and Poulsen (2015) used very weak salient labels (‘x’ and ‘y’, and ‘a’ and ‘b’

respectively). Another point of discussion is the strong focus on payoff differences by Crawford et al. (2008). The focus on payoff differences may have primed subjects to pay more attention to the payoff differences. Isoni et al. (2013) argue that such a focus may have been a factor in the strong reduction of coordination. Furthermore, they tested the effectiveness of focal points in tactic bargaining problems with payoff asymmetries and found that labels functioned as powerful focal points.

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3. Methodology

In this section the experiment will be described. Section 3.1 describes the games played in this experiment, section 3.2 contains the experimental design and procedure and in section 3.3 the hypotheses and expectations of the outcome of the experiment are discussed.

3.1 Description of games

Participants made decisions in one-shot two-player diagonal coordination games. Participants played several types of coordination games as defined in section 2.1: pure coordination games, Hi-Lo games and coordination games with asymmetric payoffs.

Diagonal coordination games have several advantages for studying focal points. Players can only differentiate between equilibria by means of the equilibrium payoff or the labels given to those equilibria. Also, the games are relatively easy to understand and the amount of information to process is small in comparison (Faillo et al., 2017).

The games differ in number of strategies and label types. The different games are described below and an overview of all games can be found in Table 1.1_{This study} explores two effects. The first is the difference in the power of saliency between small (three strategies) and large (ten strategies) games. The second is the power of saliency within different payoff structures. This is investigated by comparing between games with symmetric and asymmetric payoffs in both small and large games.

3.1.1 Word games

In the word games participants had to pick one city out of a list of cities. If the

participants picked the same city, their pay-off would be 10 points. If they both picked a different city their pay-off would be 0 points. There were two versions of this game, a small word game (SWG) and a large word game (LWG).

SWG consisted out of three options: London, Hamburg and Munich. London is the odd one out in this list. It has several salient features over Hamburg and Munich. First, it is a British city and the other two are German. Second, it is a capital city. Third, London is more famous and much larger than both Hamburg and Munich, which are of both of a similar size.

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13 In LWG the participants had ten options to choose from: London, Hamburg,

Munich, Cologne, Hanover, Dortmund, Bremen, Leipzig, Frankfurt and Stuttgart. For the same reasons as above London had the most salient features.

3.1.2 Number games

In the number games participants had to pick between pictures of handwritten numbers. If participants picked the same number, their payoff would be equal to that number of points. If they picked a different number from each other, their payoff would be zero points. This game is equivalent to what is commonly known as a ‘Hi-Lo’ game (Bardsley et al., 2010; Faillo et al., 2017).

There were two versions of this game, a small number game (SNG) and a large number game (LNG), each with two different payoff variations. The SNG has three options to choose from, twice a picture of the number 10 and once a picture of a lower number, either 5 or 7 (SNG-5 and SNG-7). The LNG has ten options to choose from, nine times the number 10 and again either 5 or 7 (LNG-5 and LNG-7). See Table 1 for an overview of each game.

Every strategy has a nondescript label, but the players are aware that the labels are not identical. This is done by displaying the choices as pictures of handwritten numbers, which were all very similar but not identical. Thus all equilibria in which both players choose the number 10 are isomorphic and hard to distinguish from each other. See figure 1 for an example of the choices in SNG-5, the other games can be found in Appendix D.

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14 Figure 1. Display for Small Number Game (SNG-5), with pictures of handwritten numbers.

3.1.3 Card games and Vegetable games

In the card games and vegetable games participants had to pick one picture out of a list of different pictures. If the participants picked the same picture, their payoff was 8, 9, 10, 11 or 12 points, depending on the game. If they both picked a different picture their payoff was zero points.

Every strategy had a label in the form of a picture. The first set of labels consisted of pictures of playing cards. It is assumed that playing cards are well known among the participants. The second set of labels consisted of pictures of a vegetable or a fruit. These were all vegetables and fruit well known in Europe, where all of the participants were recruited.

The card games and vegetable games had a small and a large version, each with two payoff variations, one with symmetric payoffs and one with asymmetric payoffs. Thus, in total eight different versions of these games were played.

The small card game with symmetric payoffs (SCG-S) had three options to choose from, the ace of hearts, the nine of spades and the three of clubs. The ace of hearts is the odd one out in the list. The ace of hearts has several salient features over the other two. First, it is often the highest card and in almost all card games a more important card

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15 than the other two. Second, the red colour stands out compared to two black cards. All the options had an equal payoff of 10 points.

The large card game with symmetric payoffs (SCG-S) had ten options to choose from: the ace of hearts and nine numbered cards either clubs or spades (see Table 1 for details). The ace of hearts is still the odd one out, for the reasons mentioned above.

The asymmetric counter parts of these two card games are denoted with SCG-A and LCG-A, respectively. SCG-A and LCG-A were the same as their symmetric counter parts, but with the payoffs changed to (11, 9) or (9, 11) depending on the card (see Table 1 for details), so there is a moderate payoff asymmetry.

The small vegetable game with symmetric payoffs (SVG-S) has three options to choose from, a picture of a strawberry, broccoli and asparagus. The strawberry is the odd one out of the list. It has several salient features over the other two choices. First, the strawberry is a fruit. Second, the colour red stands out from the two green

vegetables. All the options had an equal pay-off of 10 points. LVG-S has ten options to choose from, the strawberry is still the odd one out, for the reasons mentioned above.

In the versions of the vegetable games with asymmetric payoffs (SVG-A and LVG-A) the payoffs are changed to (12, 8) or (8, 12) depending on the picture. This creates a moderate payoff asymmetry. The payoff differences are larger than in the card games.

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Table 1: Overview of Games

Game Labels Possible Payoff

SWG s1: London; s2: Hamburg; s3: Munich (10,10) for s1,…,s3 LWG s1: London; s2: Hamburg; s3: Munich; s4: Bremen;

s5: Cologne; s6: Dortmund; s7: Frankfurt; s8: Hannover; s9: Leipzig; s10: Stuttgart

(10,10) for s1,…,s10 SNG-5 s1: (5,5); s2,s3: (10,10) (5,5) for s1; (10,10) for s2, s3 LNG-5 s1: (5,5); s2,…,s10: (10,10) (5,5) for s1; (10,10) for s2,…,s10 SNG-7 s1: (7,7); s2,s3: (10,10) (7,7) for s1; (10,10) for s2, s3 LNG-7 s1: (7,7); s2,…,s10: (10,10) (7,7) for s1; (10,10) for s2,…,s10 SCG-S s1: A♡; s2: 3♣; s3: 9♠ (10,10) for s1,…,s3 LCG-S s1: A♡; s2: 3♣; s3: 9♠; s4:2♣; s5: 4♣; s6: 6♣; s7: 7♣; s8: 3♠; s9: 5♠; s10: 6♠ (10,10) for s1,…,s10

SCG-A s1: A♡; s2: 3♣; s3: 9♠ (11,9) for s1; (9,11) for s2, s3 LCG-A s1: A♡; s2: 3♣; s3: 9♠; s4:2♣; s5: 4♣; s6: 6♣;

s7: 7♣; s8: 3♠; s9: 5♠; s10: 6♠

(11,9) for s1, s4, s5, s6, s10; (9,11) for s2, s3, s7, s8, s9; SVG-S s1: Strawberry; s2: Asparagus; s3: Broccoli (10,10) for s1,…,s3 LVG-S s1: Strawberry; s2: Asparagus; s3: Broccoli;

s4: Cabbage; s5: Carrots; s6: Courgette; s7: Fennel; s8: Lettuce; s9: Onion; s10: Peas

(10,10) for s1,…,s10

SVG-A s1: Strawberry; s2: Asparagus; s3: Broccoli (12,8) for s1; (8,12) for s2, s3 LVG-A s1: Strawberry; s2: Asparagus; s3: Broccoli;

s4: Cabbage; s5: Carrots; s6: Courgette; s7: Fennel; s8: Lettuce; s9: Onion; s10: Peas

(12,8) for s1, s4, s7, s8, s10; (8,12) for s2, s3, s5, s6, s9

This table presents an overview of all the games played in this experiment. The first column gives a shorthand notation for each game, the second column for the labels used for each strategy and the third column the corresponding payoffs if both players picked the same strategy.

3.2 Experimental design and procedure

The experiment was conducted online via an online form, over a period of 10 days.2_The online distribution provided the possibility to recruit enough participants within the schedule for writing this thesis. All participants were recruited through social networks. The participants were required to have a sufficient understanding of English and at least 18 years of age. A participant was sent an invitation to participate in the experiment with a link to the online form. The experiment consisted of two parts, the actual coordination games and a short survey. This was preceded by an introduction, instructions and test questions. The introduction text, instructions, the test questions and the experiment questions can be found in the Appendix.

After opening the link, an introduction was shown, detailing the procedure, payment and confidentiality. Payment was done with a lottery. Participants could earn points in the experimental tasks as explained in the instructions. Each point represented

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17 a lottery ticket, say a participant earned 20 points through completing the experiment, then she entered the lottery with 20 tickets. The prizes in the lottery were 25€, 15€ and 10€ in Bol.com or Amazon gift cards. The lottery was executed once all participants had completed the experiment and the end date was reached, this was explained to the participants in the introduction and also at the end of the experiment.

After the introduction the participants were presented with instructions and examples. Then came two practice questions to make sure the participant understood the payoffs and procedure of the experiment. After every practice question automated feedback was given. A wrong answer received an extra explanation combined with the correct answer. A correct answer received a message saying ‘the answer is correct’. The program was designed in a way that subjects could only go to the next question if they selected an answer. For the further duration of the experiment no feedback was given. Because there was no possibility to make sure that participants remade the practice questions until they understood everything completely, participants with wrong answers were excluded from the analysis. The practice questions and feedback can be found in Appendix C.

The start of the experiment was announced to the participant after the practice question. Every participant had to complete seven tasks. Every task consisted of a two-player one-shot coordination game; see section 3.1 for a detailed description of every type of game and Table 1 for an overview of all the games.

The questionnaire program did not allow a design were participants could play in real time against each other or were players could be paired together by the program. The players were randomly paired after the experiment was finished, so that the payoffs could be calculated. It was made clear to the participants in the introduction that they would play against another participant.

To construct a paring and to allow a comparison between games, four groups were created. In each group, subjects received seven different tasks. In each task the subject was confronted with a set of choices and was required to choose one. Each choice was associated with a specified number of points. The games were divided over the four groups in a way that group 1 and 2 played against each other and group 3 and 4. See Table 2 for an overview of games per group. To illustrate this more clearly consider the asymmetric card games. Participants from group 3 and 4 played SCG-A against each

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18 other, one from the viewpoint of player 1 and the other from the viewpoint of player 2. Participants from group 1 and 2 played LCG-A from the two viewpoints.

Table 2: Overview of Games per Group

Game Group 1 and 2 Group 3 and 4

SWG x LWG x SNG-5 x LNG-5 x SNG-7 x LNG-7 x SCG-S x LCG-S x SCG-A x LCG-A x SVG-S x LVG-S x SVG-A x LVG-A x

This table gives an overview of which games each group played.

The experiment is carefully designed to limit possible noise in the results. All

participants always saw their own possible payoff in blue and the other player’s payoff in green. All participants were randomly divided over the four groups. Within the groups the seven questions were presented in a random order. The possible answers to every question were also presented in a random order. It was also made clear to the participant that their unknown partner not necessarily saw the choices in the same order. This was to prevent coordination on the order of choices.

To limit learning effects, repetitive mistakes or heuristics, participants only did a small number of tasks. Every set of games consisted of two number games, one word game, two card games and two vegetable games. However, even with a small number of games it is possible that participants gained experience with each game.

The experiment was concluded with a survey, consisting of some background questions for age, gender and country of residence. Additionally they were asked to describe how they picked their answers and if they changed strategies between small and large games. This provided a rich control mechanism to see if the participants understood the experiment and some extra insights in their decision behaviour. The survey was partly inspired by Bardsley et al. (2010), because it gave them some extra

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19 understanding of the choices made by the participants. Survey questions can be found in Appendix E.

At the end of the experiment participants were asked, but not obliged, to provide their e-mail to participate in the lottery. Each participant got an anonymous ID that was tied to his or her choices in part 1 of the experiment. The results of part 1 and part 2 of the experiment were stored separately to avoid personal identification while analysing the game. After the participants were matched together in pairs, the points in each game were calculated and the lottery was executed. A person outside of the experiment and different from this author then matched the IDs of the winners to their e-mail addresses and distributed the payment to the winners. This way, anonymity for the participants was ensured.

When the 10-day period of conducting the experiment was finished, the lottery was executed and participants received an email with their payoff and their earnings.

3.3 Expectations and hypotheses

In each game there are multiple Nash equilibria and in every game there is one intended salient equilibrium. This intended salient equilibrium is always designed to be the ‘odd one out’ or in more than one ways distinguishable from the other equilibria. As

discussed in section 2, there may be several explanations as to why people coordinate on these salient equilibria. However, no unified theory of how people coordinate exists and it may be dependent on context (Bardsley & Ule, 2017; Faillo et al., 2017;

Hargreaves Heap et al., 2017; Parravano & Poulsen, 2015).

3.2.1 Hypothesis 1

In the pure coordination games there are as many Nash equilibria as there are strategies and all are identical in payoff (Faillo et al., 2017). If participants play according to CHT or level-k thinking, the coordination depends on the L0 players. All higher level players should copy L0 players’ strategy, as that would be the only way to coordinate. If L0 players play a strategy at random, it does not matter what higher level players do and their expected payoff would be equal to the Nash equilibrium payoff divided by m (Bardsley et al., 2010). However, if L0 players opt for the strategy with the most salient label, it would suit higher level players to do the same. If all L0 players would act this way, every participant would pick the most salient label and the expected payoff would

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20 be equal to the Nash equilibrium payoff. In reality, this might be an unlikely scenario. It may very well be that L0 players are a mix between those playing at random, and those picking the most salient label. If this is the case, the optimal strategy for higher level players is still picking the most salient label. Obviously, for L0 players to pick the most salient label, they would first have to recognize the salient features of the label. Failure to recognize the odd-one-out in list of labels (both consciously and subconsciously) would leave only randomly picking a strategy as an option for L0 players, given that in pure coordination games the strategies are otherwise identical in payoff.

Under team reasoning, players look for the best combination of strategies for all the members in the team, and then do their part (Bacharach, 2006). In a pure

coordination game with equal payoffs in each Nash equilibrium, this would mean finding a strategy that they can coordinate on. In other words, finding a strategy that stands out. Thus, it is expected that team reasoners would pick the strategy with the most salient label. Faillo et al. (2017) point out the problem with ‘naïve team reasoners’. These are players that for example fail to recognize the salient features of one of the labels. In this case, these players are similar to randomizing L0 players in CHT or level-k thinking, their only option is to pick one of the strategies as random, because none of the labels stand out to them and all diagonal payoffs are identical.

It has been noted in several studies that coordination rates depend on the

strength of the saliency. The more the label stands out of the rest of the labels, the easier it is to recognize for players and for them to act accordingly (Bardsley et al., 2010; Crawford et al., 2008; Faillo et al., 2017). In this experiment the strength of the label is not varied, instead the size of the strategy set in each games varies. It is expected that the salient features of ‘the odd one out’ in each game are more apparent in a large set of strategies than in a small set of strategies. For example, a British city would stand out more in a list next to nine German cities, than next to two German cities. Similar arguments can be made for each of the pure coordination games described in section 3.1.

In the number games it is difficult to predict what L0 players may do. Focussing on payoff salience could mean that they go for the odd one out and thus pick the lower payoff or they might be attracted to picking the highest possible payoff. One may expect that in the larger games the payoff saliency of the odd one out becomes higher. Higher level players should follow L0 players to try and coordinate.

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21 As mentioned in section 2.3, team reasoning can be used to explain why in Hi-Lo games, such as the number game here, players would choose sometimes pick the lower payoff. It is interesting to note that in SNG-5, coordinating on the number 5 or

coordinating on the two nondescript equilibria with the number 10, both have the same expected payoff. If both players coordinate on the number 5, they are guaranteed 5 points. If both players try to coordinate on the number 10, they have a chance 0.5 that they pick the same number 10 (and a chance of 0.5 of picking a different one), also resulting in an expected payoff of 5 points. For team-reasoners it may thus be difficult to choose on which of the strategies they should coordinate, because there is no team optimal strategy. In the other three games SNG-7, LNG-5 and LNG-7, they do not face this problem and they have a higher expected payoff if they would choose the odd one out: the lower number. Furthermore, with regard to the possibly naïve team-reasoners, it should be more apparent that (7, 7) is payoff dominant in LNG-7, than in SNG-7.

For all games, the odds of coordinating at random is lower in a large game, than in a small game. If this is apparent to the players, it may trigger them to finding salient features to coordinate on. For all reasons mentioned above, the primary hypothesis of this study is as follows:

H1: More participants will choose a strategy with a salient label in coordination games with a large set of strategies than in coordination games with a small set of strategies. This hypothesis will be tested by comparing the share of participants choosing the intended salient strategy between games with small and large strategy sets.

Related to this hypothesis are the findings of Hargreaves Heap et al. (2017). They find that in some pure coordination games with unrestricted strategies coordination rates are higher than in games where there is a restricted set of strategies. For example, in their experiment they used word games where players either pick from a list of fruits or word games where players could pick any fruit they could think of. Coordination rates were significantly higher in the unrestricted version of this game. While their experiment has some similarities to the one in this thesis, an unrestricted set of strategies may lead to different behaviours than a relatively large set of strategies.

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3.2.1 Hypothesis 2

In coordination games with asymmetric payoffs the coordination rate might be lower due to a conflict of interest of the players (Crawford et al., 2008). In addition to the strategies in pure coordination games, the difference in payoffs can also play a role when players choose their strategies. Also, as Faillo et al. (2017) note, the asymmetry itself can also be used as coordination device.

L0 players playing according to CHT or level-k thinking – next to playing either randomly or choosing the most salient strategy – may also be attracted to the salience of the payoffs, i.e. the highest possible payoff for themselves. For L1 players, it would then be optimal to choose a strategy which gives the highest possible payoff to their

opponent in equilibrium. If there are several equilibria with the same payoff it would be optimal for L1 players to randomize between them. Then, in level-k thinking, it would be optimal for L2 players to go for the same equilibrium as L1 players, which is the

equilibrium or equilibria with the highest possible payoff for themselves. Under CHT their optimal strategy would depend on their beliefs of the ratio of L0 and L1 players. However, it is expected that when the saliency of the labels is strong that L0 players still pick the most salient label, especially in large games where their saliency is more

apparent.

Team reasoners should notice that despite the conflict of interest for players in picking between the two equilibria, it is still beneficial to coordinate on the same

equilibrium. Therefore, one would expect that players that follow team reasoning would still go for the strategy with the most salient label.

Crawford et al. (2008) found a sharp decline in coordination when using asymmetric payoffs in their coordination games. For example, in a 2-by-2 game with payoffs of (5,5), for P1 and P2 respectively, on the diagonal, compared with (5,6) and (6,5) on the diagonal, led to a large decline in coordination. This is also supported by Parravano and Poulsen (2015), and Faillo et al. (2017), who executed similar

experiments. As labels Crawford et al. (2008) use ‘x’ and ‘y’, where ‘x’ is the supposed salient one, because ‘x marks the spot’. The saliency of this label relies on players

thinking of this idiom when seeing the labels ‘x’ and ‘y’. It may also be noted that ‘x’ may derive some saliency from being first in the alphabet, being the first option in the list, and from ‘x’ being the most used letter in algebra. However, one could argue that the saliency of this label is not very strong and that ‘x’ and ‘y’ are very similar labels. The

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23 inherent weakness of their labels may work to their advantage in testing their

hypothesis as players may focus more on the payoff asymmetry than on the weak salient features (Isoni et al., 2013). Similarly Parravano and Poulsen (2015) used labels ‘a’ and ‘b’. Faillo et al. (2017) did not use label saliency as a coordination device, but instead used payoff differences, similarly to Hi-Lo games.

In this thesis the results of Crawford et al. (2008) and Parravano and Poulsen (2015) will be retested in games with labels that have more apparent salient features. I do not expect to find the same decline in coordination as in their experiments.

Nevertheless, the hypothesis is formulated similarly to the previous literature: H2: Payoff asymmetries creating a conflict of interest between players will lead to a reduction of participants choosing the most salient label.

This hypothesis will be tested in small and large games with asymmetric payoffs. It is expected that in large games the intended salient strategy will be more apparent than in small games. Therefore it may be that even with asymmetric payoffs, the amount of players choosing the intended salient label in large games will be quite high. Thus, it is not expected that this study finds evidence to support hypothesis 2.

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4. Results

In this section the data obtained in the experiment will be analysed and compared with the previously discussed theory. In the first part I present summary statistics and the first set of results. The second and third part will evaluate the data against the

hypotheses. In the fourth part a brief review of the survey answers will be discussed.

4.1 Characteristics of the participants

A total of 102 participants engaged in the experiment. Participants who answered one of the two test questions wrong were dropped in the analysis, to ensure that only those who have understood the rules of the experiment enter the analysis.3_{This left 79}

participants, of which 42 were male and 37 were female. A large part of the participants were students in their final year or recent graduates and the mean age of participants was 32.8. The vast majority of participants lived in the Netherlands (72 out of 79 participants), 5 lived in other European countries, 1 in Canada and 1 in the United States. Participants were recruited via the social networks and participated in the experiment by means of an online form. All data was collected between 26th_{of july and} 6th_{of august.}

An overview of the characteristics of the participants can be found in Table 3. Participants were randomly assigned to groups in equal proportions. However, due to not everyone finishing the experiment, and the filtering of people on test questions, the groups in the analysis are not of identical size. Most of the base characteristics are similar across groups. Group 3 had comparatively less women, but not significantly so (χ2_{(3) = 0.92; p=0.82).}

As can be seen from Table 2 in section 3.2, group 1 and 2 played the same games, as well as group 3 and 4. The difference is the viewpoint of the player. One of the groups played from the perspective of player 1, and the other as player 2. For the analyses group 1 and 2, and group 3 and 4 are merged together.

3_{As a robustness check all analyses have been replicated with the entire group. This did} not affect any of the results or conclusions.

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Table 3: Characteristics of Participants

Group N Share Women Mean Age

Group 1 22 0.50 32.9

Group 2 23 0.52 36.4

Subtotal Group 1 and Group 2 45 0.51 34.6

Group 3 16 0.31 30.4

Group 4 18 0.50 30.7

Subtotal Group 3 and Group 4 34 0.41 30.5

Total 79 0.47 32.8

This table gives an overview of participant characteristics. For the analysis groups 1 and 2 were merged together, as well as groups 3 and 4.

4.2 Hypothesis 1 – small vs. large games

H1: More participants will choose a strategy with a salient label in coordination games with a large set of strategies than in coordination games with a small set of strategies.

4.2.1 Word games

Table 4 summarizes the results for the word games. In SWG 69% chose the intended salient strategy London compared to 65% in LWG. In both the large game and the small game a large fraction of the participants picked the intended focal point. However, the difference between the two is the opposite of what was predicted. In the large game a smaller percentage of people picked the most salient strategy. Although, when testing the difference between these proportions with a chi-square test, the difference between the two is not significant (χ2_{(1) = 0.49; p=0.48). Hence, we cannot reject the null}

hypothesis that the share of participants picking the most salient label is equal in both games.

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Table 4: Results of the Word Games

Labelled Strategy SWG LWG London 31 22 Hamburg 10 4 Munich 4 0 Bremen - 1 Cologne - 4 Dortmund - 1 Frankfurt - 1 Hanover - 1 Leipzig - 0 Stuttgart - 0 N 45 34 Share Focal 0.689 0.647 S.E. 0.069 0.082

This table contains the results for the word games. The first column shows the labels of each strategy. The second and third column show number of times a participant picked each label for the Small Word Game (SWG) and Large Word Game (LWG) respectively. N is the number of participants in each game. Share focal is the share of participants picking the most salient label (London), S.E. is the standard error of this share.

4.2.2 Number games

For the number games it was expected that the contrasting payoffs would function as salient labels. In the Hi-Lo games all the other payoffs were isomorphic, so the only way to coordinate in the larger games was to choose the notable payoff, despite it being lower then the other payoff. As was noted before, a smart team reasoner could have calculated that in SNG-5 the expected payoff of both players picking (5, 5) and both players picking one of the (10, 10) strategies are equal to each other.

Table 5 shows the results of the number games. In both the variations with (5, 5) and (7, 7) as salient strategy, more participants picked the intended focal point in the large version of the game. In LNG-5 almost twice as many people picked (5, 5) than in the small version of the game (47.1% versus 26.7%). However, the null hypothesis that the share of choosing a salient strategy is equal between the SNG-5 and LNG-5, cannot be rejected (χ2_{(1) = 1.82; p=0.18). There is also no significant difference between} SNG-7 and LNG-7 (χ2_{(1) = 1.19; p=0.27).}

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Table 5: Results of Number Games

Labelled Strategy SNG-5 LNG-5 SNG-7 LNG-7 (5, 5) 12 16 - - (7, 7) - - 14 22 (10, 10) 20 3 12 2 (10, 10) 13 2 8 1 (10, 10) - 1 - 3 (10, 10) - 2 - 1 (10, 10) - 1 - 4 (10, 10) - 0 - 3 (10, 10) - 5 - 2 (10, 10) - 1 - 5 (10, 10) - 3 - 2 N 45 34 34 45 Share Focal 0.267 0.471 0.417 0.489 S.E. 0.066 0.086 0.084 0.075

This table contains the results for the number games. The first column shows the labels of each strategy. Columns 2 to 5 show the number of times a label was chosen by participants in each game. N is the number of

participants in each game. Share focal is the share of participants picking the most salient label ((5,5) or (7,7)), S.E. is the standard error of this share.

4.2.3 Card and Vegetable games

The card and vegetable had both games with symmetric and asymmetric payoffs. Again, the prediction was that in the larger versions of each game the intended salient labels would be chosen more frequently. In both the symmetric versions of the card and the vegetable games the opposite turned out to be true, with having less players choosing the salient label in the larger games. However, again the null hypothesis that the share of choosing a salient strategy is equal between the SCG-S and LCG-S cannot be rejected (χ2_{(1) = 0.27; p=0.6). The same goes for the SVG-S and LVG-S (χ}2_{(1) = 0.49; p=0.48).} Tables 6 and 7 summarize the results for these games.

In the games with asymmetric payoffs, the predicted result for the first

hypothesis is seen: in SCG-A 67.6% of participants pick the ace of hearts, while in the LCG-A this percentage is 84.4. Yet this difference is not significant (χ2_{(1) = 0.30; p=0.59).} In the vegetable games the results were similar. The percentages of people picking the picture of a strawberry were very close in both asymmetric games, 66.7% in SVG-A vs 67.6% in LVG-A. As might be expected, this small difference is not statistically significant (χ2_{(1) = 0.49; p=0.48).}

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Table 6: Results of Card Games

Labelled Strategy SCG-S LCG-S SCG-A LCG-A

A♡ 37 25 23 38 3♣ 6 0 4 1 9♠ 2 3 7 1 2♣ - 1 - 1 4♣ - 0 - 1 6♣ - 0 - 0 7♣ - 3 - 0 3♠ - 0 - 1 5♠ - 2 - 1 6♠ - 0 - 1 N 45 34 34 45 Share Focal 0.822 0.735 0.676 0.844 S.E. 0.057 0.076 0.080 0.054

This table contains the results for the card games. The first column shows the labels of each strategy. Columns 2 to 5 show the number of times a label was chosen by participants in each game. N is the number of participants in each game. Share focal is the share of participants picking the most salient label (A♡), S.E. is the standard error of this share.

Table 7: Results of Vegetable Games

Labelled Strategy SVG-S LVG-S SVG-A LVG-A

Strawberry 26 27 30 23 Asparagus 4 6 11 1 Broccoli 4 2 4 2 Cabbage - 0 - 2 Carrots - 0 - 2 Courgette - 1 - 1 Fennel - 4 - 1 Lettuce - 1 - 0 Onion - 1 - 0 Peas - 3 - 2 N 34 45 45 34 Share Focal 0.765 0.6 0.667 0.676 S.E. 0.077 0.073 0.070 0.080

This table contains the results for the vegetable games. The first column shows the labels of each strategy. Columns 2 to 5 show the number of times a label was chosen by participants in each game. N is the number of participants in each game. Share focal is the share of participants picking the most salient label (strawberry), S.E. is the standard error of this share.

In none of the games is there a significant difference between the share of participants picking the most salient label in the small and large games. Consequently there is no evidence to support the first hypothesis of this study. It seems that the size of the game had no influence on the share of participants going for the intended focal point.

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4.3 Hypothesis 2 – symmetric vs. asymmetric games

H2: Payoff asymmetries creating a conflict of interest between players will lead to a reduction of participants choosing the most salient label.

The card and vegetable games had payoff variations with asymmetric payoffs; with these games the second hypothesis of this thesis will be tested. The difference in share of participants picking the intended salient label will be compared and tested. The results of these games can be found in Table 6 and Table 7.

The card games show opposite effects for the small and large games. In SCG-S the share of participants picking the ace of hearts is 82.2% and in SCG-A, this percentage is 67.6%. However, this is not statistically significant (χ2_{(1)=0.32; p=0.57). In the large} games the opposite effect shows: in LCG-S only 73.5% picked the ace of hearts, while this was 84.4% in LCG-A. It was expected that in the large games, the influence of payoff asymmetry might be less and in this case the share of participants picking the intended salient label is even larger in the asymmetric game, but again this effect was not

statistically significant (χ2_{(1)=0.25; p=0.61).}

For the vegetable games the results are very similar. In SVG-S 76.5% picked the salient label and in SVG-A this was 66.7% and this difference is not statistically

significant (χ2_{(1)=0.41; p=0.52). For LVG-S and LVG-A, the percentages were 60% and} 67.6% respectively. Like in the large card games, the difference is the opposite of what one might expect, but neither is it significant (χ2_{(1)=0.58; p=0.45).}

Also for the second hypothesis I find no support, as for none of the games was there a significant difference between the symmetric and asymmetric versions. This is in contrast to previous studies that did find a difference between games with symmetric and asymmetric payoff (Crawford et al., 2008; Parravano & Poulsen, 2015). However, it was expected that the results would be different from previous studies.

4.4 Survey Results

After the experiment was over, participants were asked a few survey questions, of which the results will be discussed in this section. The participation in the survey was not necessary for completing the experiment, and people who did not answer these questions would not be filtered out and were still included in the lottery. That being

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30 said, almost all participants filled out the survey. The first three questions of the survey were participant characteristics that have been discussed in Section 4.1.

The first question in the survey with regard to their strategy was ‘How did you pick your answers?’ The results of this question are shown in Table 6. The participants could answer in a free text form. Thus, it was possible that participants gave several answers. The most common answer was about the saliency of the label (45

participants). These participants said to have picked their answers based on uniqueness, the colour of the answers (sometimes referencing the only red card or the strawberry) or they had some other reference to saliency. 10 participants admitted to choosing their strategy totally at random. Some of the participants choose their strategy by intuition (7 participants) or by prettiness of the picture (2 participants), both of which may be a way of unconsciously choosing the most salient strategy. Finally, 14 participants referenced the payoff with regard to how they picked their strategy. Of these participants, 7

maximized their own payoff, while 5 participants picked the payoff that was highest for their partner. 2 participants tried to maximize the payoff of both themselves and their partner by alternating between the highest payoff for themselves and their partner.

The second strategy question was ‘Did you change strategies between small and large tasks?’ Approximately a quarter of the participants (19) answered yes. After which, they were asked how they changed their strategy (See Table 7 for a summary of these results). 7 participants answered that they focussed more on salient features in the large game. A few of these participants mentioned that they only noticed that there was an ‘odd one out’ answer, when they came to the first large game and have possibly also changed their strategies in the following small games. 3 participants mentioned switching to picking at random in the large games. Lastly, 2 participants mentioned picking the less risky answer in the number game. Most likely pertaining to picking the lower, salient option in the larger number game and picking (10, 10) in the smaller game.

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Table 8: Frequency of Answers Strategy Question One

Answer Number of Participants

Saliency 45

Randomly 10

Intuition 7

Prettiness 2

Highest Payoff 7

Highest Payoff Partner 5 Highest Payoff for Both 2

Other 6

No answer 7

Frequency of each type of answer for the question: ‘How did you pick your answers?’

Table 9: Frequency of Answers for Strategy Question Two

Answer Number of Participants

No change in strategy 60

Focussed more on saliency 7

Switched to randomization 3

Less risky in the number game 2 Switched to other strategies 4 Switched strategies, but no answer 3

Frequency of each type of answer for the question: ‘Did you change strategies between small and large tasks?’ and ‘If yes, how?’ Three participants answered the first sub question with ‘yes’, but did not answer the second sub question.

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5. Discussion

In this section the results of this study will be summarized and discussed, as well as compared to previous research. Furthermore, the validity of the experiment will be discussed. Lastly, suggestions for improvements upon this experiment and suggestions for future research will be given.

5.1 Discussion

The main hypothesis tested if more players will choose a strategy with a salient label in coordination games with a large set of strategies than in coordination games with a small set of strategies. In the games with a large set of strategies, salient features of certain labels may attract more attention. For instance, London might standout more in a list with nine German cities than in a list with two German cities. In other experiments the ‘odd one out’ rule was perceived as quite effective (Bardsley et al., 2010; Mehta et al., 1994).

In none of the games did I find support for this hypothesis. This hypothesis has not been researched before.4_{However, Hargreaphes et al. (2017) found that for a} variety of games, coordination rates were higher when players were unrestricted to their choices, than in a restricted set of choices. Nevertheless, it could be that behaviour in unrestricted games is very different from restricted behaviour in restricted games. For example, adding extra fruits to a list of fruits, might not increase the saliency of ‘apple’, it might be the first one that comes to mind when being asked ‘pick a fruit’. Thus, comparing this experiment to that of Hargreaphes et al. (2017) might be comparing apples to oranges.

While no evidence was found for the hypothesis in the games themselves, some support was found in the survey questions. Approximately a quarter of the participants said to have changed strategies between the small and large games. Here, the most common answer was an increase in focus on salient features. However, this might be counteracted by some players switching to picking at random in the large games. Perhaps, these players were overwhelmed with the number of options, did not

4_{For as far as this author knows, after extensive literature research, this specific} hypothesis has not been tested.

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33 recognize the intended salient strategy or did not think it would be possible to

coordinate at all in these large games.

For the second hypothesis of this thesis I compared games with symmetric payoffs to games with asymmetric payoffs. In coordination games with asymmetric payoffs a conflict of interest between players was created, such that they each may want to pick a different equilibrium. In these types of games Crawford et al. (2008) and Parravano and Poulsen (2015) found a sharp decrease in coordination rates when payoffs were asymmetric. However, it could be argued that in both these studies, the labels did not have very salient labels in the first place. Also priming of the participants may have been a problem (Isoni et al., 2013). Therefore, I retested these findings in games where label saliency was expected to be much stronger. As expected, I could not replicate their results.

5.2 Limitations

A couple of participants indicated that they only noticed that the games had an ‘odd one out’ choice, when they encountered the first large game. These learning effects may be one of the limitations to this study. While participants never played the small and large version of the games that were compared to each other, they did get small and large versions of different games. Upon seeing a red card in a list with nine black cards, one may be prompted to searching for the ‘odd-one-out’ in other games. A possible solution for this would be to let one group of people only play small games and let a different group only play large games. However, this may not be optimal to investigate the second hypothesis of this thesis, as participants would have had to play the symmetric and asymmetric versions of the same game. With a different experimental design this does not have to be a problem.

A second possible drawback of the experiment was the online setting. While it did give an opportunity to gather a relatively high amount of observations with virtually no cost, it has the downside that you have to convince the participants that they are really playing against another participant. In a lab setting, this is not necessarily the case. To minimize this downside, it was mentioned at several points in the introduction,

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34 Additionally it was not possible to give participants real-life feedback, so there was no guarantee that everybody understood the experimental procedure. This was partially solved by filtering out all the observations with wrong practice answers. This also led to a slightly smaller group. However, all statistical tests were replicated in the full sample and no difference in result was found.

Another potential threat to the validity of the experiment might be a lack of effort. While the lottery mimics the usual monetary incentives, the chances of winning are quite low and any lack of effort may have been exacerbated by the small chances of winning the lottery. This threat could be overcome if this experiment was repeated with proper funding for payments.

The last potential threat to the experiment was a mistake in the experimental set-up. In the small asymmetric games, the pay-off asymmetries also created a payoff

salience in the form of an odd-one-out payoff. The payoff salient strategy was also the label salient strategy. This was not a problem for the large asymmetric game. In the future, this could be avoided by not working with 3-by-3 games.

5.3 Conclusion

One may expect participants to focus more on label saliency when there are a lot of options to choose from. However, I did not find any empirical support for this

hypothesis. Nevertheless, a quarter of the participants did indicate that they did switch strategies between the small and large games, so the research question might still be relevant for future studies. The asymmetric games in this experiment had labels with more salient features than in previous research into games with asymmetric payoffs. In contrast to previous research I did not find a decrease in participants picking strategies with salient labels.

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