The Impact of Social Distance and Communication on Subjects’ Behavior in Ultimatum Games

Table of Contents

List of Figures and Tables

List of Abbreviations

1 Introduction

2 Theory
2.1 Ultimatum Game by Güth et al
2.1.1 Definition
2.1.2 The Framework of the Game
2.1.3 Predicted Subject Behavior
2.2 The Strategy Method

3 A Collection of Ultimatum Game Experiments
3.1 Experimental Results of Thirty Years of Research
3.2 Contradicting Material Opportunism
3.3 Subjects’ Reasoning in the Game
3.4 Subjects’ Motives for Contradicting Material Opportunism

4 The Impact of Social Distance on Subjects’ Behavior in Ultimatum Games
4.1 The Concept of Social Distance
4.1.1 The Term
4.1.2 Social Distance along Dimensions
4.2 Social Distance in the Ultimatum Game
4.2.1 A Procedure for Inducing Social Distance in Experimental Games
4.2.2 The Influence of Social Distance on Subjects’ Behavior

5 The Impact of Communication on Subjects’ Behavior in Ultimatum Games
5.1 The Concept of Communication
5.1.1 The Term
5.1.2 Decreased Social Distance Between Communicators
5.2 Communication in the Ultimatum Game
5.2.1 The Nature of Conversation between Subjects
5.2.2 The Impact of Pre-Play Communication on Subjects’ Behavior

6 Results and Discussion
6.1 Results
6.2 Discussion
6.2.1 Incentives Elicited by Social Distance Variations and Communication
6.2.2 Methodological Issues

7 Conclusion

References

Abstract

The discrepancy between real-life and laboratory settings regarding anonymity is relevant for researchers concerning the realism of their findings. To close this gap, some studies began to shed light on altering the social embedding of experiments, e.g. by varying the degree of anonymity and social distance between players and incorporating communication. This work presents a selective review of studies covering these issues and compares those findings. Results show that decreased social distance leads to higher offers from the proposer and to a decreased acceptance threshold of the mean responder. After communicating with the responder, proposers offer a higher amount. Responders increase their acceptance threshold in treatments with game-related discussions, but do not adjust it after game-free conversations. The implications of these findings and the determinants of players’ behavior in the Ultimatum game are clarified. Thereby, this work outlines researchers’ endeavor of reaching higher levels of realism for results in Ultimatum game experiments. It closes by indicating the trade-off between the precision of laboratory experiments, which maintain anonymity, and enhanced realism of experiments which manage to design more field-like settings.

List of Figures and Tables

Figure 1: Decision stages of a one-round Ultimatum game

Figure 2: Mean proportion offered as a function of pie size and social distance

Figure 3: Approximate scope of communication media

Table 1: Descriptive statistics of Ultimatum game behavior

List of Abbreviations

Abbildung in dieser Leseprobe nicht enthalten

1 Introduction

Human social interactions can be appropriately captured by economic games. The term ‘game’ is used to describe various interpersonal interactions while implicating that games can model those effectively. Behavioral games involve strategic components which drive people to compete and to behave strategically, although there is clear cooperation potential (Murnighan & Wang, 2016, p. 80). Players’ strategies, accurate rules for the sequence of players’ choices, the degree of available information and the evaluation of the outcome value are essential components of games (Camerer, 2003, p. 2). In experimental and behavioral economics, two-person economic games are employed to test assumptions of economic theories and to shed light on determinants of subjects’ decisions in everyday social interactions (Bechler, Green, & Myerson, 2015, p. 149). In particular, researchers have often used bargaining games for theorizing models of social preferences (Camerer, 2003, p. 113). Bargaining games are characterized by the players’ goal to overcome a distribution problem (Güth, Schmittberger, & Schwarze, 1982, p. 367). Here, experimenters were interested in whether strategic considerations, predicted by game theoretic models, or sociological or cultural factors are the primary factors for players’ behavior (Roth, 1995, p. 253).

Güth et al. (1982) commenced with experiments on bargaining with an ultimatum and introduced the Ultimatum game. Their eminent interest in studying the Ultimatum game were potential contradictions to the traditional assumptions of rationality, material opportunism and the game-theoretical analysis of fairness (Güth & Kocher, 2014, p. 397). Experimentation with Ultimatum games has become popular for its easy implementation (Camerer, 2003, p. 45). Güth and Kocher (2014) noted that not only in economics, but also in other disciplines the Ultimatum game has become a workhorse for testing various aspects of bargaining theory over the last thirty years (p. 397). Most notably, it has been used as a means of studying the impact of self-interest and altruism on players’ behavior (Bechler et al., 2015, p. 149). Nevertheless, not all questions in the field of Ultimatum games have been answered and the debate in this research field is far from being settled (Güth & Kocher, 2014, p. 397).

At first, it was not expected that the Ultimatum game is that socially, motivationally and emotionally rich (Güth & Kocher, 2014, p. 406). Instead of consistently acting strategically, players behave and decide in games similarly to how they do in social contexts (Murnighan & Wang, 2016, p. 89). Moreover, Camerer and Thaler (1995) proposed that subjects in the Ultimatum game behave according to their manners developed in everyday life. Therefore, subjects’ choices in the game comprise both their strategic considerations and their motivations resulting from social interactions (p. 218). On this account, it is essential that experimenters give special attention to the social embedding of the game which matters tremendously for subjects’ behavior (Güth & Kocher, 2014, p. 405). Roth (1995) referred to social psychology literature when emphasizing the importance of the social environment in experiments: “[…] small differences in the social environment can cause large differences in behavior” (p. 295).

In that sense, researchers began to investigate the impact of changes in the social embedding of experiments. Among various research objectives, experimenters paid attention to the social relationship of subjects in the Ultimatum game. Several Ultimatum game studies (Bechler et al., 2015; Rachlin & Jones, 2010; Charness & Gneezy, 2008) suggested that the closeness of the relationship influences subjects’ behavior. This dimension of emotional proximity between players is called social distance (Charness & Gneezy, 2008, p. 30) . Another aspect which may affect the relationship between players is communication. Studies in other contexts demonstrated that communication impacts subjects’ decisions. For instance, pre-play communication in Prisoner’s dilemma and Public good games led to higher cooperation rates in some studies (Camerer, 2003, p. 46). Beyond that, communication and its effects on players’ behavior have also been studied in the Ultimatum game (Güth & Kocher, 2014, p. 404). Incorporating communication in bargaining games may bear great potential for novel insights. Since games are models for human social interactions, this could grow to be a useful and groundbreaking tool for understanding experimental results. According to Watzlawick and Beavin (1967), communication as a concept is more appropriate to describe human interactions as well as interpersonal relations (p. 4).

In the light of these research approaches, this thesis compares empirical results of studies covering the issues of social distance and communication in Ultimatum game experiments. Furthermore, this thesis relates social distance to the concept of communication and examines the impact of the latter on social distance between players. Above all, this work seeks to answer the following research question: How does social distance and communication influence subjects’ behavior in the Ultimatum game?

The remainder of this thesis is structured as follows: Section 2 presents the rules and features of the Ultimatum game. In section 3, empirical results of different Ultimatum game experiments are analyzed. Subsequently, section 4 introduces the concept of social distance and reports results of Ultimatum game studies concerning this matter. Adhering to the same structure, section 5 deals with the concept of communication in Ultimatum game studies. In section 6, results are summarized and discussed before this thesis concludes with final remarks in section 7.

2 Theory

2.1 Ultimatum Game by Güth et al. 1982

2.1.1 Definition

Güth et al. (1982) introduced the Ultimatum game as a bargaining game with perfect information, i.e., decisions are made successively, not simultaneously and every subject has full information about the previous decisions at any time in the game (p. 367). What renders the Ultimatum game special is the form of players’ interaction. Subjects interact in anticipation to the other subject’s subsequent steps. In addition, Güth et al. (1982) considered the final decision as the most simple choice problem and all interactions originate from strategic considerations exclusively (p. 368). They put the focus on a game with two players and two stages and created a simple bargaining model involving the distribution of a given pecuniary amount (p. 367). Furthermore, Güth et al. (1982) depicted the nature of the Ultimatum game with particular characteristics. It is typical for this game that one player limits the set of possible outcomes to one single offer and specifies all the details of an agreement presetting the last decision of the game to a choice between two prespecified outcomes (p. 383).

In the Ultimatum game, a first mover, player 1, transitionally receives a given monetary amount p. He proposes to player 2 how to divide the pie between them. Player 2 either accepts the offered split or rejects. If he accepts the offer, the proposed split is implemented. Rejection leaves both players with a zero payoff (Güth et al., 1982, p. 371). Güth and Kocher (2014) put it in a more formal way:

More formally, let X be the proposer who suggests the shares x and y for him or her and the responder Y, respectively, where x and y are non-negative and add up to the positive pie size p. First, X chooses (x, y) with x, y ≥ 0 and x + y = p. Then, after learning the choice of (x, y) by X, responder Y either accepts, δ(x, y) = 1, or rejects, δ(x, y) = 0. This implies the final payoffs δ(x, y)x for X and δ(x, y)y for Y. (p. 398)

Figure 1 illustrates the decision stages of a one-round Ultimatum game and uses the notation of Güth and Kocher (2014). In this thesis, the terms proposer for player 1 and responder for player 2 will be used.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1: Decision stages of a one-round Ultimatum game (adapted from Murnighan & Wang, 2016, p. 87)

2.1.2 The Framework of the Game

The setup of the first Ultimatum game by Güth et al. (1982) showed particular concerns for the awareness of subjects. The researchers wanted to ensure the awareness of all subjects for the special game situation, the ultimatum aspect. Therefore, they concentrated on “the easiest non-trivial” Ultimatum games with two players and two decision stages in their experiment (p. 370). After introducing the subjects informally, oral instructions corresponding to written rules followed. Participants were randomly divided into two subgroups. Subjects in one of the subgroups were told to have the role of the proposer. Before the game started, they were informed that their counterparts (responders) will be matched by chance out of the other subgroup ensuring anonymity between opponents (p. 370). The instruction rules specified the experimental conditions for the subjects during the game. Proposers and responders were seated separately on opposite sides of the room on segregated desks, preventing verbal exchange between the subgroups. For proposers, a decision form was prepared that indicated the pie size p and provided a blank which should be filled in with the claim x of the proposer. Subjects could see the participants of the other subgroup, albeit they did not know who was their direct counterpart as the proposers’ decision forms were spread randomly among responders. Knowing the amount p and the proposer’s offer (p - x = y), responders had ten minutes for their decision. Verbal interruptions via questions or remarks were not allowed during the experiment (p. 386).

A typical Ultimatum game experiment juxtaposes anonymously paired subjects (Camerer, 2003, p. 48) and puts emphasis on subjects’ physical distance to minimize confounding effects of face-to-face bargaining (Güth & Kocher, 2014, p. 397). However, subjects could recognize that they are not confronted with a preprogrammed strategy but with an opponent in flesh and blood while observing each other (Güth et al., 1982, p. 370).

2.1.3 Predicted Subject Behavior

According to traditional homo oeconomicus models, humans maximize their personal payoff no matter the social and emotional context. Following material opportunism, decision makers’ thinking is deliberate, free from biases and utility-maximizing (Wischniewski, Windmann, Juckel, & Brüne, 2009, p. 305). Relating this to analytical game theory, a clear prediction for the behavior of the proposer and responder in the Ultimatum game can be deduced: assuming subjects to be self-interested in the sense of material opportunism, the responder will accept any offer. If the proposer expects the responder to maximize, she will offer the smallest possible amount y’. Theoretically, the proposer can capitalize on his first mover advantage, which is the entire bargaining power, since a self-interested responder takes what is on offer (Camerer, 2003, p. 9).

The equilibrium point implies the identical solution. Every unlasting game has at least one subgame perfect equilibrium point (Selten, 1975, p. 25). For the Ultimatum game, there is only one subgame perfect equilibrium obligating the responder to accept any offer and the proposer to offer the smallest possible amount (Greiner, Caravella, & Roth, 2014, p. 375).

Extending the notation of Güth and Kocher (2014) by integrating the assumptions of material opportunism, leads to the following principles for the subjects in the normative solution. The responder needs to accept any positive offer y: δ(x, y) = 1 for y > 0. The selfish proposer X should offer the smallest possible amount y’ to the responder Y, so that she is awarded with nearly all of p (p - y’ = x’) (p. 398).

2.2 The Strategy Method

The strategy method is a methodical modification of the standard Ultimatum game. It intends to evoke the full strategy vector of the responder, instead of solely measuring the responder’s reaction to one specific offer. The strategy method elicits how responders react to each possible allocation. It therefore provides further insight into the driving forces for responders’ choices since responders’ strategies can be analyzed across the full range of possible outcomes (Bahry & Wilson, 2006, p. 38).

Güth and Kocher (2014) differentiate among the direct response method of the standard Ultimatum game as the ‘hot play’ and the strategy method as the ‘cold play’ (p. 403). This designation might be because the strategy method turns the game into a simultaneous-moves game with less excitement as the last decision stage merges with the first one. In the experimental game, the responder is asked to decide whether he will accept or reject any possible offer before being informed about the actual offer from the proposer (Güth & Tietz, 1990, p. 418). Applying this, responders are asked to state a minimum acceptable offer y* (MAO) in the experiments (Camerer, 2003, p. 48).

For the responder’s strategy, function δ(·) assigns a decision δ(x) = 1 or δ(x) = 0 to all possible demands x by the proposer (Güth & Tietz, 1990, p. 428). Güth et al. (1982) described the decision strategy of the responder under the application of the strategy method as follows: If the offer from the proposer exceeds the MAO (p - x ≥ y*), the responder accepts the proposed allocation (δ(x) = 1) and receives the payoff y while the proposer yields p – y = x. Otherwise, when the offer is smaller than the MAO (p - x < y*), the responder rejects the offer and thus conflict ensues (p. 378).

3 A Collection of Ultimatum Game Experiments

Güth and Tietz (1990) identified one-round Ultimatum games as “one of the most critical paradigms for testing the predictive power of the game-theoretic solution” (p. 419). First of all, Güth et al. (1982) wanted to discover if subjects behave in the game according to the normative solution. And if not, the reasons for and the direction of deviating were of interest (p. 368). In the meantime, thousands of Ultimatum game experiments and variations of the standard form have been conducted by economists and psychologists (Güth & Kocher, 2014, p. 396). This chapter outlines the results of the ‘easy games’ from Güth et al. (1982) and robust findings of studies over the last thirty years. The focus will be on one-round experiments with unexperienced players as experience and aspects of social learning will not be covered by this thesis.

3.1 Experimental Results of Thirty Years of Research

Güth et al. (1982) reported that many proposers offered an equal split (7 out of 21, 33%) but the vast majority offered less than p/2 and tried to exploit the ultimatum aspect. The average offer was about 35%. Because it overlooks the varying amount p, this is not a meaningful measure. Two out of 21 responders (9.5%) rejected the offered division and turned down positive amounts of money (p. 375).

Oosterbeek, Sloof, and van de Kuilen (2004) identified factors that vary the amounts offered and the rejection rates. The rejection rate is the fraction of proposals that is not accepted. If it is the mean of the indicated minimum acceptable offers, the strategy method is applied (p. 176). What Oosterbeek et al. (2004) found is that the shares offered by the proposer are smaller for larger pie sizes and when the strategy method is in use. Rejection rates are expectably lower for higher offers. What is more, responders more frequently accept larger pie sizes and when the strategy method is used (p. 178). They also described the players and their typical way of playing the Ultimatum game in the laboratory. They found that proposers offered more money than the minimum and responders rejected offers that are higher than the smallest possible amount (p. 171). Camerer (2003) compared figures from many studies of Ultimatum game experiments and found systematic results. On average, proposers offer 30 to 40% of the pie size to the responder. Modal offers are regularly 40 to 50%. Proposals of 40 to 50% are hardly ever turned down in contrast to small ones of 20% or less, which are rejected in about 50% of the cases (p. 49).

More recent studies are expanding this pattern of results. In comparison with earlier compilations, Greiner et al. (2014) adjusted the modal offer to 50% based on the replications of the standard form of the Ultimatum game over the last thirty years (p. 375). Greiner et al. (2014) emphasized that any offer smaller than the equal split is frequently turned down (p. 375). Güth and Kocher (2014) also refer to the modal equal split as a robust phenomenon and they further attribute the 40% and 50% split to be payoff maximizing. However, they reported even more extreme rejection behavior. Practically, all responders reject offers below 20% and in many cases, low offers below p/3 are not accepted (p. 398).

3.2 Contradicting Material Opportunism

The results of the first Ultimatum game already showed that the responder does not consistently go for the alternative which generates the highest payoff (Güth et al., 1982, p. 374). That a responder rejects offers and a proposer offers more than the minimum, clearly demonstrates that the players are not maximizing their own earnings under any circumstances (Camerer, 2003, p. 11). Subjects’ behavior in Ultimatum game experiments diverges systematically from predictions and counters the concept of material opportunism (Güth & Kocher, 2014, p. 397). In addition, the structure of behavioral results also contradicts the rationality condition of game theory and economic theory in general (Güth & Tietz, 1990, p. 446). Camerer (2003) highlighted that this fact does not refute game theory in itself (p. 46), even though it is not of great support in explaining bargaining behavior (Güth et al., 1982, p. 385). According to experimental results, the game-theoretic solution introduced in section 2.1.3 seems to be socially quite intolerable (Güth & Tietz, 1990, p. 417).

In a broader sense, however, subjects do not inevitably disregard rationality. Indeed, there can be many aspects they take into account (Güth & Kocher, 2014, p. 397). Subjects are capable of strategic thinking. They adhere to the strategic concepts of game theory but in their personal format by balancing their own wishes according to their strategic principles (Camerer, 2003, p. 11).

3.3 Subjects’ Reasoning in the Game

As mentioned before, people behave in games like they do in other social contexts. Their decisions are rather automatic results from social and personal rules, norms and heuristics than a pure product of strategic thinking (Murnighan & Wang, 2016, p. 89). Against this background, it is apparent that there have to be the most diverse motives behind players’ decisions because of their individuality. This is what has been reflected by Güth and Kocher (2014) as they were recapping the scientific debate on the Ultimatum game. Initially, scholars declared the Ultimatum game to be “one of the behaviorally most complex games in experimental economics” (p. 397). However, complexity does not arise from the game structure which is very simple, but from diverse motivations behind subjects’ decisions in the Ultimatum game (p. 397). According to implicit assumptions of behavioral games, subjects’ underlying motives are reflected by their strategies, i.e., by the way players compete or cooperate. Players’ strategies are captured by experimental games and this enables researchers to investigate subjects’ motives (Murnighan & Wang, 2016, p. 81).

In the game, subjects make efforts to balance several desires depending on their personal preferences (Camerer, 2003, p. 11). To do so, Wischniewski et al. (2009) claim that players make use of certain cognitive mechanisms for several reasons. First, they need to envision different scenarios of cooperation, defection, and even sanctioning of unfair behavior (p. 305). Second, putting themselves in the position of others, interpreting intentions and developing a theory of others’ minds requires a certain cognitive effort (p. 309). Subjects anticipate the decision behavior of their counterpart in order to make their decisions (Güth et al., 1982, p. 369). Third, they need to balance cognitive and emotional motives involved in decision-making in complex social interactions (Wischniewski et al., 2009, p. 306).

The experimental results of decades indicate that “the usual backward induction procedure underlying the concept of subgame perfect equilibria is no reliable behavioral concept” (Güth & Tietz, 1990, p. 447). Starting from the responder’s mindset (backward induction) and deducing her and, subsequently, the proposer’s decision behavior while assuming payoff maximization (cf. section 2.1.3) does not lead to dependable behavior predictions. “Actual decision behavior is obviously a result of both forward and backward induction” (Güth & Tietz, 1990, p. 447).

Forward induction involves the anticipation by subjects, in particular this of the proposer. If the proposer is capable of anticipating that responders turn down low offers and want to maximize earnings, she will not stick to the normative split. She will take into account her anticipations which indicate that low offers are also unattractive for herself (Güth & Kocher, 2014, p. 398). Güth et al. (1982) outlined the players’ considerations. The usual consideration of responders seems to be as follows: ‘If the proposer leaves a fair amount to me, I will accept. If not and if I do not sacrifice too much, I will punish him by rejecting the offer.’ Accordingly, a proposer typically will argue like: ‘I have to leave at least an appropriate amount for the responder so that he will consider the costs of rejecting as too high’ (p. 384).

The responder’s way of thinking reflects her motivation which is twofold: cooperative and competitive (Murnighan & Wang, 2016, p. 81). Sanfey, Rilling, Aronson, Nystrom, and Cohen (2003) claim that unfair offers in the Ultimatum game can confront the responder with two competing goals: the rational (cognitive) motivation to accept as well as the irrational (emotional) motive to reject the offer at one’s own costs (p. 1756). Responders sacrifice their potential payoff to punish their opponent if the proposer demands ‘too much’ and if it is not too costly for themselves (Güth & Tietz, 1990, p. 447).

3.4 Subjects’ Motives for Contradicting Material Opportunism

Responders punish proposers for not cooperating and experience the feeling of reward for trying to reinforce cooperation (Wischniewski et al., 2009, p. 312). As a form of negative reciprocity, responders “reciprocate unfair behavior by harming the person who treated them unfairly” (Camerer, 2003, p. 10). Fairness seems to be one of the motives which subjects factor into their strategic considerations. Additionally, equality plays an important role for players, especially for the responder. “Fairness is a judgment people make about an action players take or its consequences, and that judgment affects their preferences for actions and allocations” (Camerer, 2003, p. 114). Responders prefer to be treated fairly (Camerer, 2003, p. 24), but both responders and proposers are influenced by the perceived fairness of a certain distribution (Bechler et al., 2015, p. 149). Subjects in the Ultimatum game define a fair split as close to half (Camerer, 2003, p. 10). As experimental results have verified, players rely on the 50-50 split which they consider a justified result (Güth et al., 1982, p. 384). When evaluating the fairness of offers, responders take absolute and relative amounts into consideration and compare them to the proposer’s payoff (Croson, 1996, p. 198; Bechler et al., 2015, p. 153). Seemingly fair behavior of the proposer results from two motives: some taste for fairness and the risk aversion present through the anticipation of the rejection of low offers (Oosterbeek et al., 2004, p. 171). Murnighan and Wang (2016) claim that proposers tend to be risk averse rather than fair while they make relatively large offers. This suggests that offerers act strategically by making themselves seem fair even when they are not (p. 86). Proposers have social concerns and do not want to appear selfish to others or themselves (p. 87). In line of this explanation, Andreoni and Rao (2011) identify this kind of behavior as self-image maintenance and self-deception (p. 514).

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