Decision making in the prisoner's dilemma game: The effect of exit on cooperation and social welfare

The prisoner's dilemma game is a mixed‐motive game that offers two players the simultaneous choice between a cooperative and a defective alternative. An often neglected aspect of such a binary‐choice game, however, is that in many real‐life encounters, people can choose not only to cooperate or defect, but they also have a third option: to exit the social dilemma. Although in the literature a consensus has emerged that the addition of an exit opportunity benefits cooperation, there is only scant research into its effect on social welfare. In order to allow a direct comparison of cooperation rates and welfare levels across binary‐choice and trinary‐choice games, in this study, we used a design in which the same participants played similar games with and without an exit option (i.e., a within‐subjects design), and this in a range of structural variations. The findings of our study indicated that the aggregated outcome of both players is generally lower in games with an exit option than in games without an exit option. Moreover, our results showed that the efficiency of the exit option strongly depends on the specific outcome structure of the game (in terms of its endowment size, (a)symmetry, and level of noncorrespondence). In the discussion, it is argued that the implementation of an exit option as a strategy to increase social welfare should be critically assessed.     

Distributive judgments under uncertainty: Paccioli's game revisited

Many decision biases arise from the inability to ignore past events. The coherence of decisions is also compromised by the inability to fully use information related to the future. In Paccioli's game, a stake of money goes to the first player to score a certain number of wins. When the game is prematurely interrupted, they may divide the stake according to the proportions of wins relative to rounds played. Alternatively, they may assess the probability that a player would reach the criterion number of wins first if the game were continued. The first decision rule (ratio), which is past-oriented, leads to contradictions across games. The second rule (probability), which is future-oriented, does not. In seven studies, use of the ratio rule emerges across testing methods, in games of chance and games of skill, and independently of extraneous factors (such as random responding, lack of awareness, or proneness to other past-oriented biases).     

不同博弈情境下社会排斥对社会决策的影响作用

本研究借助经典的最后通牒博弈范式(UG)和独裁者博弈范式(DG),将回应者/接受者作为研究对象,考察了不同公平条件、平等条件下社会排斥对社会决策的影响作用。实验结果发现:(1)在面对高不公平性的分配方案时,被排斥组比被接纳组更倾向于拒绝接受该分配方案;(2)被排斥组对高不公平性分配方案的满意度要显著低于被接纳组;(3)被排斥组在不平等的博弈(DG)条件下对分配方案的满意度显著低于平等博弈(UG)条件下对分配方案的满意度。本研究结果说明,社会排斥情境下的被试对公平与平等因素更加敏感:在高不公平条件下,被排斥的个体表现出更少的合作互惠行为,甚至不惜放弃自身经济利益,也要惩罚博弈对方的不公平行为;此外,在不平等的博弈条件下,被排斥的个体产生了更多的消极情绪体验。本文的研究结果提高了社会决策研究的生态效度和传统决策模型的预测效度,有利于更加完整透彻地了解社会决策的影响因素。     

Information and the complementarity game

Complementarity games are explorative games between two players. The deterministic rules of the game are known to both players. The first player freely chooses among a finite number of states of the game but tells nobody of this decision. The second player accesses the game only by primitive, symbolic input‐output interfaces. The task of the second player is to find out the unknown state by input‐output experiments. The logic resulting from this scenario resembles‐ quantum logic in many aspects. It is the empirical logic of choice for virtual realities.     

Melioration behaviour in the Harvard game is reduced by simplifying decision outcomes

Self-control experiments have previously been highlighted as examples of suboptimal decision making. In one such experiment, the Harvard game, participants make repeated choices between two alternatives. One alternative has a higher immediate pay-off than the other, but with repeated choices results in a lower overall pay-off. Preference for the alternative with the higher immediate pay-off seems to be impulsive and will result in a failure to maximize pay-offs. We report an experiment that modifies the Harvard game, dividing the pay-off from each choice into two separate consequences—the immediate and the historic components. Choosing the alternative with the higher immediate pay-off ends the session prematurely, leading to a loss of opportunities to earn further pay-offs and ultimately to a reduced overall pay-off. This makes it easier for participants to learn the outcomes of their actions. It also provides the opportunity for a further test of normative decision making by means of one of its most specific and paradoxical predictions—that the truly rational agent should switch from self-control to impulsivity toward the end of the experimental sessions. The finding that participants maximize their expected utility by both overcoming impulsivity and learning to switch implies that melioration behaviour is not due to the lure of impulsivity, but due to the difficulty of learning which components are included in the pay-off schedules.     

Using a group game increases preschoolers' step count

Children should engage in at least 60 min of physical activity daily to develop or maintain healthy habits (Centers for Disease Control and Prevention, 2021a). Previous research suggests that contingent attention is a powerful tool for increasing moderate to vigorous physical activity. In this study, the researchers examined the effects of a group game on steps per minute at recess in an inclusive classroom with preschoolers. The researcher taught the game called the T-Rex game in which the game rules (chasing students who were moving) involved contingencies for natural attention to follow moderate to vigorous physical activity. The results showed a functional relation between step count and the group game in which students engaged in higher step counts when the group game was in place than during baseline. These findings extend other work by demonstrating that contingent attention embedded in group games can increase step count.     

Concerning a Moral Duty to Cheat in Games

Stimulated by Hugh Upton's recent article in this journal, in which he argues that there can be a moral duty to cheat in games, I attempt to examine his claims. Much of what he writes revolves around examples from two sports, cricket and rugby, and with differing connections to those games' rules. While the example from cricket is said to involve a breach of the spirit of that game, it is contravention of the written rules of rugby on which the latter part of Upton's case focuses. Given limited space I concentrate on the cricketing example, but several of the points I make about that apply also to when rule-breaking itself is involved. My conclusions express doubts about whether a case for a moral duty to cheat in games has been established.     

Focusing failures in competitive environments: explaining decision errors in the Monty Hall game,the Acquiring a Company problem,and multiparty ultimatums

This paper offers a unifying conceptual explanation for failures in competitive decision making across three seemingly unrelated tasks: the Monty Hall game (Nalebuff, 1987), the Acquiring a Company problem (Samuelson & Bazerman, 1985), and multiparty ultimatums (Messick, Moore, & Bazerman, 1997). We argue that the failures observed in these three tasks have a common root. Specifically, due to a limited focus of attention, competitive decision makers fail properly to consider all of the information needed to solve the problem correctly. Using protocol analyses, we show that competitive decision makers tend to focus on their own goals, often to the exclusion of the decisions of the other parties, the rules of the game, and the interaction among the parties in light of these rules. In addition, we show that the failure to consider these effects explains common decision failures across all three games. Finally, we suggest that this systematic focusing error in competitive contexts can serve to explain and improve our understanding of many additional, seemingly disparate, competitive decision‐making failures. Copyright © 2003 John Wiley & Sons, Ltd.     

亲社会视频游戏中的合作对博弈决策中合作行为的影响

以38名大学生和研究生为被试,采用Chicken Game实验范式测量合作行为,考察了单人和双人合作模式游戏后,性别和游戏习惯对玩家在博弈决策中合作行为的影响。结果表明：（1）双人合作模式游戏可以促进玩家在博弈决策中的合作行为;（2）双人合作模式游戏后,男玩家（相比女玩家）在博弈决策中的合作行为更多;（3）玩游戏的习惯影响博弈决策中的合作行为,相比于经常习惯与现实朋友玩游戏和独自玩游戏的玩家,经常习惯与网友玩游戏的玩家在双人合作模式游戏后的合作行为更多。本研究不仅证实了一般学习模型,也证实了亲社会合作类视频游戏可以有效促进博弈决策中的合作行为。     

Play as co‐created narrative in computer game consumption: The hero's journey in Warcraft III

Computer games are now a significant consumption activity in consumer culture. Informed by interdisciplinary studies and drawing on data from in‐depth interviews with players of the Warcraft III computer game, we explore the relationship between play and storytelling during digital play. Understanding that such play is determined by systems of game rules and that computer game characters and settings are capable of conveying cultural meanings to players, we found that the rules of play in computer games can be designed in ways that encourage consumers to co‐create meaningful story plots derived from their knowledge of myth and fiction. In the case of Warcraft, these plots resembled the archetypal plot of the hero's journey. We conclude that computer games immerse consumers in a form of playful consumption that engages them in memorialised, co‐authored storytelling. Copyright © 2012 John Wiley & Sons, Ltd.     

What you don’t know won’t hurt me: Costly (but quiet) exit in dictator games

We used simple economic games to examine pro-social behavior and the lengths that people will take to avoid engaging in it. Over two studies, we found that about one-third of participants were willing to “exit” a $10 dictator game and take $9 instead. The exit option left the receiver nothing, but also ensured that the receiver never knew that a dictator game was to be played. Because most social utility models are defined over monetary outcomes, they cannot explain choosing the ($9, $0) exit outcome over the dominating $10 dictator game, since the game includes outcomes of ($10, $0) and ($9, $1). We also studied exiting using a “private” dictator game. In the private game, the receiver never knew about the game or from where any money was received. Gifts in this game were added innocuously to a payment for a separate task. Almost no dictators exited from the private game, indicating that receivers’ beliefs are the key factor in the decision to exit. When, as in the private game, the receivers’ beliefs and expectations cannot be manipulated by exit, exit is seldom taken. We conclude that giving often reflects a desire not to violate others’ expectations rather than a concern for others’ welfare per se. We discuss the implications of our results for understanding ethical decisions and for testing and modeling social preferences. An adequate specification of social preferences should include “psychological” payoffs that directly incorporate beliefs about actions into the utility function.     

Behavioural Consistency Within the Prisoner's Dilemma Game: The Role of Personality and Situation

Mixed‐motive games represent situations that confront people with a conflict between cooperative and non‐cooperative alternatives. Despite this common basis, recent research has shown that the consistency of people's choices across different mixed‐motive games is rather low. The present research examined behavioural consistency within the same mixed‐motive game, by presenting participants with a series of one‐shot Prisoner's Dilemma Games. Across this set of games, payoffs were manipulated in order to intensify or weaken the conflict between self and the other party while maintaining the game's underlying structure. Our findings indicate that significant differences in choice behaviour are observed as a function of both situational (i.e. manipulations of the Prisoner's Dilemma Game's payoff structure) and personality differences (i.e. individual differences in personality and motivational traits). Moreover, our included situational variables and personality features did not interact with each other and were about equally impactful in shaping cooperation. Crucially, however, despite the significant behavioural differences across game variants, considerable consistency in choices was found as well, which suggests that the game's motivational basis reliably impacts choice behaviour in spite of situational and personality variations. We discuss implications for theorizing on mixed‐motive situations and elaborate on the question how cooperation can be promoted. © 2018 European Association of Personality Psychology     

Expectation and cooperation in prisoner’s dilemmas: The moderating role of game riskiness

This paper investigated the effect of risk orientation, game riskiness, and expectation of cooperation on cooperation in one-shot prisoner’s dilemmas (PD). Participants in pairs played PD games that varied on game riskiness such that for half of the games cooperation was more risky than defection (more risky games) while for another half cooperation was less risky (less risky games). They estimated how likely it was that the other player was going to cooperate (expectation of cooperation) before they made their cooperation/defection decision on each game. Supporting the Goal/Expectation Hypothesis, we replicated the effect that expectation of cooperation enhanced cooperation. We also found that risk-seeking individuals cooperated more in more risky games whereas risk-averse individuals cooperated more in less risky games. More importantly, we found that game riskiness moderated the effect of expectation of cooperation on cooperation. The positive effect of expectation of cooperation on cooperation was stronger for more risky games than for less risky games. Our results illustrated how the relation between expectation and cooperation as stipulated by the Goal/Expectation Hypothesis was moderated by riskiness of the situations.     

Model and interactive algorithm of bi‐level multi‐objective decision‐making with multiple interconnected decision makers

Furthering a prior research on two‐person bi‐level multi‐objective decision‐making problems of the leader‐follower Stackelberg game, we present an extended model of bi‐level multi‐objective decision‐making with multiple interconnected decision makers at the lower level. In the model, the upper level decision maker acts as a leader and the lower level decision makers behave as the followers, and inter‐connections and interactions exist among these followers in decision‐making scenarios. Following the rules of leader‐follower Stackelberg game, we develop an interactive algorithm of the model for solving multi‐objective decision‐making problems and reflecting the interactive natures among the decision makers. Finally, the authors exemplify the model and algorithm, and draw a conclusion on points of contributions and the significance of this study in decision‐making and support. Copyright © 2001 John Wiley & Sons, Ltd.     

The spiral of distrust: (Non‐)cooperation in a repeated trust game is predicted by anger and individual differences in negative reciprocity orientation

This study investigated state anger and individual differences in negative reciprocity orientation as predictors of individuals' willingness to cooperate with strangers. In order to observe real behaviour, we used a trust game that was played over six periods. In the trust game, a first player (sender) determines how much of a certain endowment she/he wants to share with a second player (trustee), who then can give something back. We varied whether participants received feedback [feedback (yes, no)] about the trustee's behavioural decision (amount sent back). Supporting our hypotheses, the results suggest that feedback compared with no feedback about the trustee's behaviour increased anger. Specifically, information about low back transfers triggered anger and non‐cooperation in return. Importantly, participants with a strong negative reciprocity orientation reported higher levels of anger and were less willing to cooperate with the trustee compared with those with low negative reciprocity orientation. Moreover, even when anger was low, individuals with a strong negative reciprocity orientation were less willing to cooperate compared with those with a low negative reciprocity orientation. Thus, negative reciprocity orientation seems to arouse a spiral of distrust. Theoretical and practical implications of these findings are discussed.     

When to (or not to) trust intelligent machines: Insights from an evolutionary game theory analysis of trust in repeated games

The actions of intelligent agents, such as chatbots, recommender systems, and virtual assistants are typically not fully transparent to the user. Consequently, users take the risk that such agents act in ways opposed to the users’ preferences or goals. It is often argued that people use trust as a cognitive shortcut to reduce the complexity of such interactions. Here we formalise this by using the methods of evolutionary game theory to study the viability of trust-based strategies in repeated games. These are reciprocal strategies that cooperate as long as the other player is observed to be cooperating. Unlike classic reciprocal strategies, once mutual cooperation has been observed for a threshold number of rounds they stop checking their co-player’s behaviour every round, and instead only check it with some probability. By doing so, they reduce the opportunity cost of verifying whether the action of their co-player was actually cooperative. We demonstrate that these trust-based strategies can outcompete strategies that are always conditional, such as Tit-for-Tat, when the opportunity cost is non-negligible. We argue that this cost is likely to be greater when the interaction is between people and intelligent agents, because of the reduced transparency of the agent. Consequently, we expect people to use trust-based strategies more frequently in interactions with intelligent agents. Our results provide new, important insights into the design of mechanisms for facilitating interactions between humans and intelligent agents, where trust is an essential factor.     

Cooperative group learning in a team game: role of verbal exchanges among peers

Few studies concern cooperative learning in Physical Education (PE). The purpose of this experimental design was to analyze the role of verbal exchanges (discussions about the game) among peers within teams in a cooperative perspective. The participants were 17 boys and 13 girls from a French primary school (average age: 9.4 years). They were randomly assigned to two control and experimental groups. The study examined the effect of verbal exchanges on inter-personal relationships and on shooting and skill level in a team game of basketball (with adapted rules). Participants were videotaped during the games in the two groups and during discussions in the case of the experimental group. The experimental design took place during 10 physical education lessons. The results showed positive effects of discussions within each team on the skill level in the game at the deferred post-test. On the other hand, no effect was found on inter-personal relationships. These data strengthen previous findings in the theoretical cooperation framework and in the team sports domain.     

Risk and Prisoner's Dilemma: A Reinterpretation of Coombs' Re‐parameterization

We propose a model to measure risk in a prisoner's dilemma based on Coombs' (1973) re‐parameterization of the game as an individual risk decision‐making task that chooses between a gamble of cooperation and another gamble of defection. Specifically, we propose an index, r, to represent the risk associated with cooperation relative to defection. In conjunction with Rapoport's (1967) index of cooperation (K), our formulation of risk allows us to construct games that vary in risk (as indexed by r) while controlling for cooperativeness (as indexed by K). Following utility analysis that models risk seeking as a convex utility function and risk averse as a concave function, we predict that risk‐seeking people cooperate more in games that the cooperation choice is more risky, whereas risk‐averse people cooperate more in games that the cooperation choice is less risky. In the three studies that we varied game parameters, used different measures of risk orientation and prosocial orientation and used different experimental procedures, we found robust results supporting our predictions. Theoretical analysis of our formulation further suggests that risk and cooperativeness of a prisoner's dilemma game is not entirely independent. Games that have a higher cooperativeness index are necessarily more risky. Copyright © 2011 John Wiley & Sons, Ltd.     

Be loyal but not addicted: Effect of online game social migration on game loyalty and addiction

To increase game loyalty but decrease game addiction, this study examines online game social migration and tests the mediating effects of offline social value and maladaptive cognition on the basis of the theory of consumption value and the cognitive behavioral model of pathological Internet use. The results are as follows: (i) Overall, online game social migration is associated with greater game loyalty and less game addiction; (ii) The positive association between online game social migration and game loyalty was mediated by offline social value; and (iii) Online game social migration is associated with lower game addiction. This paper provides a new perspective (taking into account both business interests and players' psychological health) for online game research and also offers practical guidance for cooperation between game companies and the public. Copyright © 2017 John Wiley & Sons, Ltd.     

To be at the tail of the lions or the head of the foxes?

Agents seeking an opportunity for profit often have to compete with others who pursue the same opportunity. When having to choose between a number of opportunities differing in their value and if individuals differ in their chances of outperforming others, the choice can be cognitively and emotionally demanding. We explore choice between opportunities using stylized Lions–Foxes games. In such a game, each of three players, with different odds of beating others, has to choose one of two contests that offer different rewards. After game theoretically analyzing the games, which we have experimentally employed, we report four experiments that vary in choice elicitation (repeated play or strategy method), in players' matching (random strangers or partners) and in rewards. Regarding contest choices, we found the choice of the higher value (and seemingly more prestigious) contest to be positively related to winning odds, contrary to what four out of the five (mixed, partially mixed, or pure) equilibria predict. Participants started out rather optimistic, with a large majority choosing the higher value option, but with experience, they approached the only viable of two pure strategy equilibria. Still, mixing continued via reacting to past play and outcome, apparently balancing dissatisfaction from choosing either contest.