HOBBES AND GAME THEORY REVISITED: ZERO‐SUM GAMES IN THE STATE OF NATURE

The aim of this paper is to critically review the game‐theoretic discussion of Hobbes and to develop a game‐theoretic interpretation that gives due attention both to Hobbes's distinction between “moderates” and “dominators” and to what actually initiates conflict in the state of nature, namely, the competition for vital goods. As can be shown, Hobbes's state of nature contains differently structured situations of choice, the game‐theoretic representation of which requires the prisoner's dilemma and the assurance game and the so‐called assurance dilemma. However, the “state of war” ultimately emerges from situations that cannot be described by any of these games because they represent zero‐sum games in which the outcome of mutual cooperation does not exist.     

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.     

The Role of Subsidies in Coordination Games with Interconnected Risk

Can subsidies promote Pareto‐optimum coordination? We found that partially subsidizing the cooperative actions for two out of six players in a laboratory coordination game usually produced better coordination and higher total social welfare with both deterministic and stochastic payoffs. Not only were the subsidized players more likely to cooperate (choose the Pareto‐optimum action), but the unsubsidized players increased their expectations on how likely others would cooperate, and they cooperated more frequently themselves. After removal of the subsidy, high levels of coordination continued in most groups with stochastic payoffs but declined in deterministic ones. This carry‐over disparity between the deterministic and stochastic settings was consistent with the economic theories that agents were more likely to keep the status quo option under uncertainty than without uncertainty. Hence, players with stochastic payoffs were more likely to keep the high coordination level (status quo) brought by the subsidy in the previous subsidy session. A post‐game survey also indicated that with stochastic payoffs, players focused on risk reduction. Temporary subsidies promoted lasting coordination because even after subsidy was removed, players still assumed that others players would prefer reduced risks from cooperation. With deterministic payoffs, however, the subsidy might crowd out other rationales for coordination, with many players indicating that the subsidy was the only reason for anyone to cooperate. Hence, the coordination level dropped when the subsidy was removed. Copyright © 2014 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.     

Framing prisoners and chickens: Valence effects in the prisoner’s dilemma and the chicken game

In an experimental study, we investigated how decisions in social dilemmas are affected by the valence of outcomes that are at stake. Prospect theory states that individuals are risk-averse when outcomes are framed as gains, and risk-seeking when outcomes are framed as losses. On the basis of this framework, previous research on social dilemmas has addressed the question of whether people are more cooperative in the negative domain than in the positive domain, but this research has led to inconsistent results. A possible explanation for this is that in many social dilemmas it is unclear whether cooperation or defection is the risky choice. In the current paper, we compare the well-studied prisoner’s dilemma with the less studied chicken game. Whereas in the prisoner’s dilemma it is unclear what constitutes the risky option, in the chicken game the risky option is quite clear. Consistent with predictions, we found in the chicken game more defection in the loss frame than in the gain frame, but no difference between the gain and loss frame in the prisoner’s dilemma. Moreover, choices were predicted by risk attitude in the chicken game, but not in the prisoner’s dilemma.     

Dynamic probability of reinforcement for cooperation: Random game termination in the centipede game

Experimental games have previously been used to study principles of human interaction. Many such games are characterized by iterated or repeated designs that model dynamic relationships, including reciprocal cooperation. To enable the study of infinite game repetitions and to avoid endgame effects of lower cooperation toward the final game round, investigators have introduced random termination rules. This study extends previous research that has focused narrowly on repeated Prisoner's Dilemma games by conducting a controlled experiment of two‐player, random termination Centipede games involving probabilistic reinforcement and characterized by the longest decision sequences reported in the empirical literature to date (24 decision nodes). Specifically, we assessed mean exit points and cooperation rates, and compared the effects of four different termination rules: no random game termination, random game termination with constant termination probability, random game termination with increasing termination probability, and random game termination with decreasing termination probability. We found that although mean exit points were lower for games with shorter expected game lengths, the subjects' cooperativeness was significantly reduced only in the most extreme condition with decreasing computer termination probability and an expected game length of two decision nodes.     

Modeling alliance activity: Opportunity cost effects and manipulations in an iterated prisoner’s dilemma with exit option

We model the two-firm alliance as an iterated prisoners’ dilemma game with an exit option and test several theoretical predictions over two experimental studies. A new major effect on alliance performance arises by including the exit option (i.e., the option to end the alliance and receive a fixed payoff that is less than the payoff for mutual cooperation but greater than the payoff for mutual defection). The opportunity cost levels of the firms either directly or indirectly influence alliance cooperation and alliance payoffs through affecting the alliance strategies that the firms choose. Implications for partner selection, alliance selection and structuring, and strategy choices along the alliance lifespan, build on these results.     

Is behavioral pro-sociality game-specific? Pro-social preference and expectations of pro-sociality

We observed the behaviors of the same people across five games – two prisoner’s dilemma games, a trust game (in which the subject took on the role of both truster and trustee), a dictator game, and a faith game – any pair of which was separated by an interval of several months to reduce potential carry-over effects, and found strong consistency in behaviors among these games. We also found consistency between the expectations of other players’ behaviors and the player’s own behavior across games. We further found that the consistent behavioral pro-sociality observed across different games was related to the general measures of pro-social value orientation and perceiving the game situations. These findings suggest that individual and cultural differences in game behaviors can reflect both the ways in which people perceive game situations and their general social preferences.     

Effect of playing violent video games cooperatively or competitively on subsequent cooperative behavior

Research on video games has yielded consistent findings that violent video games increase aggression and decrease prosocial behavior. However, these studies typically examined single-player games. Of interest is the effect of cooperative play in a violent video game on subsequent cooperative or competitive behavior. Participants played Halo II (a first-person shooter game) cooperatively or competitively and then completed a modified prisoner's dilemma task to assess competitive and cooperative behavior. Compared with the competitive play conditions, players in the cooperative condition engaged in more tit-for-tat behaviors-a pattern of behavior that typically precedes cooperative behavior. The social context of game play influenced subsequent behavior more than the content of the game that was played.     

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.     

Defection in the dark? A randomized‐response investigation of cooperativeness in social dilemma games

As previous research has demonstrated numerous times, humans show a robust tendency for cooperation. However, part—or indeed all—of this cooperativeness may be due to socially desirable responding. To address this problem, we propose and apply a new approach for the unbiased measurement of cooperativeness in social dilemma games. Specifically, we employ an extension of the randomized‐response technique (RRT). The RRT protects the privacy of respondents by adding random noise to their responses. It thus encourages more honest responding and thereby provides less biased estimates of sensitive attributes. In a large‐scale study with 2043 respondents we maximized anonymity in a one‐shot prisoner's dilemma game through use of the RRT. Comparing the prevalence rates for cooperation obtained via the RRT with those from direct self‐report showed that traditional direct questioning formats overestimate cooperation rates, with a relative bias of 18%. This finding suggests that to a considerable extent, self‐reported cooperation is due to socially desirable responding, rather than actual cooperativeness. However, our results also demonstrate that cooperation remains substantial even under conditions of maximized anonymity. Copyright © 2011 John Wiley & Sons, Ltd.     

Contingencies of reinforcement in a five-person prisoner's dilemma

As in studies of self-control, a tit-for-tat contingency in an iterated prisoner's dilemma game creates a conflict between maximization of local and global reinforcement. The present experiments examine this conflict in a multiplayer prisoner's dilemma game. Versus tit for tat, cooperation corresponds to self-control; defection, always immediately reinforced, corresponds to impulsiveness. Three experiments examined sensitivity of behavior to the global reinforcement contingency imposed by tit for tat. Undergraduates played a five-player prisoner's dilemma game against four dummy players programmed to play tit for tat or randomly. With tit for tat, a player's cooperation (or defection) increased dummy players' cooperation (or defection) on subsequent trials-reinforcing cooperation and punishing defection in the long run. Participants cooperated at a higher rate when the dummy players played tit for tat than when the dummy players played randomly. These results are consistent with findings in corresponding studies of self-control. Some participants, caught in a trap of mutual defection with the tit-for-tat playing dummy players, came to cooperate when the tit-for-tat contingency was reset ("forgiving" participants' previous defections) during a pause in the game. This increase was a result of the combined effects of a pause and reset; neither pausing nor resetting independently resulted in an increase in cooperation.     

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。     

There's no “I” in team: Effects of cooperative video games on cooperative behavior

The present research tests the idea that playing a team‐player video game in which players work together as teammates and assist each other in achieving a common goal increases cooperative behavior toward a new partner. In fact, relative to a single‐player mode, cooperatively playing a video game increased cooperation in a mixed‐motive decision dilemma task. Because the players were exposed to the same video game content in both experimental conditions, the effect on cooperative behavior can only be accounted for by the different way the game was played. Mediation analyses revealed that cooperative team play promoted feelings of cohesion, which activated trust (i.e., the expectation of reciprocal cooperation), which in turn increased cooperative behavior. Copyright © 2013 John Wiley & Sons, Ltd.     

Lead Us (Not) into Temptation: Testing the Motivational Mechanisms Linking Honesty–Humility to Cooperation

Over the past decades, there has been considerable interest in individual differences in cooperative behaviour and how these can be explained. Whereas the Honesty–Humility dimension from the HEXACO model of personality has been identified as a consistent predictor of cooperation, the underlying motivational mechanisms of this association have remained unclear—especially given the confound between the temptation to exploit others and the fear of being exploited as motivational drivers of defection in social dilemmas. In a reanalysis and a new experiment, we tease apart these mechanisms by manipulating the rank order of pay‐offs in a symmetric two‐person game paradigm, essentially implementing the classic prisoner's dilemma, stag hunt, and chicken games. Results revealed that Honesty–Humility predicted cooperation specifically in the games in which temptation was a potential motivator of defection, whereas it did not account for cooperation in those games in which only fear implied defection. Our findings thereby shed light on the underlying motivational mechanisms of the Honesty–Humility–cooperation link and, more generally, demonstrate how economic games can be used to disentangle such mechanisms. Copyright © 2018 European Association of Personality Psychology     

同伴特点如何影响人们的合作与冲突行为?

人类的生存繁衍依赖于人们之间的相互合作,合作与冲突行为的研究近年来成为心理学的研究热点。本研究通过实验程序操纵Chicken Game中博弈同伴的特点,考察个体在社会困境中面对不同特点同伴时的合作行为。结果发现：(1)同伴道义论组和功利论组总和解率没有显著差异,同伴竞争组和合作组的总和解率也没有显著差异。(2)在与道义论以及合作型的同伴互动时,个体的行为没有明显受到上次博弈反馈的影响。(3)当同伴为功利论时,相比于上次博弈个体选择和解而同伴选择进攻,双方都选择和解时个体在当前博弈中更倾向于和解;(4)在同伴竞争组中,相比于上次博弈个体选择进攻而同伴选择和解,双方都选择和解时被试在当前博弈中会更倾向于和解。实验结果表明个体在博弈任务中会受到同伴特点的影响,并且同伴在博弈中的行为特点的影响更为显著。本研究从同伴特点来考察个体的合作行为,揭示了影响个体博弈行为的一种因素。     

Game Theory in Philosophy

Game theory is the mathematical study of strategy and conflict. It has wide applications in economics, political science, sociology, and, to some extent, in philosophy. Where rational choice theory or decision theory is concerned with individual agents facing games against nature, game theory deals with games in which all players have preference orderings over the possible outcomes of the game. This paper gives an informal introduction to the theory and a survey of applications in diverse branches of philosophy. No criticism is reviewed. Game theory is shown at work in discussions about epistemological dependence (prisoner’s dilemma), liberalism and efficiency (Nash equilibrium), Hume’s concept of convention (correlated equilibrium), morality and rationality (bargaining games), and distributive justice and egalitarianism (evolutionary game theory). A guide to the literature provides hints at applications in collective intentionality, epistemology, ethics, history of philosophy, logic, philosophy of language, and political philosophy.     

Why are online games so self‐involving: A social identity analysis of massively multiplayer online role‐playing games

This article investigates the ways in which players of massively multiplayer online role‐playing games (MMORPGs) internalize being a player into their self‐concept. In accordance with the social identity framework, we assume that being a player and being a member of a guild within the game can both shape the social identity of members. In two studies, we survey players inside or outside the MMORPG. Players are interviewed either at an interguild comparison level or at the more inclusive level of MMORPG players. Study 1 (n = 84) reveals favoritism for the in‐group guild in a within‐game context, and Study 2 (n = 200) shows that valuation of and identification with the in‐group are moderated by the interview context and the level of category inclusion: Inside the game, the guild is more valued and identification is emphasized. In contrast, valuation of and identification with MMORPG players is not influenced by the interview context. Together, by examining both valuation and identification processes, this research reveals that playing online games may be self‐involving because being a player, but also being a member of a guild, directly contribute to the social identity. Copyright © 2015 John Wiley & Sons, Ltd.     

Of virtual victims and victimized virtues: differential effects of experienced aggression in video games on social cooperation

Two experimental studies were used to investigate how interacting with aggressive virtual characters in video games affects trust and cooperation of players. Study 1 demonstrates that experiencing virtual aggression from a victim's perspective can impair players' investments in a subsequent common goods dilemma situation. This effect is mediated by reduced expectations of trust in the cooperativeness of interaction partners. In Study 2 the same effect was replicated by using a different cooperation task and by investigating the moderating role of justice sensitivity from a victim's perspective as a dispositional factor. Participants transferred less money to an unknown partner in a trust game after exposure to aggressive nonplayer characters in a video game. This effect was stronger for people high in victim sensitivity. Results of both studies can be interpreted in line with the sensitivity to mean intentions model and add to the body of research on violent media effects.