Action being character: a promising perspective on the solution concept of game theory

The inconsistency of predictions from solution concepts of conventional game theory with experimental observations is an enduring question. These solution concepts are based on the canonical rationality assumption that people are exclusively self-regarding utility maximizers. In this article, we think this assumption is problematic and, instead, assume that rational economic agents act as if they were maximizing their implicit utilities, which turns out to be a natural extension of the canonical rationality assumption. Implicit utility is defined by a player's character to reflect his personal weighting between cooperative, individualistic, and competitive social value orientations. The player who actually faces an implicit game chooses his strategy based on the common belief about the character distribution for a general player and the self-estimation of his own character, and he is not concerned about which strategies other players will choose and will never feel regret about his decision. It is shown by solving five paradigmatic games, the Dictator game, the Ultimatum game, the Prisoner's Dilemma game, the Public Goods game, and the Battle of the Sexes game, that the framework of implicit game and its corresponding solution concept, implicit equilibrium, based on this alternative assumption have potential for better explaining people's actual behaviors in social decision making situations.     

How inconsistency between attitude and behavior persists through cultural transmission

Individuals tend to conform their behavior to that of the majority. Consequently, an individual's behavior is not always consistent with his or her attitude, and such inconsistency sometimes causes mental distress. Understanding the mechanism of sustaining inconsistency between attitude and behavior is a challenging problem from the viewpoint of evolutionary theory. We constructed an evolutionary game theory model in which each player has an attitude and behavior toward a single social norm, and the players' attitudes and behaviors are affected by three types of cultural transmission: vertical, oblique, and horizontal. We assumed that strategy is a combination of attitude and behavior and that the process of learning or transmitting the social norm depends on the life stage of each player. Adults play a coordination game in which players whose behaviors match those of the majority obtain a high payoff, which is diminished by any inconsistency between attitude and behavior. The adults' strategies are passed to newborns via vertical transmission, and the frequency of a newborn's replication of strategy is proportional to the corresponding adult's payoff. Newborns imitate behaviors of unrelated adults via oblique transmission. Juveniles change their attitudes or behaviors by observing other juveniles' behaviors or inferring other juveniles' attitudes (horizontal transmission). We conclude that the key factor for sustaining inconsistency between attitude and behavior is the ability of players to infer and imitate others' attitudes, and that oblique transmission promotes inconsistency.     

Implicit and Explicit Illusory Correlation as a Function of Political Ideology

Research has demonstrated that people who embrace different ideological orientations often show differences at the level of basic cognitive processes. For instance, conservatives (vs. liberals) display an automatic selective attention for negative (vs. positive) stimuli, and tend to more easily form illusory correlations between negative information and minority groups. In the present work, we further explored this latter effect by examining whether it only involves the formation of explicit attitudes or it extends to implicit attitudes. To this end, following the typical illusory correlation paradigm, participants were presented with members of two numerically different groups (majority and minority) each performing either a positive or negative behaviour. Negative behaviors were relatively infrequent, and the proportion of positive and negative behaviors within each group was the same. Next, explicit and implicit (i.e., IAT-measured) attitudes were assessed. Results showed that conservatives (vs. liberals) displayed stronger explicit as well as implicit illusory correlations effects, forming more negative attitudes toward the minority (vs. majority) group at both the explicit and implicit level.     

Is it better to give information, receive it, or be ignorant in a two-player game?

The standard approach in a biological two-player game is toassume both players choose their actions independently of oneanother, having no information about their opponent's action(simultaneous game). However, this approach is not realisticin some circumstances. In many cases, one player chooses hisaction first and then the second player chooses her action withinformation about his action (Stackelberg game). We comparethese two games, which can be mathematically analyzed into twotypes, depending on the direction of the best response function(BRF) at the evolutionarily stable strategy in the simultaneousgame (ESS_sim). We subcategorize each type of game into two cases,depending on the change in payoff to one player, when both playersare at the ESS_sim, and the other player increases his action.Our results show that in cases where the BRF is decreasing atthe ESS_sim, the first player in the Stackelberg game receivesthe highest payoff, followed by both players in the simultaneousgame, followed by the second player in the Stackelberg game.In these cases, it is best to be the first Stackelberg player.In cases where the BRF is increasing at the ESS_sim, both Stackelbergplayers receive a higher payoff than players in a simultaneousgame. In these cases, it is better for both players to playa Stackelberg game rather than a simultaneous game. However,in some cases the first Stackelberg player receives a higherpayoff than the second Stackelberg player, and in some casesthe opposite is true.     

Decisions among the Undecided: Implicit Attitudes Predict Future Voting Behavior of Undecided Voters

Implicit attitudes have been suggested as a key to unlock the hidden preferences of undecided voters. Past research, however, offered mixed support for this hypothesis. The present research used a large nationally representative sample and a longitudinal design to examine the predictive utility of implicit and explicit attitude measures in the 2008 U.S. presidential election. In our analyses, explicit attitudes toward candidates predicted voting better for decided than undecided voters, but implicit candidate attitudes were predictive of voting for both decided and undecided voters. Extending our examination to implicit and explicit racial attitudes, we found the same pattern. Taken together, these results provide convergent evidence that implicit attitudes predict voting about as well for undecided as for decided voters. We also assessed a novel explanation for these effects by evaluating whether implicit attitudes may predict the choices of undecided voters, in part, because they are neglected when people introspect about their confidence. Consistent with this idea, we found that the extremity of explicit but not implicit attitudes was associated with greater confidence. These analyses shed new light on the utility of implicit measures in predicting future behavior among individuals who feel undecided. Considering the prior studies together with this new evidence, the data seem to be consistent that implicit attitudes may be successful in predicting the behavior of undecided voters.     

Do Implicit Attitudes Predict Actual Voting Behavior Particularly for Undecided Voters?

The prediction of voting behavior of undecided voters poses a challenge to psychologists and pollsters. Recently, researchers argued that implicit attitudes would predict voting behavior particularly for undecided voters whereas explicit attitudes would predict voting behavior particularly for decided voters. We tested this assumption in two studies in two countries with distinct political systems in the context of real political elections. Results revealed that (a) explicit attitudes predicted voting behavior better than implicit attitudes for both decided and undecided voters, and (b) implicit attitudes predicted voting behavior better for decided than undecided voters. We propose that greater elaboration of attitudes produces stronger convergence between implicit and explicit attitudes resulting in better predictive validity of both, and less incremental validity of implicit over explicit attitudes for the prediction of voting behavior. However, greater incremental predictive validity of implicit over explicit attitudes may be associated with less elaboration.     

Connections with Nature and Environmental Behaviors

The influence of environmental attitudes on environmental behaviors has long been discussed. However, few studies have addressed the foundation of such attitudes. In the present study, we explored primitive belief underlying environmental attitudes, i.e., connections with nature, and its relationship with pro-environmental behaviors. Specifically, we used scales, a computerized Implicit Association Test, and a situational simulation experiment to examine both explicit and implicit connections with nature, both deliberate and spontaneous environmental behaviors, and to find correlations between environmental connectedness and environmental behaviors. Results showed that explicit connectedness was positively correlated with deliberate environmental behaviors, while implicit connectedness was positively correlated with spontaneous environmental behaviors. Additionally, explicit and implicit connectedness was independent of each other. In conclusion, the current study confirms the positive role played by connections with nature in promoting environmental behavior, and accordingly suggests means to encourage pro-environmental behavior by enhancing people’s connectedness to nature.     

War of attrition with implicit time cost

In the game-theoretic model war of attrition, players are subject to an explicit cost proportional to the duration of contests. We construct a model where the time cost is not explicitly given, but instead depends implicitly on the strategies of the whole population. We identify and analyse the underlying mechanisms responsible for the implicit time cost. Each player participates in a series of games, where those prepared to wait longer win with higher certainty but play less frequently. The model is characterized by the ratio of the winner's score to the loser's score, in a single game. The fitness of a player is determined by the accumulated score from the games played during a generation. We derive the stationary distribution of strategies under the replicator dynamics. When the score ratio is high, we find that the stationary distribution is unstable, with respect to both evolutionary and dynamical stability, and the dynamics converge to a limit cycle. When the ratio is low, the dynamics converge to the stationary distribution. For an intermediate interval of the ratio, the distribution is dynamically but not evolutionarily stable. Finally, the implications of our results for previous models based on the war of attrition are discussed.     

The influence of cultural framing on play in the trust game: a Maasai example

The effects of cultural framing on behavior in experimental games were explored with a trust game and the Maasai concept of osotua. Maasai use the term osotua to refer to gift-giving relationships based on obligation, need, respect, and restraint. In the trust game, the first player is given money and an opportunity to give any portion of it to the second player. The amount given is then multiplied by the experimenter, and the second player has an opportunity to give any amount back to the first player. Fifty trust games were played by Maasai men at a field site in north central Kenya. Half of the games were played without deliberate framing, and half were framed with the statement, “This is an osotua game.” Compared to games with no deliberate framing, those played within the osotua rhetorical frame were associated with lower transfers by both players and with lower expected returns on the part of the first players. Osotua rhetorical framing is also associated with a negative correlation between amounts given by the first player and amounts returned by the second. These results have implications both for the experimental game method and for our understanding of the relationship between culture and behavior.     

Overweight People Have Low Levels of Implicit Weight Bias,but Overweight Nations Have High Levels of Implicit Weight Bias

Although a greater degree of personal obesity is associated with weaker negativity toward overweight people on both explicit (i.e., self-report) and implicit (i.e., indirect behavioral) measures, overweight people still prefer thin people on average. We investigated whether the national and cultural context – particularly the national prevalence of obesity – predicts attitudes toward overweight people independent of personal identity and weight status. Data were collected from a total sample of 338,121 citizens from 71 nations in 22 different languages on the Project Implicit website (https://implicit.harvard.edu/) between May 2006 and October 2010. We investigated the relationship of the explicit and implicit weight bias with the obesity both at the individual (i.e., across individuals) and national (i.e., across nations) level. Explicit weight bias was assessed with self-reported preference between overweight and thin people; implicit weight bias was measured with the Implicit Association Test (IAT). The national estimates of explicit and implicit weight bias were obtained by averaging the individual scores for each nation. Obesity at the individual level was defined as Body Mass Index (BMI) scores, whereas obesity at the national level was defined as three national weight indicators (national BMI, national percentage of overweight and underweight people) obtained from publicly available databases. Across individuals, greater degree of obesity was associated with weaker implicit negativity toward overweight people compared to thin people. Across nations, in contrast, a greater degree of national obesity was associated with stronger implicit negativity toward overweight people compared to thin people. This result indicates a different relationship between obesity and implicit weight bias at the individual and national levels.     

Effects of the number of players and game type constraints on heart rate, rating of perceived exertion, and technical actions of small-sided soccer games

The purpose of this study was to identify the variation of heart rate (HR), rating of perceived exertion (RPE), and technical actions between 2 soccer small-sided games (SSGs; 3 × 3 and 4 × 4) in 3 game type constraints (when playing only offense [OFF], playing only defense [DEF], and both situations [GAME]). Sixteen high-level young male players were analyzed (age 15.75 ± 0.45 years; height 172.4 ± 4.83 cm; body mass 64.5 ± 6.44 kg; HRmax199.1 ± 9.08 b·min(-1); and 8.06 ± 1.98 years of soccer practice). All tasks were performed in 4 periods of 4 minutes interspersed with 2 minutes of active recovery. The HR was measured continuously and then analyzed by the time spent into 4 training zones according to individual %HRmax (zone 1 <75%; zone 2 75-84.9%; zone 3 85-89.9%; and zone 4 ≥90%). Results identified that players were most frequently in zones 2 and 3. The 3 × 3 SSGs elicited higher HR and RPE and the most intense situation was GAME. Despite the known higher frequencies from technical actions in SSGs with fewer players, player effectiveness in 3 × 3 and 4 × 4 was identical. The use of GAME, OFF, and DEF game type constraints should be carefully planned. Using the 3 × 3 format seems more adequate when aiming for aerobic performance optimal effects; however, DEF situations should only be used to promote aerobic recovery effects. The inclusion of an additional player in SSGs had different interactions in game type constraints, and only GAME presented adequate intensity.     

Effect of the presence of empty sites on the evolution of cooperation by costly punishment in spatial games

Cooperation and spiteful behavior are still evolutionary puzzles. Costly punishment, for which the game payoff is the same as that of spiteful behavior, is one mechanism for promoting the evolution of cooperation. A spatially structured population facilitates the evolution of either cooperation or spite/punishment if cooperation is linked explicitly or implicitly with spite/punishment; a cooperator cooperates with another cooperator and punishes/spites the other type of player. Different updating rules in the evolutionary game produce different evolutionary outcomes: with one updating rule—the score-dependent viability model, in which a player dies with a probability inversely proportional to the game score and the resulting unoccupied site is colonized by one player chosen randomly—the evolution of spite/punishment is promoted more than with the other updating rule—the score-dependent fertility model, in which, after a player dies randomly, the site is colonized by a player with a higher game score. If the population has empty sites, spiteful players or punishers should have less chance to interact with others and then spite/punish others. Thus the presence of empty sites would affect the evolutionary dynamics of spite/punishment. Here, we investigated whether the presence of empty sites discourages the evolution of spite/punishment in both a lattice-structured population and a completely mixing population where players interact with others randomly, especially when the score-dependent viability model is adopted. In the lattice-structured population adopting this viability model, the presence of empty sites promoted the evolution of cooperation and did not reduce the effect of spite/punishment. In the completely mixing population, the presence of empty sites did not promote evolution of cooperation by punishment. The evolutionary dynamics of the score-dependent viability model with empty sites were close to those of the score-dependent fertility model.     

Facing Off with Unfair Others: Introducing Proxemic Imaging as an Implicit Measure of Approach and Avoidance during Social Interaction

Nonverbal behavior expresses many of the dynamics underlying face-to-face social interactions, implicitly revealing one’s attitudes, emotions, and social motives. Although research has often described nonverbal behavior as approach versus avoidant (i.e., through the study of proxemics), psychological responses to many social contexts are a mix of these two. Fairness violations are an ideal example, eliciting strong avoidance-related responses such as negative attitudes, as well as strong approach-related responses such as anger and retaliation. As such, nonverbal behavior toward unfair others is difficult to predict in discrete approach versus avoidance terms. Here we address this problem using proxemic imaging, a new method which creates frequency images of dyadic space by combining motion capture data of interpersonal distance and gaze to provide an objective but nuanced analysis of social interactions. Participants first played an economic game with fair and unfair players and then encountered them in an unrelated task in a virtual environment. Afterwards, they could monetarily punish the other players. Proxemic images of the interactions demonstrate that, overall, participants kept the fair player closer. However, participants who actively punished the unfair players were more likely to stand directly in front of those players and even to turn their backs on them. Together these patterns illustrate that fairness violations influence nonverbal behavior in ways that further predict differences in more overt behavior (i.e., financial punishment). Moreover, they demonstrate that proxemic imaging can detect subtle combinations of approach and avoidance behavior during face-to-face social interactions.     

Hormonal underpinnings of status conflict: Testosterone and cortisol are related to decisions and satisfaction in the hawk-dove game

A contribution to a special issue on Hormones and Human Competition.Testosterone is theorized to influence status-seeking behaviors such as social dominance and competitive behavior, but supporting evidence is mixed. The present study tested the roles of testosterone and cortisol in the hawk-dove game, a dyadic economic decision-making paradigm in which earnings depend on one's own and the other player's choices. If one person selects the hawk strategy and the other person selects the dove strategy, the player who selected hawk attains a greater financial pay-off (status differentiation). The worst financial outcome occurs when both players choose the hawk strategy (status confrontation). Ninety-eight undergraduate students (42 men) provided saliva samples and played ten rounds of the hawk-dove game with another same-sex participant. In support of the hypothesis that testosterone is related to status concern, individuals higher in basal testosterone made more hawk decisions — decisions that harmed the other player. Acute decreases in cortisol were also associated with more hawk decisions. There was some empirical support for the dual-hormone hypothesis as well: basal testosterone was positively related to satisfaction in the game among low basal-cortisol individuals but not among high basal-cortisol individuals. There were no significant sex differences in these hormonal effects. The present findings align with theories of hormones and status-seeking behavior at the individual level, but they also open up new avenues for research on hormone profiles at the collective level. Our results suggest that the presence of two or more high-testosterone members increases the likelihood of status confrontations over a limited resource that can undermine collective outcomes.     

Optimal Cooperation-Trap Strategies for the Iterated Rock-Paper-Scissors Game

In an iterated non-cooperative game, if all the players act to maximize their individual accumulated payoff, the system as a whole usually converges to a Nash equilibrium that poorly benefits any player. Here we show that such an undesirable destiny is avoidable in an iterated Rock-Paper-Scissors (RPS) game involving two rational players, X and Y. Player X has the option of proactively adopting a cooperation-trap strategy, which enforces complete cooperation from the rational player Y and leads to a highly beneficial and maximally fair situation to both players. That maximal degree of cooperation is achievable in such a competitive system with cyclic dominance of actions may stimulate further theoretical and empirical studies on how to resolve conflicts and enhance cooperation in human societies.     

Evolution of Cooperation in Spatial Traveler's Dilemma Game

Traveler''s dilemma (TD) is one of social dilemmas which has been well studied in the economics community, but it is attracted little attention in the physics community. The TD game is a two-person game. Each player can select an integer value between and () as a pure strategy. If both of them select the same value, the payoff to them will be that value. If the players select different values, say and (), then the payoff to the player who chooses the small value will be and the payoff to the other player will be . We term the player who selects a large value as the cooperator, and the one who chooses a small value as the defector. The reason is that if both of them select large values, it will result in a large total payoff. The Nash equilibrium of the TD game is to choose the smallest value . However, in previous behavioral studies, players in TD game typically select values that are much larger than , and the average selected value exhibits an inverse relationship with . To explain such anomalous behavior, in this paper, we study the evolution of cooperation in spatial traveler''s dilemma game where the players are located on a square lattice and each player plays TD games with his neighbors. Players in our model can adopt their neighbors'' strategies following two standard models of spatial game dynamics. Monte-Carlo simulation is applied to our model, and the results show that the cooperation level of the system, which is proportional to the average value of the strategies, decreases with increasing until is greater than the critical value where cooperation vanishes. Our findings indicate that spatial reciprocity promotes the evolution of cooperation in TD game and the spatial TD game model can interpret the anomalous behavior observed in previous behavioral experiments.     

Implicit and Explicit Anti-Fat Bias among a Large Sample of Medical Doctors by BMI,Race/Ethnicity and Gender

Overweight patients report weight discrimination in health care settings and subsequent avoidance of routine preventive health care. The purpose of this study was to examine implicit and explicit attitudes about weight among a large group of medical doctors (MDs) to determine the pervasiveness of negative attitudes about weight among MDs. Test-takers voluntarily accessed a public Web site, known as Project Implicit®, and opted to complete the Weight Implicit Association Test (IAT) (N = 359,261). A sub-sample identified their highest level of education as MD (N = 2,284). Among the MDs, 55% were female, 78% reported their race as white, and 62% had a normal range BMI. This large sample of test-takers showed strong implicit anti-fat bias (Cohen’s d = 1.0). MDs, on average, also showed strong implicit anti-fat bias (Cohen’s d = 0.93). All test-takers and the MD sub-sample reported a strong preference for thin people rather than fat people or a strong explicit anti-fat bias. We conclude that strong implicit and explicit anti-fat bias is as pervasive among MDs as it is among the general public. An important area for future research is to investigate the association between providers’ implicit and explicit attitudes about weight, patient reports of weight discrimination in health care, and quality of care delivered to overweight patients.     

Evolutionary Stability in the Asymmetric Volunteer's Dilemma

It is often assumed that in public goods games, contributors are either strong or weak players and each individual has an equal probability of exhibiting cooperation. It is difficult to explain why the public good is produced by strong individuals in some cooperation systems, and by weak individuals in others. Viewing the asymmetric volunteer''s dilemma game as an evolutionary game, we find that whether the strong or the weak players produce the public good depends on the initial condition (i.e., phenotype or initial strategy of individuals). These different evolutionarily stable strategies (ESS) associated with different initial conditions, can be interpreted as the production modes of public goods of different cooperation systems. A further analysis revealed that the strong player adopts a pure strategy but mixed strategies for the weak players to produce the public good, and that the probability of volunteering by weak players decreases with increasing group size or decreasing cost-benefit ratio. Our model shows that the defection probability of a “strong” player is greater than the “weak” players in the model of Diekmann (1993). This contradicts Selten''s (1980) model that public goods can only be produced by a strong player, is not an evolutionarily stable strategy, and will therefore disappear over evolutionary time. Our public good model with ESS has thus extended previous interpretations that the public good can only be produced by strong players in an asymmetric game.     

Interpersonal coordination analysis of tennis players from different levels during official matches

The purpose of this study was to assess the interpersonal coordination during official male tennis matches in players of different skill levels. Players’ trajectories of three levels (Juvenile, ATP-Future, ATP-250) were obtained using video-based tracking system. A vector coding technique was applied to obtain players’ interpersonal coordination in four coordination patterns: “anti-phase”, “in-phase”, “serving player phase” and “returning player phase”. These patterns allowed identification of the nature of the coupling and lead/lag relations between players. In all categories, players presented higher degree of “anti-phase” and “serving player phase” (when only the serving player is moving on the court or his opponent is moving with a time lag) coordination. Young players spent more time in “serving player phase” during lateral displacements than professional players. On the other hand, professional players spent more time in “returning player phase” (when only the returning player is moving on the court or his opponent is moving with a time lag) during antero posterior displacements, than young players. Interpersonal coordination did not change from the first to the second set of the match, showing that tennis players maintain their displacement characteristics and strategy, independently of proficiency level. The vector coding technique allowed to identify new coordination patterns in tennis, providing additional information about tennis dynamics and how players from different categories and proficiency levels behave during the matches.     

Indirect reciprocity under incomplete observation

Indirect reciprocity, in which individuals help others with a good reputation but not those with a bad reputation, is a mechanism for cooperation in social dilemma situations when individuals do not repeatedly interact with the same partners. In a relatively large society where indirect reciprocity is relevant, individuals may not know each other's reputation even indirectly. Previous studies investigated the situations where individuals playing the game have to determine the action possibly without knowing others' reputations. Nevertheless, the possibility that observers of the game, who generate the reputation of the interacting players, assign reputations without complete information about them has been neglected. Because an individual acts as an interacting player and as an observer on different occasions if indirect reciprocity is endogenously sustained in a society, the incompleteness of information may affect either role. We examine the game of indirect reciprocity when the reputations of players are not necessarily known to observers and to interacting players. We find that the trustful discriminator, which cooperates with good and unknown players and defects against bad players, realizes cooperative societies under seven social norms. Among the seven social norms, three of the four suspicious norms under which cooperation (defection) to unknown players leads to a good (bad) reputation enable cooperation down to a relatively small observation probability. In contrast, the three trustful norms under which both cooperation and defection to unknown players lead to a good reputation are relatively efficient.