An Application of Evolutionary Game Theory to Social Dilemmas: The Traveler's Dilemma and the Minimum Effort Coordination Game

The Traveler''s Dilemma game and the Minimum Effort Coordination game are two social dilemmas that have attracted considerable attention due to the fact that the predictions of classical game theory are at odds with the results found when the games are studied experimentally. Moreover, a direct application of deterministic evolutionary game theory, as embodied in the replicator dynamics, to these games does not explain the observed behavior. In this work, we formulate natural variants of these two games as smoothed continuous-strategy games. We study the evolutionary dynamics of these continuous-strategy games, both analytically and through agent-based simulations, and show that the behavior predicted theoretically is in accord with that observed experimentally. Thus, these variants of the Traveler''s Dilemma and the Minimum Effort Coordination games provide a simple resolution of the paradoxical behavior associated with the original games.     

Nash Equilibria in Multi-Agent Motor Interactions

Social interactions in classic cognitive games like the ultimatum game or the prisoner''s dilemma typically lead to Nash equilibria when multiple competitive decision makers with perfect knowledge select optimal strategies. However, in evolutionary game theory it has been shown that Nash equilibria can also arise as attractors in dynamical systems that can describe, for example, the population dynamics of microorganisms. Similar to such evolutionary dynamics, we find that Nash equilibria arise naturally in motor interactions in which players vie for control and try to minimize effort. When confronted with sensorimotor interaction tasks that correspond to the classical prisoner''s dilemma and the rope-pulling game, two-player motor interactions led predominantly to Nash solutions. In contrast, when a single player took both roles, playing the sensorimotor game bimanually, cooperative solutions were found. Our methodology opens up a new avenue for the study of human motor interactions within a game theoretic framework, suggesting that the coupling of motor systems can lead to game theoretic solutions.     

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.     

Prey preferences of free‐ranging cheetahs on farmland: scat analysis versus farmers' perceptions

Human–predator conflict is one of the biggest threats to large carnivore species worldwide. Its intensity is closely linked to farmer's attitudes and perceptions of predators. As a result, farmers' estimates of the number of livestock or game‐stock animals killed by predators are often formed based on the perceived number of predators present and their perceivably favoured prey species. This study aims to examine the prey preferences of cheetahs Acinonyx jubatus in relation to farmers' perceptions and the relative contribution of livestock and game‐stock to the cheetahs' diet. Cheetahs' prey preferences were determined through the cross‐sectional analysis of prey hair, found in cheetah scat. Cheetahs were found to predominantly prey on free‐ranging abundant game species, primarily kudu Tragelaphus strepsiceros. Game ranchers overestimated the prominence of game‐stock to the cheetahs' diet, especially springbok Antidorcas marsupialis. Potential reasons for these discrepancies and the importance of abundant natural prey as a potential human–predator coexistence strategy are discussed.     

A behavioral test of accepting benefits that cost others: associations with conduct problems and callous-unemotionality

Background

Youth with conduct problems (CP) often make decisions which value self-interest over the interests of others. Self-benefiting behavior despite loss to others is especially common among youth with CP and callous-unemotional traits (CU). Such behavioral tendencies are generally measured using self- or observer-report. We are unaware of attempts to measure this tendency with a behavioral paradigm.

Methods/Principal Findings

In our AlAn''s (altruism-antisocial) game a computer program presents subjects with a series of offers in which they will receive money but a planned actual charity donation will be reduced; subjects decide to accept or reject each offer. We tested (1) whether adolescent patients with CP (n = 20) compared with adolescent controls (n = 19) differed on AlAn''s game outcomes, (2) whether youths with CP and CU differed significantly from controls without CP or CU, and (3) whether AlAn''s game outcomes correlated significantly with CP and separately, CU severity. Patients with CP and CU compared with controls without these problems took significantly more money for themselves and left significantly less money in the charity donation; AlAn''s game outcomes were significantly correlated with CU, but not CP.

Conclusions/Significance

In the AlAn''s game adolescents with conduct problems and CU traits, compared with controls without CP/CU, are disposed to benefit themselves while costing others even in a novel situation, devoid of peer influences, where anonymity is assured, reciprocity or retribution are impossible, intoxication is absent and when the “other” to be harmed is considered beneficent. AlAn''s game outcomes are associated with measures of CU. Results suggest that the AlAn''s game provides an objective means of capturing information about CU traits. The AlAn''s game, which was designed for future use in the MRI environment, may be used in studies attempting to identify the neural correlates of self-benefiting decision-making.     

The Relationship between Trait Emotional Intelligence and Interaction with Ostracized Others' Retaliation

Background

Regulation of emotions in others is distinct from other activities related to trait emotional intelligence in that only such behavior can directly change other people''s psychological states. Although emotional intelligence has generally been associated with prosociality, emotionally intelligent people may manipulate others'' behaviors to suit their own interests using high-level capabilities to read and manage the emotions of others. This study investigated how trait emotional intelligence was related to interacting with ostracized others who attempt retaliation.

Method

We experimentally manipulated whether two people were simultaneously ostracized or not by using an online ball-tossing game called Cyberball. Eighty university students participated in Cyberball for manipulating ostracism and a “recommendation game,” a variation of the ultimatum game for assessing how to interact with others who attempt retaliation, with four participants. After the recommendation game, participants rated their intention to retaliate during the game.

Results

People with higher interpersonal emotional intelligence were more likely to recommend that the ostracized other should inhibit retaliation and maximize additional rewards when they have a weaker intention to retaliate. However, they were more likely to recommend that the ostracized other should retaliate against the ostracizers when they have a stronger intention to retaliate.

Conclusion

This is the first laboratory study that empirically reveals that people with high interpersonal emotional intelligence influence others'' emotions based on their own goals contrary to the general view. Trait emotional intelligence itself is neither positive nor negative, but it can facilitate interpersonal behaviors for achieving goals. Our study offers valuable contributions for the refinement of the trait emotional intelligence concept in the respect of its social function.     

Accidental Outcomes Guide Punishment in a “Trembling Hand” Game

How do people respond to others'' accidental behaviors? Reward and punishment for an accident might depend on the actor''s intentions, or instead on the unintended outcomes she brings about. Yet, existing paradigms in experimental economics do not include the possibility of accidental monetary allocations. We explore the balance of outcomes and intentions in a two-player economic game where monetary allocations are made with a “trembling hand”: that is, intentions and outcomes are sometimes mismatched. Player 1 allocates $10 between herself and Player 2 by rolling one of three dice. One die has a high probability of a selfish outcome, another has a high probability of a fair outcome, and the third has a high probability of a generous outcome. Based on Player 1''s choice of die, Player 2 can infer her intentions. However, any of the three die can yield any of the three possible outcomes. Player 2 is given the opportunity to respond to Player 1''s allocation by adding to or subtracting from Player 1''s payoff. We find that Player 2''s responses are influenced substantially by the accidental outcome of Player 1''s roll of the die. Comparison to control conditions suggests that in contexts where the allocation is at least partially under the control of Player 1, Player 2 will punish Player 1 accountable for unintentional negative outcomes. In addition, Player 2''s responses are influenced by Player 1''s intention. However, Player 2 tends to modulate his responses substantially more for selfish intentions than for generous intentions. This novel economic game provides new insight into the psychological mechanisms underlying social preferences for fairness and retribution.     

Cognitive and Motivational Requirements for the Emergence of Cooperation in a Rat Social Game

Background

Game theory and the Prisoner''s Dilemma (PD) game in particular, which captures the paradox of cooperative interactions that lead to benefits but entail costs to the interacting individuals, have constituted a powerful tool in the study of the mechanisms of reciprocity. However, in non-human animals most tests of reciprocity in PD games have resulted in sustained defection strategies. As a consequence, it has been suggested that under such stringent conditions as the PD game humans alone have evolved the necessary cognitive abilities to engage in reciprocity, namely, numerical discrimination, memory and control of temporal discounting.

Methodology/Principal Findings

We use an iterated PD game to test rats (Rattus norvegicus) for the presence of such cognitive abilities by manipulating the strategy of the opponent, Tit-for-Tat and Pseudo-Random, or the relative size of the temptation to defect. We found that rats shape their behaviour according to the opponent''s strategy and the relative outcome resulting from cooperative or defective moves. Finally, we show that the behaviour of rats is contingent upon their motivational state (hungry versus sated).

Conclusions/Significance

Here we show that rats understand the payoff matrix of the PD game and the strategy of the opponent. Importantly, our findings reveal that rats possess the necessary cognitive capacities for reciprocity-based cooperation to emerge in the context of a prisoner''s dilemma. Finally, the validation of the rat as a model to study reciprocity-based cooperation during the PD game opens new avenues of research in experimental neuroscience.     

Long-term social bonds promote cooperation in the iterated Prisoner's Dilemma

Reciprocal altruism, one of the most probable explanations for cooperation among non-kin, has been modelled as a Prisoner''s Dilemma. According to this game, cooperation could evolve when individuals, who expect to play again, use conditional strategies like tit-for-tat or Pavlov. There is evidence that humans use such strategies to achieve mutual cooperation, but most controlled experiments with non-human animals have failed to find cooperation. One reason for this could be that subjects fail to cooperate because they behave as if they were to play only once. To assess this hypothesis, we conducted an experiment with monogamous zebra finches (Taeniopygia guttata) that were tested in a two-choice apparatus, with either their social partner or an experimental opponent of the opposite sex. We found that zebra finches maintained high levels of cooperation in an iterated Prisoner''s Dilemma game only when interacting with their social partner. Although other mechanisms may have contributed to the observed difference between the two treatments, our results support the hypothesis that animals do not systematically give in to the short-term temptation of cheating when long-term benefits exist. Thus, our findings contradict the commonly accepted idea that reciprocal altruism will be rare in non-human animals.     

Behavioral and Network Origins of Wealth Inequality: Insights from a Virtual World

Almost universally, wealth is not distributed uniformly within societies or economies. Even though wealth data have been collected in various forms for centuries, the origins for the observed wealth-disparity and social inequality are not yet fully understood. Especially the impact and connections of human behavior on wealth could so far not be inferred from data. Here we study wealth data from the virtual economy of the massive multiplayer online game (MMOG) Pardus. This data not only contains every player''s wealth at every point in time, but also all actions over a timespan of almost a decade. We find that wealth distributions in the virtual world are very similar to those in Western countries. In particular we find an approximate exponential distribution for low wealth levels and a power-law tail for high levels. The Gini index is found to be , which is close to the indices of many Western countries. We find that wealth-increase rates depend on the time when players entered the game. Players that entered the game early on tend to have remarkably higher wealth-increase rates than those who joined later. Studying the players'' positions within their social networks, we find that the local position in the trade network is most relevant for wealth. Wealthy people have high in- and out-degrees in the trade network, relatively low nearest-neighbor degrees, and low clustering coefficients. Wealthy players have many mutual friendships and are socially well respected by others, but spend more time on business than on socializing. Wealthy players have few personal enemies, but show animosity towards players that behave as public enemies. We find that players that are not organized within social groups are significantly poorer on average. We observe that “political” status and wealth go hand in hand.     

THE RELEVANT USE OF THE TRADITIONAL TUNISIAN GAME ‘‘RAQASSA’’ FOR CARDIOVASCULAR STIMULATION IN SCHOOLCHILDREN

The aim of this study was to investigate the heart rate (HR) responses, the rate of perceived exertion (RPE), and the feeling during physical education schooling while performing traditional games activities compared to intermittent exercise. Nineteen pre-pubertal children randomly performed on different days two types of lessons (intermittent running mode vs. traditional Tunisian “Raqassa” game) lasting 12-min each. HR was continuously recorded during both lessons, while ratings of perceived exertion and Feeling values were recorded after the sessions. The mean HR value during the traditional game was significantly higher than during intermittent exercise (p<0.05). Conversely, the perceived exertion score was significantly higher after intermittent exercise than the traditional exercise game (p<0.05), showing that the higher cardiovascular strain of the game was perceived as “lighter” than the run. Simultaneously, the children''s Feeling was significantly higher after the traditional game than intermittent exercise (p<0.001), showing a higher satisfaction from playing with respect to running. Exercise based on the “Raqassa” traditional game could be used in pre-pubertal children as an alternative or as an additional method for suitable cardiovascular stimulation during physical education lessons with lower perceived exertion and better feeling compared to intermittent running.     

Like or Dislike? Affective Preference Modulates Neural Response to Others' Gains and Losses

Previous studies have demonstrated that the brain responds differentially to others'' gains and losses relative to one''s own, moderated by social context factors such as competition and interpersonal relationships. In the current study, we tested the hypothesis that the neural response to others'' outcomes could be modulated by a short-term induced affective preference. We engaged 17 men and 18 women in a social-exchange game, in which two confederates played fairly or unfairly. Both men and women rated the fair player as likable and the unfair players as unlikable. Afterwards, ERPs were recorded while participants observed each confederates playing a gambling game individually. This study examines feedback related negativity (FRN), an ERP component sensitive to negative feedback. ANOVA showed a significant interaction in which females but not males displayed stronger FRNs when observing likable players'' outcomes compared to unlikable ones''. However, males did not respond differently under either circumstance. These findings suggest that, at least in females, the neural response is influenced by a short-term induced affective preference.     

The Development of Indonesian Online Game Addiction Questionnaire

Online game is an increasingly popular source of entertainment for all ages, with relatively prevalent negative consequences. Addiction is a problem that has received much attention. This research aims to develop a measure of online game addiction for Indonesian children and adolescents. The Indonesian Online Game Addiction Questionnaire draws from earlier theories and research on the internet and game addiction. Its construction is further enriched by including findings from qualitative interviews and field observation to ensure appropriate expression of the items. The measure consists of 7 items with a 5-point Likert Scale. It is validated by testing 1,477 Indonesian junior and senior high school students from several schools in Manado, Medan, Pontianak, and Yogyakarta. The validation evidence is shown by item-total correlation and criterion validity. The Indonesian Online Game Addiction Questionnaire has good item-total correlation (ranging from 0.29 to 0.55) and acceptable reliability (α = 0.73). It is also moderately correlated with the participant''s longest time record to play online games (r = 0.39; p<0.01), average days per week in playing online games (ρ = 0.43; p<0.01), average hours per days in playing online games (ρ = 0.41; p<0.01), and monthly expenditure for online games (ρ = 0.30; p<0.01). Furthermore, we created a clinical cut-off estimate by combining criteria and population norm. The clinical cut-off estimate showed that the score of 14 to 21 may indicate mild online game addiction, and the score of 22 and above may indicate online game addiction. Overall, the result shows that Indonesian Online Game Addiction Questionnaire has sufficient psychometric property for research use, as well as limited clinical application.     

The Anterior Insula Tracks Behavioral Entropy during an Interpersonal Competitive Game

In competitive situations, individuals need to adjust their behavioral strategy dynamically in response to their opponent’s behavior. In the present study, we investigated the neural basis of how individuals adjust their strategy during a simple, competitive game of matching pennies. We used entropy as a behavioral index of randomness in decision-making, because maximizing randomness is thought to be an optimal strategy in the game, according to game theory. While undergoing functional magnetic resonance imaging (fMRI), subjects played matching pennies with either a human or computer opponent in each block, although in reality they played the game with the same computer algorithm under both conditions. The winning rate of each block was also manipulated. Both the opponent (human or computer), and the winning rate, independently affected subjects’ block-wise entropy during the game. The fMRI results revealed that activity in the bilateral anterior insula was positively correlated with subjects’ (not opponent’s) behavioral entropy during the game, which indicates that during an interpersonal competitive game, the anterior insula tracked how uncertain subjects’ behavior was, rather than how uncertain subjects felt their opponent''s behavior was. Our results suggest that intuitive or automatic processes based on somatic markers may be a key to optimally adjusting behavioral strategies in competitive situations.     

Why Darwin would have loved evolutionary game theory

Humans have marvelled at the fit of form and function, the way organisms'' traits seem remarkably suited to their lifestyles and ecologies. While natural selection provides the scientific basis for the fit of form and function, Darwin found certain adaptations vexing or particularly intriguing: sex ratios, sexual selection and altruism. The logic behind these adaptations resides in frequency-dependent selection where the value of a given heritable phenotype (i.e. strategy) to an individual depends upon the strategies of others. Game theory is a branch of mathematics that is uniquely suited to solving such puzzles. While game theoretic thinking enters into Darwin''s arguments and those of evolutionists through much of the twentieth century, the tools of evolutionary game theory were not available to Darwin or most evolutionists until the 1970s, and its full scope has only unfolded in the last three decades. As a consequence, game theory is applied and appreciated rather spottily. Game theory not only applies to matrix games and social games, it also applies to speciation, macroevolution and perhaps even to cancer. I assert that life and natural selection are a game, and that game theory is the appropriate logic for framing and understanding adaptations. Its scope can include behaviours within species, state-dependent strategies (such as male, female and so much more), speciation and coevolution, and expands beyond microevolution to macroevolution. Game theory clarifies aspects of ecological and evolutionary stability in ways useful to understanding eco-evolutionary dynamics, niche construction and ecosystem engineering. In short, I would like to think that Darwin would have found game theory uniquely useful for his theory of natural selection. Let us see why this is so.     

Switching Dynamics in an Interpersonal Competition Brings about “Deadlock” Synchronization of Players

In competitive sport game behavior, certain interpersonal patterns of movement coordination evolve even though each individual player only intends to exert their own strategy to win. To investigate this interpersonal pattern formation process, we asked pairs of naïve participants to engage in a play-tag game in which they had to remove a tag fastened to their partner''s hip. Relative phase analysis of the players'' step towards-away velocities indicated that anti-phase synchronization evolved across 10 repetitions of the game. We clarified evolution of this synchronization process using a dynamical model with an attractor (at relative phase) and a repeller (at relative phase) and discuss the self-organized nature of model and its ability to embody general solution for martial art interpersonal coordination.     

Equity or equality? Moral judgments follow the money

Previous research emphasizes people''s dispositions as a source of differences in moral views. We investigate another source of moral disagreement, self-interest. In three experiments, participants played a simple economic game in which one player divides money with a partner according to the principle of equality (same payoffs) or the principle of equity (payoffs proportional to effort expended). We find, first, that people''s moral judgment of an allocation rule depends on their role in the game. People not only prefer the rule that most benefits them but also judge it to be more fair and moral. Second, we find that participants'' views about equality and equity change in a matter of minutes as they learn where their interests lie. Finally, we find limits to self-interest: when the justification for equity is removed, participants no longer show strategic advocacy of the unequal division. We discuss implications for understanding moral debate and disagreement.     

Direct Sum Matrix Game with Prisoner's Dilemma and Snowdrift Game

A direct sum form is proposed for constructing a composite game from two games, prisoner''s dilemma and snowdrift game. This kind of direct sum form game is called a multiple roles game. The replicator dynamics of the multiple roles game with will-mixed populations is explored. The dynamical behaviors on square lattice are investigated by numerical simulation. It is found that the dynamical behaviors of population on square lattice depend on the mixing proportion of the two simple games. Mixing SD activities to pure PD population inhibits the proportion of cooperators in PD, and mixing PD activities to pure SD population stimulates the proportion of cooperators in SD. Besides spatial reciprocity, our results show that there are roles reciprocities between different types of individuals.     

Virtual bargaining: a theory of social decision-making

An essential element of goal-directed decision-making in social contexts is that agents'' actions may be mutually interdependent. However, the most well-developed approaches to such strategic interactions, based on the Nash equilibrium concept in game theory, are sometimes too broad and at other times ‘overlook’ good solutions to fundamental social dilemmas and coordination problems. The authors propose a new theory of social decision-making—virtual bargaining—in which individuals decide among a set of moves on the basis of what they would agree to do if they could openly bargain. The core principles of a formal account are outlined (vis-à-vis the notions of ‘feasible agreement’ and explicit negotiation) and further illustrated with the introduction of a new game, dubbed the ‘Boobytrap game’ (a modification on the canonical Prisoner''s Dilemma paradigm). In the first empirical data of how individuals play the Boobytrap game, participants'' experimental choices accord well with a virtual bargaining perspective, but do not match predictions from a standard Nash account. Alternative frameworks are discussed, with specific empirical tests between these and virtual bargaining identified as future research directions. Lastly, it is proposed that virtual bargaining underpins a vast range of human activities, from social decision-making to joint action and communication.     

Is the repeated prisoner's dilemma a good model of reciprocal altruism?

Axelrod and Hamilton (1981) used the repeated prisoner's dilemma game as a basis for their widely cited analysis of the evolution of reciprocal altruism. Recently, it has been argued that the repeated prisoner's dilemma is not a good model for this task. Some critics have argued that the single period prisoner's dilemma represents mutualistic rather than altruistic social interactions. Others have argued that reciprocal altruism requires that the opportunities for altruism occur sequentially, first one individual and then after some delay the other. Here I begin by arguing that the single period prisoner's dilemma game is consistent with the definition of altruism that is widely accepted in evolutionary biology. Then I present two modified versions of the repeated prisoner's dilemma, one in which behavior is sequential, and a second in which behavior occurs in continuous time. Each of these models shares the essential qualitative properties with the version used by Axelrod and Hamilton.