Frequency-dependent payoffs and sequential decision-making favour consistent tactic use

Although natural selection should have favoured individuals capable of adjusting the weight they give to personal and social information according to circumstances, individuals generally differ consistently in their individual weighting of both types of information. Such individual differences are correlated with personality traits, suggesting that personality could directly affect individuals' ability to collect personal or social information. Alternatively, the link between personality and information use could simply emerge as a by-product of the sequential decision-making process in a frequency-dependent context. Indeed, when the gains associated with behavioural options depend on the choices of others, an individual's sequence of arrival could constrain its choice of options leading to the emergence of correlated behaviours. Any factor such as personality that affects decision order could thus be correlated with information use. To test this new explanation, we developed an individual-based model that simulates a group of animals engaged in a game of sequential frequency-dependent decision: a producer-scrounger game. Our results confirm that the sequence of decision, in this case enforced by the order in which animals enter a foraging area, consistently influences their mean tactic use and their individual plasticity, an outcome reminiscent of the correlation reported between personality and social information use.     

Altruism may arise from individual selection

The fact that humans cooperate with non-kin in large groups, or with people they will never meet again, is a long-standing evolutionary puzzle. Altruism, the capacity to perform costly acts that confer benefits on others, is at the core of cooperative behavior. Behavioral experiments show that humans have a predisposition to cooperate with others and to punish non-cooperators at personal cost (so-called strong reciprocity) which, according to standard evolutionary game theory arguments, cannot arise from selection acting on individuals. This has led to the suggestion of group and cultural selection as the only mechanisms that can explain the evolutionary origin of human altruism. We introduce an agent-based model inspired on the Ultimatum Game, that allows us to go beyond the limitations of standard evolutionary game theory and show that individual selection can indeed give rise to strong reciprocity. Our results are consistent with the existence of neural correlates of fairness and in good agreement with observations on humans and monkeys.     

Evolutionary dynamics in structured populations

Evolutionary dynamics shape the living world around us. At the centre of every evolutionary process is a population of reproducing individuals. The structure of that population affects evolutionary dynamics. The individuals can be molecules, cells, viruses, multicellular organisms or humans. Whenever the fitness of individuals depends on the relative abundance of phenotypes in the population, we are in the realm of evolutionary game theory. Evolutionary game theory is a general approach that can describe the competition of species in an ecosystem, the interaction between hosts and parasites, between viruses and cells, and also the spread of ideas and behaviours in the human population. In this perspective, we review the recent advances in evolutionary game dynamics with a particular emphasis on stochastic approaches in finite sized and structured populations. We give simple, fundamental laws that determine how natural selection chooses between competing strategies. We study the well-mixed population, evolutionary graph theory, games in phenotype space and evolutionary set theory. We apply these results to the evolution of cooperation. The mechanism that leads to the evolution of cooperation in these settings could be called ‘spatial selection’: cooperators prevail against defectors by clustering in physical or other spaces.     

From reciprocity to unconditional altruism through signalling benefits

Cooperation among genetically unrelated individuals is commonly explained by the potential for future reciprocity or by the risk of being punished by group members. However, unconditional altruism is more difficult to explain. We demonstrate that unconditional altruism can evolve as a costly signal of individual quality (i.e. a handicap) as a consequence of reciprocal altruism. This is because the emergent correlation between altruism and individual quality in reciprocity games can facilitate the use of altruism as a quality indicator in a much wider context, outside the reciprocity game, thus affecting its further evolution through signalling benefits. Our model, based on multitype evolutionary game theory shows that, when the additive signalling benefit of donating help exceeds the cost for only some individuals (of high-quality state) but not for others (of low-quality state), the population possesses an evolutionarily stable strategy (ESS) profile wherein high-quality individuals cooperate unconditionally while low-quality individuals defect or play tit-for-tat (TfT). Hence, as predicted by Zahavi's handicap model, signalling benefits of altruistic acts can establish a stable generosity by high-quality individuals that no longer depends on the probability of future reciprocation or punishment.     

Good predictors for the fixation probability on complex networks of multi-player games using territorial interactions

In 2012 Broom and Rychtar developed a new framework to consider the evolution of a population over a non-homogeneous underlying structure, where fitness depends upon multiplayer interactions amongst the individuals within the population played in groups of various sizes (including one). This included the independent model, and as a special case the territorial raider model, which has been considered in a series of subsequent papers. Here individuals are based upon the vertex of a graph but move to interact with their neighbours, sometimes meeting in large groups. The most important single property of such populations is the fixation probability, the probability of a single mutant completely replacing the existing population. In a recent paper we considered the fixation probability for the Birth Death Birth (BDB) dynamics for three games, a Public Goods game, the Hawk–Dove game and for fixed fitnesses for a large number of randomly generated graphs, in particular seeing if important underlying graph properties could be used as predictors. We found two good predictors, temperature and mean group size, but some interesting and unusual features for one type of graph, Barabasi–Albert graphs. In this paper we use a regression analysis to investigate (the usual) three alternative evolutionary dynamics (BDD, DBB, DBD) in addition to the original BDB. In particular, we find that the dynamics split into two pairs, BDB/DBD and BDD/DBB, each of which give essentially the same results and found a good fit to the data using a quadratic regression involving the above two variables. Further we find that temperature is the most important predictor for the Hawk–Dove game, whilst for the Public Goods game the group size also plays a key role, and is more important than the temperature for the BDD/DBB dynamics.     

Synergy and discounting of cooperation in social dilemmas

The emergence and maintenance of cooperation by natural selection is an enduring conundrum in evolutionary biology, which has been studied using a variety of game theoretical models inspired by different biological situations. The most widely studied games are the Prisoner's Dilemma, the Snowdrift game and by-product mutualism for pairwise interactions, as well as Public Goods games in larger groups of interacting individuals. Here, we present a general framework for cooperation in social dilemmas in which all the traditional scenarios can be recovered as special cases. In social dilemmas, cooperators provide a benefit to the group at some cost, while defectors exploit the group by reaping the benefits without bearing the costs of cooperation. Using the concepts of discounting and synergy for describing how benefits accumulate when more than one cooperator is present in a group of interacting individuals, we recover the four basic scenarios of evolutionary dynamics given by (i) dominating defection, (ii) coexistence of defectors and cooperators, (iii) dominating cooperation and (iv) bi-stability, in which cooperators and defectors cannot invade each other. Generically, for groups of three or more interacting individuals further, more complex, dynamics can occur. Our framework provides the first unifying approach to model cooperation in different kinds of social dilemmas.     

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.     

Skills,division of labour and economies of scale among Amazonian hunters and South Indian honey collectors

In foraging and other productive activities, individuals make choices regarding whether and with whom to cooperate, and in what capacities. The size and composition of cooperative groups can be understood as a self-organized outcome of these choices, which are made under local ecological and social constraints. This article describes a theoretical framework for explaining the size and composition of foraging groups based on three principles: (i) the sexual division of labour; (ii) the intergenerational division of labour; and (iii) economies of scale in production. We test predictions from the theory with data from two field contexts: Tsimane'' game hunters of lowland Bolivia, and Jenu Kuruba honey collectors of South India. In each case, we estimate the impacts of group size and individual group members'' effort on group success. We characterize differences in the skill requirements of different foraging activities and show that individuals participate more frequently in activities in which they are more efficient. We evaluate returns to scale across different resource types and observe higher returns at larger group sizes in foraging activities (such as hunting large game) that benefit from coordinated and complementary roles. These results inform us that the foraging group size and composition are guided by the motivated choice of individuals on the basis of relative efficiency, benefits of cooperation, opportunity costs and other social considerations.     

A TEST OF THE SEQUENTIAL ASSESSMENT GAME: FIGHTING IN THE BOWL AND DOILY SPIDER FRONTINELLA PYRAMITELA

Male bowl and doily spiders (Frontinella pyramitela: Linyphiidae) engage in dangerous fights over access to females. Relatively smaller individuals are more at risk of fatal injury than their larger opponents. Males assess relative fighting ability during contests: smaller individuals tend to give up quickly. Fights occur between a male with information about the value of the contested female (number of fertilizable eggs) and an intruding male with less information. In this paper, a sequential assessment game (a game theory model of fighting behavior) is adapted to male combat in the bowl and doily spider to attempt a quantitative test. The model makes predictions about fight duration, probability of winning, and the occurrence of fatalities as a function of resource value and size asymmetry. Comparison with empirical data from staged contests yields a generally good quantitative agreement with the predictions. A few deviations are also noted.     

Interaction rates,vital rates,background fitness and replicator dynamics: how to embed evolutionary game structure into realistic population dynamics

In this paper we are concerned with how aggregated outcomes of individual behaviours, during interactions with other individuals (games) or with environmental factors, determine the vital rates constituting the growth rate of the population. This approach needs additional elements, namely the rates of event occurrence (interaction rates). Interaction rates describe the distribution of the interaction events in time, which seriously affects the population dynamics, as is shown in this paper. This leads to the model of a population of individuals playing different games, where focal game affected by the considered trait can be extracted from the general model, and the impact on the dynamics of other events (which is not neutral) can be described by an average background fertility and mortality. This leads to a distinction between two types of background fitness, strategically neutral elements of the focal games (correlated with the focal game events) and the aggregated outcomes of other interactions (independent of the focal game). The new approach is useful for clarification of the biological meaning of concepts such as weak selection. Results are illustrated by a Hawk–Dove example.     

Free-Riding Behavior in Vaccination Decisions: An Experimental Study

Individual decision-making regarding vaccination may be affected by the vaccination choices of others. As vaccination produces externalities reducing transmission of a disease, it can provide an incentive for individuals to be free-riders who benefit from the vaccination of others while avoiding the cost of vaccination. This study examined an individual''s decision about vaccination in a group setting for a hypothetical disease that is called “influenza” using a computerized experimental game. In the game, interactions with others are allowed. We found that higher observed vaccination rate within the group during the previous round of the game decreased the likelihood of an individual''s vaccination acceptance, indicating the existence of free-riding behavior. The free-riding behavior was observed regardless of parameter conditions on the characteristics of the influenza and vaccine. We also found that other predictors of vaccination uptake included an individual''s own influenza exposure in previous rounds increasing the likelihood of vaccination acceptance, consistent with existing empirical studies. Influenza prevalence among other group members during the previous round did not have a statistically significant effect on vaccination acceptance in the current round once vaccination rate in the previous round was controlled for.     

The Study of Cognitive Characteristics in Asperger’s Disorder by Using a Modified Prisoner’s Dilemma Game with a Variable Payoff Matrix

Individuals with Asperger’s Disorder (ASP) have difficulties in social reciprocity and in providing appropriate cooperative behavior. The Prisoner’s Dilemma (PD) is a well-known model in game theory that illustrates the paradoxical disposition of interaction between two individuals with opposing interests, and may be a useful tool in the diagnosis of ASP in early childhood. In this study, we investigated the cognitive characteristics of ASP by using a modified PD game. The subjects were 29 individuals with ASP and 28 age- and IQ-matched controls. In the PD game, each of two players has two cards: card 1 represents cooperation and card 2 betrayal. The score each player obtains is decided according to a 2 x 2 payoff matrix and depends on the combination of their selections. The P-score (“P” for punishment) is defined as the score that is given when they both select betrayal. Comparing the two groups, the mean P-score at the end of the game and the mean total score were significantly higher in the ASP group, while the rate of selection of cooperative choice in both groups did not differ significantly. The classification of the shape of the graph according to fluctuation of the P-score revealed that in the ASP group only 2 cases (6.9%) showed continuous decrease of P-score compared to 8 control cases (28.6%) demonstrating similar results. However, the reasons were thought to be different: ASP subjects presumably selected card 2 because of a preference for the number itself, whereas control subjects preferentially chose this card to enhance their chance of winning the competition. It is often difficult to diagnose ASP in the young especially when they lack the distinctive clinical features of ASD in early childhood. Given the limited number of objective tools to evaluate the cognitive characteristics of ASP subjects, the PD game might be a useful diagnostic support tool for ASP.     

The shared reward dilemma

One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma, namely the prisoner's dilemma (PD). Specifically, for a group of players that collect payoffs by playing a pairwise PD game with their partners, we consider an external entity that distributes a fixed reward equally among all cooperators. Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will obtain a poor reward and defectors will outperform them. By appropriately tuning the amount to be shared a vast variety of scenarios arises, including the traditional ones in the study of cooperation as well as more complex situations where unexpected behavior can occur. We provide a complete classification of the equilibria of the n-player game as well as of its evolutionary dynamics.     

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.     

The spatial Ultimatum game revisited

We revisit the issue of the emergence of fair behavior in the framework of the spatial Ultimatum game, adding many important results and insights to the pioneering work by Page et al. [2000. The spatial Ultimatum game. Proc. R. Soc. London B 267, 2177], who showed in a specific example that on a two-dimensional setup evolution may lead to strategies with some degree of fairness. Within this spatial framework, we carry out a thorough simulation study and show that the emergence of altruism is a very generic phenomenon whose details depend on the dynamics considered. A very frequent feature is the spontaneous emergence and fixation of quasiempathetic individuals, whose offers are very close to their acceptance thresholds. We present analytical arguments that allow an understanding of our results and give insights on the manner in which local effects in evolution may lead to such non-rational or apparently maladaptive behaviors.     

Strategic mating with common preferences

We present a two-sided search model in which individuals from two groups (males and females, employers and workers) would like to form a long-term relationship with a highly ranked individual of the other group, but are limited to individuals who they randomly encounter and to those who also accept them. This article extends the research program, begun in Alpern and Reyniers [1999. J. Theor. Biol. 198, 71-88], of providing a game theoretic analysis for the Kalick-Hamilton [1986. J. Personality Soc. Psychol. 51, 673-682] mating model in which a cohort of males and females of various 'fitness' or 'attractiveness' levels are randomly paired in successive periods and mate if they accept each other. Their model compared two acceptance rules chosen to represent homotypic (similarity) preferences and common (or 'type') preferences. Our earlier paper modeled the first kind by assuming that if a level x male mates with a level y female, both get utility -|x-y|, whereas this paper models the second kind by giving the male utility y and the female utility x. Our model can also be seen as a continuous generalization of the discrete fitness-level game of Johnstone [1997. Behav. Ecol. Sociobiol. 40, 51-59]. We establish the existence of equilibrium strategy pairs, give examples of multiple equilibria, and conditions guaranteeing uniqueness. In all equilibria individuals become less choosy over time, with high fitness individuals pairing off with each other first, leaving the rest to pair off later. This route to assortative mating was suggested by Parker [1983. Mate Choice, Cambridge University Press, Cambridge, pp. 141-164]. If the initial fitness distributions have atoms, then mixed strategy equilibria may also occur. If these distributions are unknown, there are equilibria in which only individuals in the same fitness band are mated, as in the steady-state model of MacNamara and Collins [1990. J. Appl. Prob. 28, 815-827] for the job search problem.     

The evolution of n-player cooperation-threshold games and ESS bifurcations

An evolutionary game of individuals cooperating to obtain a collective benefit is here modelled as an n-player Prisoner's Dilemma game. With reference to biological situations, such as group foraging, we introduce a threshold condition in the number of cooperators required to obtain the collective benefit. In the simplest version, a three-player game, complex behaviour appears as the replicator dynamics exhibits a catastrophic event separating a parameter region allowing for coexistence of cooperators and defectors and a region of pure defection. Cooperation emerges through an ESS bifurcation, and cooperators only thrive beyond a critical point in cost-benefit space. Moreover, a repelling fixed point of the dynamics acts as a barrier to the introduction of cooperation in defecting populations. The results illustrate the qualitative difference between two-player games and multiple player games and thus the limitations to the generality of conclusions from two-player games. We present a procedure to find the evolutionarily stable strategies in any n-player game with cost and benefit depending on the number of cooperators. This was previously done by Motro [1991. Co-operation and defection: playing the field and the ESS. J. Theor. Biol. 151, 145-154] in the special cases of convex and concave benefit functions and constant cost.     

Variable valuations and voluntarism under group selection: An evolutionary public goods game

In biological systems, as in human society, competing social groups may depend heavily on a small number of volunteers to advance the group’s prospects. This phenomenon can be understood as the solution to an evolutionary public goods game, in which a beneficent individual or a small number of individuals may place the highest value on group success and contribute the most to achieving it while profiting very little. Here we demonstrate that this type of solution, recently recognized in the social sciences, is evolutionarily stable and evolves in evolutionary simulations sensitive to alternative ways of gaining fitness beyond the present social group. The public goods mechanism may help explain biological voluntarism in cases like predator inspection and foraging on behalf of non-relatives and may determine the extent of commitment to group welfare at different intensities of group selection.     

Natural selection and social preferences

A large number of individuals are randomly matched into groups, where each group plays a finite symmetric game. Individuals breed true. The expected number of surviving offspring depends on own material payoff, but may also, due to cooperative breeding and/or reproductive competition, depend on the material payoffs to other group members. The induced population dynamic is equivalent with the replicator dynamic for a game with payoffs derived from those in the original game. We apply this selection dynamic to a number of examples, including prisoners' dilemma games with and without a punishment option, coordination games, and hawk-dove games. For each of these, we compare the outcomes with those obtained under the standard replicator dynamic. By way of a revealed-preference argument, our selection dynamic can explain certain "altruistic" and "spiteful" behaviors that are consistent with individuals having social preferences.     

The donation game with roles played between relatives

We consider a social game with two choices, played between two relatives, where roles are assigned to individuals so that the interaction is asymmetric. Behaviour in each of the two roles is determined by a separate genetic locus. Such asymmetric interactions between relatives, in which individuals occupy different behavioural contexts, may occur in nature, for example between adult parents and juvenile offspring. The social game considered is known to be equivalent to a donation game with non-additive payoffs, and has previously been analysed for the single locus case, both for discrete and continuous strategy traits. We present an inclusive fitness analysis of the discrete trait game with roles and recover equilibrium conditions including fixation of selfish or altruistic behaviour under both behavioural contexts, or fixation of selfish behaviour under one context and altruistic behaviour under the other context. These equilibrium solutions assume that the payoff matrices under each behavioural context are identical. The equilibria possible do depend crucially, however, on the deviation from payoff additivity that occurs when both interacting individuals act altruistically.