The evolution of cooperation through imitation

EPL (Europhysics Letters), 2008

How did cooperative behavior evolve is a big open question in both biology as well as in social sciences. This problem is frequently addressed through the evolutionary game theory. However, very often it is not obvious which game is the more appropriate to use. Furthermore, an empirical determination of the payoffs can be very difficult while variations in the payoff values can dramatically alter theoretical predictions. Here, to overcome the above difficulties, I propose a very minimal model without payoff parameters. Instead, starting with random heterogeneous distributions of payoffs, by the process of natural selection itself, definite payoff matrices are produced. The system evolves from a completely heterogeneous distribution of payoffs to a situation in which very few payoff matrices coexist. When the initial set of games consists of dilemma games, the emerging game is the "Stag Hunt". The fraction of cooperator agents converges in all the cases examined to non-zero values.

le.ac.uk

Player I chooses between rows C (cooperate) and row D (defect), Player II chooses between columns C and D, and the pair of numbers in each cell are the payoffs to Players I and II respectively in the corresponding outcome. Each player does better by choosing D than C irrespective of what the co-player chooses; the D strategy is the unconditionally best or dominant strategy for both players. The puzzle arises from the fact that if both players choose D, as they are bound to if they are rational, then each is worse off than if both choose C, and many people ...

2010

We utilize evolutionary game theory to study the evolution of cooperative societies and the behaviors of individual agents (i.e., players) in it. We present a novel player model based upon empirical evidence from the social and behavioral sciences, stating that: (1) an individual's behavior may often be motivated not only by self-interest but also by the consequences for the others, and (2) individuals vary in their interpersonal social tendencies, which reflect stable personal orientations that influence their choices. Alongside the formal player model we provide an analysis that considers possible interactions between different types of individuals.

Abstract—In this study the hypothesis that zero-sum (ie strictly competitive) games are more difficult targets for coevolution than non-zero-sum (ie games that are not strictly competitive nor strictly cooperative) games is examined. Our method is to compare the co-evolutionary behavior of a three move zero-sum game (rock paper scissors) with that of a three move non-zero-sum game (coordination prisoner's dilemma) as well as with intermediate games obtained using weighted averages of the games's payoff matrices.

Palgrave Macmillan UK eBooks, 2005

A surprising prediction from a simple evolutionary game-theoretic model, based on meagre assumptions, is that a form of cooperation can evolve among agents acting without any deliberate intention to cooperate. There are circumstances in which agents can learn to behave cooperatively without even becoming aware of their strategic interdependence. This phenomenon occurs in what are called minimal social situations, through an unconscious mechanism of adaptive learning in pairs or groups of agents lacking any deliberate intention to cooperate. 1 Whether or not it is reasonable to interpret this as a form of teamwork is debatable. The argument pivots on what are considered to be the essential or prototypic features of teamwork, and other contributors to this volume are better qualified than I to analyse this conceptual issue. But what seems uncontroversial is that minimal social situations represent special or limiting cases that should interest people who study teamwork and may help to throw light on more complex forms of teamwork. Minimal social situations are curiosities, outside the mainstream of evolutionary game theory, but the underlying theory is intrinsically interesting and may turn out to have some utility in explaining the evolution of social behaviour in conditions of incomplete information. The increasing popularity of evolutionary games, from the closing decades of the second millennium onwards, has been fuelled by a growing suspicion that orthodox game theory, based on ideally rational players, may be irredeemably indeterminate. Orthodox game theory seeks to specify the strategies that would be chosen by rational players -rational in the sense of invariably acting to maximize their expected utilities relative to their knowledge and beliefs. It is easy to prove, via the celebrated Indirect Argument 2 of von Neumann and Morgenstern (1944, pp. 146-8), that if a game has a uniquely rational solution, then that solution necessarily comprises a profile of strategies that we now call a Nash equilibrium in which each strategy is a utility-maximizing best reply to the combined strategies of the remaining players. But most interesting games, apart from those that are strictly competitive (finite, two-person, zero-sum), have multiple Nash equilibria that are neither equivalent nor interchangeable, and this implies that rational players, having identified the equilibria of a game, are left with a problem of equilibrium selection. It is in this sense that classical game theory, based on Nash equilibrium, is indeterminate. Evolutionary game theory came into its own following the partial eclipse of the purely rational and normative approach set out by the founding game theorists. 3 It deals with nonrational strategic interaction driven by mindless adaptive processes based on trial and error. It can be traced to a passage in John Nash's doctoral thesis, completed in 1950 but not published in full until more than half a century later . Evolutionary game models are designed to explore the behaviour of goal-directed automata in simulated strategic interactions (Hofbauer and Sigmund, 1998;. In some models, based on adaptive learning mechanisms, individual automata adjust their strategy choices in response to the payoffs they receive in simulated interactions; in others, based on replicator dynamics, the relative proportions of different types of automata in the population change in response to payoffs. In either case, the interacting automata are programmed to maximize their individual payoffs, even though their strategy choices are made without conscious thought or deliberate choice. Evolutionary models generally converge to the vicinity of evolutionarily stable strategies, 4 which are invulnerable to evolutionary invasion by alternative strategies and (it

Royal Society Open Science

Cooperation declines in repeated public good games because individuals behave as conditional cooperators. This is because individuals imitate the social behaviour of successful individuals when their payoff information is available. However, in human societies, individuals cooperate in many situations involving social dilemmas. We hypothesize that humans are sensitive to both success (payoffs) and how that success was obtained, by cheating (not socially sanctioned) or good behaviour (socially sanctioned and adds to prestige or reputation), when information is available about payoffs and prestige. We propose and model a repeated public good game with heterogeneous conditional cooperators where an agent's donation in a public goods game depends on comparing the number of donations in the population in the previous round and with the agent's arbitrary chosen conditional cooperative criterion. Such individuals imitate the social behaviour of role models based on their payoffs an...

2014

We consider games of strategic substitutes and strategic complements on networks. We introduce two different evolutionary dynamics in order to refine their multiplicity of equilibria, and we analyse the system through a mean field approach. We find that for the best-shot game, taken as a model for substitutes, a replicator-like dynamics does not lead to Nash equilibria, whereas it leads to unique equilibria (full cooperation or full defection, depending on the initial condition and the game parameter) for complements, represented by a coordination game. On the other hand, when the dynamics becomes more cognitively demanding in the form of a best response evolution, predictions are always Nash equilibria (at least when individuals are fully rational): For the best-shot game we find equilibria with a definite value of the fraction of contributors, whereas for the coordination game symmetric equilibria arise only for low or high initial fractions of cooperators. We also extend our study by considering complex heterogeneous topologies, and show that the nature of the selected equilibria does not change for the best-shot game. However for coordination games we reveal an important difference, namely that on infinitely large scale-free networks cooperation arises for any value of the incentive to cooperate.

Nature Communications, 2017

Human cooperation has been explained through rationality as well as heuristics-based models. Both model classes share the feature that knowledge of payoff functions is weakly beneficial for the emergence of cooperation. Here, we present experimental evidence to the contrary. We let human subjects interact in a competitive environment and find that, in the long run, access to information about own payoffs leads to less cooperative behaviour. In the short run subjects use naive learning heuristics that get replaced by better adapted heuristics in the long run. With more payoff information subjects are less likely to switch to pro-cooperative heuristics. The results call for the development of two-tier models for the evolution of cooperation.

Physical Review E

Imitation and aspiration update rules are frequently observed in human and animal populations. While the imitation process entails payoff comparisons with surroundings, the aspiration process refers to self-evaluation. This work explores the evolution of cooperation in dyadic games under the coexistence of these two dynamics in an infinitely large well-mixed population. Two situations have been explored: (i) individuals adopt either an imitation or aspiration update rule with a certain probability, and (ii) the entire population is divided into two groups where one group only uses imitative rules and the other obeys aspiration updating alone. Both premises have been modeled by taking an infinite approximation of the finite population. In particular, the second mixing principle follows an additive property: the outcome of the whole population is the weighted average of outcomes from imitators and aspiration-driven individuals. Our work progressively investigates several variants of aspiration dynamics under strong selection, encompassing symmetric, asymmetric, and adaptive aspirations, which then coalesce with imitative dynamics. We also demonstrate which of the update rules performs better, under different social dilemmas, by allowing the evolution of the preference of update rules besides strategies. Aspiration dynamics always outperform imitation dynamics in the prisoner's dilemma, however, in the chicken and stag-hunt games the predominance of either update rule depends on the level of aspirations as well as on the extent of greed and fear present in the system. Finally, we examine the coevolution of strategies, aspirations, and update rules which leads to a binary state of obeying either imitation or aspiration dynamics. In such a circumstance, when aspiration dynamics prevail over imitation dynamics, cooperators and defectors coexist to an equal extent.

The European Physical Journal B, 2009

The usual mechanism for modeling learning in spatially structured evolutionary games has to date been imitation of some successful neighbor. However, it seems natural that individuals hesitate to imitate their neighbor's acts, specially if they can imply high costs. Here we study the effect of incorporating resistance to imitation on these models. Our framework is the spatial Continuous Prisoner's Dilemma. For this evolutionary game, it has been reported that occasional errors in the imitation process can explain the emergence of cooperation from a non-cooperative initial state. In this work, we show that this only occurs for particular regimes of low costs of cooperation. Furthermore, we display how resistance gets greater the range of scenarios where cooperative individuals can invade selfish populations. In this context, where resistance to imitation can be interpreted as a general rule of gradual learning, our results show that the less that is learnt in a single step from a successful neighbors, the larger the degree of global cooperation finally attained. In general, the effect of step-by-step learning can be more efficient for the evolution of cooperation than a full blast one. PACS. PACS-02.50Le Decision theory and game theory -PACS-89.75Fb Structures and organization in complex systems Send offprint requests to: Raúl Jiménez a e-mail: raul.jimenez@uc3m.es Jiménez et al.: Gradual learning and cooperation theory, researchers from many fields have attempted to shed light on the underlying mechanisms that outperform the vulnerability of cooperation of being cheated [6]. Models with spatial structures have been considered by these researches to mimic real population where individuals do not interact with everybody else. In these models, individuals are located on the nodes of a network, play repeatedly with their neighbors, and update their strategies by imitating (with occasional errors) the strategy of some more successful neighbor. Different update rules respond to the same evolutionary principle of reproduction of successful strategies [7] and are usually implemented through two basic operators: Selection, in which individuals identify whom to imitate, and mutation, occasional errors in the imitation process.