In conjunction with
The European Conference on Mathematical and Theoretical Biology (ECMTB 2016)

Jul. 12, 2016 @ Nottingham


This minisymposium presents a showcase of cutting-edge models and results in game-theoretical studies on the evolution of cooperation. A common language through the minisymposium is evolutionary game theory. Evolutionary game theory is a popular mathematical tool that has been developed for investigating the population dynamics of strategies in nature and human communities. Even nearly a half-century after the seminal work by Maynard Smith on evolutionary game theory, the exploration of game-theoretical models for the evolution of cooperation remains at the forefront of evolutionary biology and the social sciences. In particular recent efforts and intensive research have shed new light on direct and indirect reciprocity, two strands of the major mechanisms for cooperation. The minisymposium brings together researchers who take novel approaches to understanding the evolution of reciprocal cooperation. The symposium provides an opportunity to be open to new insights and implications for the evolution of cooperation in terms of evolutionary game theory.


Tatsuya Sasaki (Faculty of Mathematics, University of Vienna)

Isamu Okada (Soka University)


Direct reciprocity and repeated interactions are important mechanisms for maintaining cooperation. However, the recently discovered class of zero-determinant (ZD) strategies has cast some doubt on the effectiveness of direct reciprocity - it was shown that repeated interaction do not only allow for cooperation, but also for extortion. Using an extortionate strategy, an individual can enforce the co-player to cooperate, although the individual itself is not fully cooperative. In my talk, I will explain these strategies, and I will review recent theoretical and experimental results to discuss when extortion pays and when it does not.

Despite vast amounts of intensive efforts since Nowak and Sigmund (1998) published in Nature, the studies on indirect reciprocity seldom break down an assumption of public information. Under the assumption, players are not allowed having their private assessments of the other players. Errors in perception happen on a public media, and all players must hold by the public and shared reputation broadcasted by the media. In contrast to the public information, players in private information privately observe plays among the others and assess them. Respecting a pioneering work by Uchida (2010) published in Physical Review E, we theoretically analyze the comparison of the private information with the public information. Here we show that the tolerant indirect reciprocity with justified defection increases the Pareto efficiency in combination with the unconditional cooperators in the private information than in the public one. Our result sheds light on the role of unconditional cooperators while so far they were unvalued as a second-order free-riders.

There are many studies to explore which types of discriminator can maintain cooperation robustly. Previous studies have clarified robustness of each norms such as image scoring, standing, extra standing and some other norms. For example, they have analyzed the stability of cooperation among pure defector, pure cooperator and discriminator (ex. image scoring, standing). However they could not clarify the process of evolution of such norms. We have analyzed that which type of norms can evolve from a state where norm is not shared among agents. Taking second-order information into model, there are a total of 2^4=16 norms. An agent has these norms and evolves norms using genetic algorithm. We analyze which norms can dominate when cooperation established in the society. We consider that the evolution of cooperation is divided into promoting phase and maintaining one. When a cooperative regime is promoted, players should adopt the strictest strategy to survive in a severe environment huge where perfect defectors swarm in. After perfect defectors were mostly driven out, a different strategy is required to maintain a cooperative regime. The tolerant strategies and perfect cooperators are suitable in the cooperative society.

Indirect reciprocity is one of fundamental mechanisms that facilitate mutual cooperation among individuals. Its models generally include two different dynamics. One describes learning process (i.e., how individuals update their strategies from time to time) and the other evaluation process (i.e., how reputations of individuals change in time). In this talk, we investigate two types of models of the learning processes which are based on "individualism" and "dividualism". The former model assumes that each strategy is not dividual and is updated as a whole and the latter assumes that parts of a strategy can be updated separately. We find that these different assumptions critically influence the results obtained from the model. We also discuss the effects of the ratio of the time scales between the learning process and the evaluation process on evolution of cooperation.