Dynamics in games

(with K. Kaneko)

Regarding dynamics in static games, I would like to investigate in detail the relation between the rules of games and the dynamics emerged from (fixed or static) games; namely, dynamics of the strategiesevolution, or the dynamics that can observed in the playerscommunication patterns. Thus, by analyzing various types of games with various parameters, I would like to know what types of games produce the static phenomena, such as the end of the strategiesevolution, and especially, on the contrary, what conditions of games can cause the dynamical phenomena.

As a part of this work, I have already completed a work focusing on the qualitative difference between the games of two players and those of more than two players (3, 4, 5, . A non-zero-sum 3-person coalition game is presented in order to study the evolution of complexity and diversity in communication and strategies, where the population dynamics of players with strategies is given according to their scores in the iterated game and mutations. Communication rules are self-organized in a society through evolution. The co-evolution of diversity and complexity of strategies and communications are found at later stages of the simulation. By extending this work to more number of players or by exploring other setting of games, such as the number of feasible strategies for a player, symmetric or asymmetric pay-off matrices for players, and so on, I would like to study the mechanism of the dynamical phenomena observed in the various types communities in our world from the game theoretical point of view; that is, the mathematical formulation of the relationship among plural agents, such as the coalition structures, the nature of dilemma, and so on. As the next step of this work, I would study four and five person coalition games by conducting computer simulations in which only the number of players is changed from the previous research. (The fundamental difference between the number of players, four and five, is already found out, which difference is caused by the conflictive structure between coalitions in more-than-five-person games. However, what type of effect such a difference actually has on the social and evolutionary phenomena is not known.)