Contributed talk in ALife in Social Sciences 1, Aug. 1, 2019, 12:30 p.m. in room USB.G.003

On the Expected Number and Distribution of Equilibria in Multi-player Evolutionary Games

Hong Duong, The Anh Han

watch Publication Random evolutionary games in which the payoff entries are random variables form an important subclass of Evolutionary Game Theory (EGT). They are necessary to model social and biological systems in which very limited information is available, or where the environment changes so rapidly and frequently that one cannot describe the payoffs of their inhabitants' interactions. As in classical game theory with the Nash equilibrium, the analysis of properties of equilibrium points in EGT has been of special interest. These equilibrium points predict the composition of strategy frequencies where all the strategies have the same average fitness. In random games, due to the randomness of the payoff entries, it is essential to study statistical properties of equilibria. In this extended abstract, we present a summary of our recent works in which we analyze random evolutionary games with an arbitrary number of players. By connecting EGT to random polynomial theory, we have achieved new results on the expected number and distribution of internal equilibria in multi-player multi-strategy games. Our studies provide new insights into the overall complexity of dynamical systems, including biological, social and Artificial Life ones, as the numbers of players and strategies in an interaction within the systems increase. We expect that our novel approach can be extended to obtain results for other more complex models in population dynamics such as the replicator-mutator equation and evolutionary games with environmental feedback.