Modeling poker challenges by evolutionary game theory

We introduce a model for studying the evolutionary dynamics of Poker. Notably, despite its wide diffusion and the raised scientific interest around it, Poker still represents an open challenge. Recent attempts for uncovering its real nature, based on statistical physics, showed that Poker in some conditions can be considered as a skill game. In addition, preliminary investigations reported a neat difference between tournaments and ‘cash game’ challenges, i.e., between the two main configurations for playing Poker. Notably, these previous models analyzed populations composed of rational and irrational agents, identifying in the former those that play Poker by using a mathematical strategy, while in the latter those playing randomly. Remarkably, tournaments require very few rational agents to make Poker a skill game, while ‘cash game’ may require several rational agents for not being classified as gambling. In addition, when the agent interactions are based on the ‘cash game’ configuration, the population shows an interesting bistable behavior that deserves further attention. In the proposed model, we aim to study the evolutionary dynamics of Poker by using the framework of Evolutionary Game Theory, in order to get further insights on its nature, and for better clarifying those points that remained open in the previous works (as the mentioned bistable behavior). In particular, we analyze the dynamics of an agent population composed of rational and irrational agents, that modify their behavior driven by two possible mechanisms: self-evaluation of the gained payoff, and social imitation. Results allow to identify a relation between the mechanisms for updating the agents’ behavior and the final equilibrium of the population. Moreover, the proposed model provides further details on the bistable behavior observed in the ‘cash game’ configuration.