"Population dynamics and games of variable size"Chalub, FabioIn this talk, we introduce the concept of Variable Size Game Theory (VSGT), in which the number of players in a game is a strategic decision made by the players themselves. We start by discussing the main examples in game theory: dominance, coexistence, and coordination. We show that the same set of pay-offs can result in coordination-like or coexistence-like depending on the strategic decision of each player type. In the sequel, we consider a game involving prosocial and antisocial players, i.e., individuals who tend to play with large groups and small groups, respectively. In this game, a certain task should be performed, that will benefit one of the participants at the expense of the other players. We show that individuals able to gather large groups to perform the task may prevail, even if this task is costly, providing a possible scenario for the evolution of eusociality. In the last example, we generalize to three types of populations the previous analysis and study compartmental epidemic models: in particular, we recast the SIRS model into the VSGT framework: Susceptibles play 2-player games, while Infectious and Removed play a 1-player game. The SIRS epidemic model is then obtained as the replicator equation of the VSGT. |
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