Random multi-player games
Natalia L. Kontorovsky, Juan Pablo Pinasco, Federico Vazquez

TL;DR
This paper generalizes evolutionary game theory to include multi-player interactions with varying group sizes, analyzes equilibria in a duel-truel game, and explores how network structure influences these dynamics.
Contribution
It introduces a formal framework for multi-player evolutionary stable strategies with probabilistic group sizes and studies their equilibria and stability in networked populations.
Findings
Existence of pure and mixed equilibria depending on probability p
All mixed equilibria identified are evolutionarily stable strategies (ESS)
Network structure influences phase transitions between equilibria
Abstract
The study of evolutionary games with pairwise local interactions has been of interest to many different disciplines. Also local interactions with multiple opponents had been considered, although always for a fixed amount of players. In many situations, however, interactions between different numbers of players in each round could take place, and this case can not be reduced to pairwise interactions. In this work we formalize and generalize the definition of evolutionary stable strategy (ESS) to be able to include a scenario in which the game is played by two players with probability , and by three players with the complementary probability . We show the existence of equilibria in pure and mixed strategies depending on the probability , on a concrete example of the duel-truel game. We find a range of values for which the game has a mixed equilibrium and the proportion of…
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