Multigame effect in finite populations induces strategy linkage between two games

- A finite population playing two 2-strategy games is investigated.
- The stochastic process is approximated by stochastic differential equations.
- Specific linkages between the strategies of the games emerge by finite size effects.
- Several numerical simulations confirm the theoretical consequents.

Evolutionary game dynamics with two 2-strategy games in a finite population has been investigated in this study. Traditionally, frequency-dependent evolutionary dynamics are modeled by deterministic replicator dynamics under the assumption that the population size is infinite. However, in reality, population sizes are finite. Recently, stochastic processes in finite populations have been introduced into evolutionary games in order to study finite size effects in evolutionary game dynamics. However, most of these studies focus on populations playing only single games. In this study, we investigate a finite population with two games and show that a finite population playing two games tends to evolve toward a specific direction to form particular linkages between the strategies of the two games.