Numerical Study of Game Theory
Game-theoretic approach has been providing a powerful tool in qualitative understanding of macroscopic social phenomena in social sciences, e.g., in economics and political science. Recently, researchers in physics, especially in statistical physics, use these game-theoretic approaches but in more quantitative way and have been producing a variety of interesting results in the new research area called 'sociophysics' by studying human society as a complex system. This work introduces recent works that have tackled combinatorial complexities arising in game-theoretic studies with the aid of simplified assumptions and numerical computations. We first show how cooperation emerges in the prisoner's dilemma game when each player's memory capacity is enhanced and suggest that the intelligent tit-for-tat strategy plays a crucial role in the history of cooperation. And then it is numerically shown that there is a certain case of simultaneous coordination among many players where the system has a high risk of failure when everyone is willing to follow the coordination, which is actually higher than when some are not concerned about it. Lastly, we discuss mathematical treatment of an equilibrium solution for a reverse auction game, which is a variant of the minority game, and its computational approach. ; Artikel på koreanska, abstract på engelska.