Note: Evolutionary Game Theory Focus Informational Health: The Cocktail Party Effect Through Werewolfgame under Incomplete Information and ESS Search Method Using Expected Gains of Repeated Dilemmas

We explore the state of information disruption caused by the cocktail party effect within the framework of non-perfect information games and evolutive games with multiple werewolves. In particular, we mathematically model and analyze the effects on the gain of each strategy choice and the formation process of evolutionary stable strategies (ESS) under the assumption that the pollution risk of fake news is randomly assigned in the context of repeated dilemmas. We will develop the computational process in detail, starting with the construction of the gain matrix, modeling the evolutionary dynamics using the replicator equation, and identifying the ESS. In addition, numerical simulations will be performed to observe system behavior under different initial conditions and parameter settings to better understand the impact of the spread of fake news on strategy evolution. This research will provide theoretical insights into the complex issues of contemporary society regarding the authenticity of information and expand the range of applications of evolutionary game theory.This paper is partially an attempt to utilize "Generative AI" and was written with educational intent. There are currently no plans for it to become a peer-reviewed paper.