Convergence of True Cooperations in Bayesian Reputation Game

In a distributed environment in which multiple self-interested entities interact, knowing who to interact with is an important decision to make. Reputation is one metric to help with the decision. However, when there are a massive number of entities, a centralized reputation management doesn´t scale up. We introduce bayesian reputation game where players have only private information about others with no centralized management. We design a game in a way that the reputation values are used as a part of payoffs and analyze the game when it is infinitely repeated. We define two types of interactions where one is honest and the other is dishonest. We show that the true cooperation is sustained when the game is repeated even when we applied dynamic type changes. As a result, the average reputation values of players increase over time and converge. The game models the real world situation well and it provides a guideline for designing distributed entities from software agents to Internet of things where no centralized authority exists.