Sequential Chinese Restaurant Game

Abstract

In a social network, agents are intelligent and have the capability to make decisions to maximize their utilities. They can either make wise decisions by taking advantages of other agents' experiences through learning, or make decisions earlier to avoid competitions from huge crowds. Both these two effects, social learning and negative network externality, play important roles in the decision process of an agent. While there are existing works on either social learning or negative network externality, a general study on considering both effects is still limited. We find that Chinese restaurant process, a popular random process, provides a well-defined structure to model the decision process of an agent under these two effects. By introducing the strategic behavior into the non-strategic Chinese restaurant process, we propose a new game, called the Chinese restaurant game, to formulate the social learning problem with negative network externality. Through analyzing the proposed Chinese restaurant game, we derive the optimal strategy of each agent and provide a recursive method to achieve the optimal strategy. How social learning and negative network externality influence each other under various settings is studied through simulations. We also illustrate the spectrum access problem in cognitive radio networks as one of the application of Chinese restaurant game. We find that the proposed Chinese restaurant game theoretic approach indeed helps users make better decisions and improves the overall system performance.