How users in a dynamic system perform learning and make decision become more and more important in numerous research fields. Although there are some works in the social learning literatures regarding how to construct belief on an uncertain system state, few study has been conducted on incorporating social learning with decision making. Moreover, users may have multiple concurrent decisions on different objects/resources and their decisions usually negatively influence each others utility, which makes the problem even more challenging. In this paper, we propose an Indian Buffet Game to study how users in a dynamic system learn the uncertain system state and make multiple concurrent decisions by not only considering the current myopic utility, but also taking into account the influence of subsequent users decisions. We analyze the proposed Indian Buffet Game under two different scenarios: customers request multiple dishes without budget constraint and with budget constraint. For both cases, we design recursive best response algorithms to find the subgame perfect Nash equilibrium for customers and characterize special properties of the Nash equilibrium profile under homogeneous setting. Moreover, we introduce a non-Bayesian social learning algorithm for customers to learn the system state, and theoretically prove its convergence. Finally, we conduct simulations to validate the effectiveness and efficiency of the proposed algorithms.
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