Indian Buffet Game With Negative Network Externality and Non-Bayesian Social Learning
In a dynamic system, how to perform learning and make decisions are becoming more and more important for users. Although there are some works in social learning-related literature regarding how to construct belief for an uncertain system state, few studies have been conducted on incorporating social learning with decision making. Moreover, users may have multiple concurrent options on different objects/resources and their decisions usually negatively influence each other's 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 about the uncertain system state and make multiple concurrent decisions by not only considering the current myopic utility, but also the influence of subsequent users' decisions. We analyze the proposed Indian Buffet Game under two different scenarios: 1) on customers requesting multiple dishes without budget constraint and 2) with budget constraint. For both cases, we design recursive best response algorithms to find the subgame perfect Nash equilibrium (NE) for customers and characterize special properties of the NE 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.