  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 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 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.
