Optimal Bidding in Repeated Wireless Spectrum Auctions with Budget Constraints

Abstract: Small operators who take part in secondary wireless spectrum markets typically have strict budget limits. In this paper, we study the bidding problem of a budget constrained operator in repeated secondary spectrum auctions. In existing truthful auctions, truthful bidding is the optimal strategy of a bidder. However, budget limits impact bidding behaviors and make bidding decisions complicated, since bidders may behave differently to avoid running out of money. We formulate the problem as a dynamic auction game between operators, where knowledge of other operators is limited due to the distributed nature of wireless networks/markets. We first present a Markov Decision Process (MDP) formulation of the problem and characterize the optimal bidding strategy of an operator, provided that opponents' bids are i.i.d. Next, we generalize the formulation to a Markov game that, in conjunction with model-free reinforcement learning approaches, enables an operator to make inferences about its opponents based on local observations. Finally, we present a fully distributed learning-based bidding algorithm which relies only on local information. Our numerical results show that our proposed learning-based bidding results in a better utility than truthful bidding.