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

Optimal Bidding in Repeated Wireless Spectrum Auctions with Budget Constraints