Lowest unique bid auctions with resubmission opportunities

The recent online platforms propose multiple items for bidding. The state of the art, however, is limited to the analysis of one item auction. In this paper we study multi-item lowest unique bid auctions (LUBA) in discrete bid spaces under budget constraints. We show the existence of mixed Bayes-Nash equilibria for an arbitrary number of bidders and items. The equilibrium is explicitly computed in two bidder setup with resubmission possibilities. In the general setting we propose a distributed strategic learning algorithm to approximate equilibria. Computer simulations indicate that the error quickly decays in few number of steps by means of speedup techniques. When the number of bidders per item follows a Poisson distribution, it is shown that the seller can get a non-negligible revenue on several items, and hence making a partial revelation of the true value of the items.