  The recent online platforms propose multiple items for bidding. The state of
the art, however, is limited to the analysis of one item auction without
resubmission. In this paper we study multi-item lowest unique bid auctions
(LUBA) with resubmission in discrete bid spaces under budget constraints. We
show that the game does not have pure Bayes-Nash equilibria (except in very
special cases). However, at least one mixed Bayes-Nash equilibria exists for
arbitrary number of bidders and items. The equilibrium is explicitly computed
for 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. 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. Finally, the
attitude of the bidders towards the risk is considered. In contrast to
risk-neutral agents who bids very small values, the cumulative distribution and
the bidding support of risk-sensitive agents are more distributed.
