# Lowest Unique Bid Auctions with Resubmission Opportunities

## TL;DR

This paper analyzes multi-item lowest unique bid auctions with resubmission options, revealing equilibrium properties, proposing a learning algorithm, and examining revenue and bidder risk attitudes.

## Contribution

It introduces the first analysis of multi-item LUBA with resubmission, including equilibrium computation and a distributed learning approach.

## Key findings

- Mixed Bayes-Nash equilibria exist for arbitrary bidders and items.
- The seller can achieve significant revenue on multiple items.
- Risk-sensitive bidders have more dispersed bidding behaviors.

## Abstract

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.