Competing Auctions with Discrete Valuations

This paper considers a situation of two sellers of perfectly substitutable items competing in publicly announced reserve prices to induce potential bidders participation at their auction. After learning their own valuations and upon observing the reserve prices, potential bidders make a participation decision consisting of a unique auction to visit. The participation decision is modelled as a standard Bayesian- Nash game. Once participation decisions are realized, each bidder observes the aggregate number of bidders at the auction, and bidding games unfold. For extreme parameter values of the distribution of potential-bidders' valuation, it is shown that a unique, symmetric, pure-strategy equilibrium in reserve prices exists. For other values however, no equilibrium in pure strategy exists. The results share the non-existence feature of Hotelling location type models. The model also contributes to the recent literature on directed search.