Why do bidders drop out from a sequential auction

In actual sequential auctions, 1) bidders typically incur a cost in continuing from one sale to the next, and 2) bidders decide whether or not to continue. To investigate the question "why do bidders drop out," we define a sequential auction model with continuation costs and an endogenously determined number of bidders at each sale, and we characterize the equilibria in this model. Simple examples illustrate the effect of several possible changes to this model.

Synergies and price trends in sequential auctions

In this paper we consider sequential auctions where an individual’s value for a bundle of objects is either greater than the sum of the values for the objects separately (positive synergy) or less than the sum (negative synergy). We show that the existence of positive synergies implies declining expected prices. When synergies are negative, expected prices are increasing. There are several corollaries. First, the seller is indi¤erent between selling the objects simultaneously as a bundle or sequentially when synergies are positive. Second, when synergies are negative, the expected revenue generated by the simultaneous auction can be larger or smaller than the expected revenue generated by the sequential auction. In addition, in the presence of positive synergies, an option to buy the additional object at the price of the …rst object is never exercised in the symmetric equilibrium and the seller’s revenue is unchanged. Under negative synergies, in contrast, if there is an equilibrium where the option is never exercised, then equilibrium prices may either increase or decrease and, therefore, the net e¤ect on the seller’s revenue of the introduction of an option is ambiguous. Finally, we examine two special cases with asymmetric players. In the …rst case, players have distinct synergies. In this example, even if one player has positive synergies and the other has negative synergies, it is still possible for expected prices to decline. In the second case, one player wants two objects and the remaining players want one object each. For this example, we show that expected prices may not necessarily decrease as predicted by Branco (1997). The reason is that players with singleunit demand will generally bid less than their true valuations in the …rst period. Therefore, there are two opposing forces; the reduction in the bid of the player with multiple-demand in the last auction and less aggressive bidding in the …rst auction by the players with single-unit demand.

Approximate recursive equilibrium with minimal state space

This paper shows existence of approximate recursive equilibrium with minimal state space in an environment of incomplete markets. We prove that the approximate recursive equilibrium implements an approximate sequential equilibrium which is always close to a Magill and Quinzii equilibrium without short sales for arbitrarily small errors. This implies that the competitive equilibrium can be implemented by using forecast statistics with minimal state space provided that agents will reduce errors in their estimates in the long run. We have also developed an alternative algorithm to compute the approximate recursive equilibrium with incomplete markets and heterogeneous agents through a procedure of iterating functional equations and without using the rst order conditions of optimality.

Sequential cost-reimbursement rules

This paper studies cost-sharing rules under dynamic adverse selection. We present a typical principal-agent model with two periods, set up in Laffont and Tirole's (1986) canonical regulation environment. At first, when the contract is signed, the firm has prior uncertainty about its efficiency parameter. In the second period, the firm learns its efficiency and chooses the level of cost-reducing effort. The optimal mechanism sequentially screens the firm's types and achieves a higher level of welfare than its static counterpart. The contract is indirectly implemented by a sequence of transfers, consisting of a fixed advance payment based on the reported cost estimate, and an ex-post compensation linear in cost performance.

Sequential auctions with continuation costs

In actual sequential auctions, 1) bidders typically incur a cost in continuing from one sale to the next, and 2) bidders decide whether or not to continue. To investigate the question "when do bidders drop out," we define a sequential auction model with continuation costs and an endogenously determined number of bidders at each sale, and we characterize the equilibria in this modele Simple examples illustrate the effect of several possible changes to this modele