Motty Perry

Perfect sequential equilibrium

Abstract Our equilibrium concept is a restriction of sequential equilibrium. A player chooses a “metastrategy” which specifies his act as a function of his belief. This permits players to evaluate how a game will evolve if new beliefs are assigned to a given node, and enables us to develop a restriction on the beliefs “off the equilibrium path.” A perfect sequential equilibrium is supported by beliefs p which prevent a player from deviating to an unreached node, when there is no belief q which, when assigned to the node, makes it optimal for a deviation to occur with probability q.

Strategic Delay in Bargaining

This paper analyses a bargaining model with incomplete information in which the time between offers is an endogenous strategic variable. We find equilibria involving a delay to agreement that is due to the use of strategic time delay by bargainers to signal their relative strength. Under some specifications of the parameters, delay is present in the unique sequential equilibrium whose beliefs satisfy one intuitive restriction. This delay does not vanish as the minimal time between offers becomes small.

Sequential Bargaining Under Asymmetric Information

We analyze an infinite stage, alternating offer bargaining game in which the buyer knows the gains from trade but the seller does not. Under weak assumptions the game has a unique candidate Perfect Sequential Equilibrium, and it can be solved by backward induction. Equilibrium involves the seller making an offer which is accepted by buyers with high gains from trade, while buyers with medium gains reject and make a counteroffer which the seller accepts. Buyers with low gains make an unacceptable offer, and then the whole process repeats itself, Numerical simulations demonstrate the effects of uncertainty on the length of bargaining.

A Noncooperative View of Coalition Formation and the Core

A noncooperative implementation of the core is provided for games with transferable utility. The implementation obtained here is meant to reflect the standard motivation for the core as closely as possible. In the model proposed, time is continuous. This idealized treatment of time is most amenable for capturing an essential feature of the core--there is always time to reject a noncore proposal before it is consumated. Copyright 1994 by The Econometric Society.

An Efficient Auction

An analogue of Vickreys (1961) multi-unit auction is provided when bidders have interdependent values and one-dimensional private information. The analogue is strategically equivalent to a collection of two-bidder single-unit second-price auctions and it possesses an efficient ex-post equilibrium.

On the failure of the linkage principle in multi-unit auctions

It is shown that the linkage principle (Milgrom and Weber (1982)) does not extend to the multi-unit auction setting. An analysis of the equilibium bidding strategies is carried out for the general two-agent/two-unit Vickrey auction in order to provide economic insight into the nature of the failure. In addition, an explicit counterexample is provided. ∗ Both authors acknowledge support from the Binational Science Foudation (grant#9500023/1). Reny also acknowledges support from the National Science Foundation (grant# SBR-970932), and the University of Pittsburgh’s Faculty of Arts and Sciences.

Tournaments with Midterm Reviews

In many tournaments investments are made over time. The question whether to conduct a review once at the end, or additionally at points midway through the tournament, is a strategic decision. If the latter course is chosen, then the designer must establish both a rule for aggregating the results of the different reviews and a rule for determining compensations. We first study the case of a fixed, exogenously given prize and then extend the analysis to the case where the prize is not fixed but may vary with the tournaments outcome. It is shown that (1) it is always optimal to assign a higher weight to the final review; (2) this weight increases with the dominance of the first-stage effort in determining the final reviews outcome. When the prize is not fixed, the optimal design generates an asymmetric tournament in the second stage that favors the winner of the midterm review.

A Sealed-Bid Auction that Matches the English Auction

This paper analyzes a two-stage sealed-bid auction that is frequently employed in privatization, takeover, and merger and acquisition contests. This auction format yields the same expected revenue as the open ascending (English) auction, yet is less susceptible to preemptive bidding and collusion.

Search in a Known Pattern

In this paper a market where a buyer (job seeker) is searching in a known order among sellers (e.g., a motorist driving along a road looking for gasoline) is described. Both sellers and buyers are assumed to behave strategically. There are many types of buyers. The sellers know only the distribution of all possible buyers; similarly, buyers have imperfect information about sellers. The analysis is conducted by modeling the market as a game with incomplete information; the equilibrium is characterized. A central feature of the game is that both buyers and sellers rationally update their prior information about each other as the game unfolds sequentially. It is shown that prices need not vary monotonically along the search process.

Wage Bargaining, Labor Turnover, and the Business Cycle: A Model with Asymmetric Information

This paper presents a wage-bargaining model in which the employer and employee are each uncertain about the others reservation wage. Under specified circumstances, the models equilibrium is shown to involve unilateral wage setting and inefficient labor turnover. In addition, aggregate demand shocks affect the equilibrium in a way that produces procyclical quits and countercyclical layoffs. These results are obtained without resorting to assumptions of nominal wage rigidity, long-term contracting, or aggregate price misperceptions.