This paper analyzes all-pay auctions where the bidders have affiliated values for the object for sale and where the signals take binary values. Since signals are correlated, high signals indicate a high degree of competition in the auction and since even losing bidders must pay their bid, non-monotonic equilibria arise.We show that the game has a unique symmetric equilibrium, and that whenever the equilibrium is non-monotonic the contestants earn no rents. All-pay auctions result in low expected rents to the bidders, but also induce inefficient allocations in models with affiliated private values. With two bidders, the effect on rent extraction dominates, and all-pay auction outperforms standard auctions in terms of expected revenue. With many bidders, this revenue ranking is reversed for some parameter values and the inefficient allocations persist even in large auctions.JEL CLASSIFICATION: D44, D82

This paper analyzes relational contracts under moral hazard. We first show that if the available information (signal) about effort satisfies a generalized monotone likelihood ratio property, then irrespective of whether the first-order approach (FOA) is valid or not, the optimal bonus scheme takes a simple form. The scheme rewards the agent a fixed bonus if his performance index exceeds a threshold, like the FOA contract of Levin (2003), but the threshold can be set differently. We next derive a sufficient and necessary condition for non-verifiable information to improve a relational contract. Our new informativeness criterion sheds light on the nature of an ideal performance measure in relational contracting.

We study the war of attrition between two players when the players' signals are binary and affiliated. Our model covers both the case of common values and affiliated private values. We characterize the unique symmetric equilibrium and demonstrate the possibility of nonmonotonic symmetric equilibria, i.e. equilibria where the player with a lower signal wins with positive probability. Such an outcome is inefficient in the case of private valuations. We compare the war of attrition to other related mechanisms, the all-pay auction and standard firstand second-price auctions. The war of attrition dissipates the bidders' rents more effectively but at the same time distorts the allocation more severely than the other mechanisms. In terms of expected revenues, the war of attrition dominates the standard auctions, but the ranking against the all-pay auction is ambiguous.JEL CLASSIFICATION: D44, D82

This paper studies a symmetric two-bidder all-pay auction where the bidders compete for a prize whose unknown common value is either high or low. The bidders' private signals (or types) are discrete and affiliated through the value. Even with affiliated signals, monotonicity of equilibria can fail in the sense that the bidder with a higher signal does not always win the auction. I show that when monotonicity fails, there exist multiple symmetric equilibria but the bidder's type-dependent payoff is invariant across the equilibria. The paper provides a closed-form formula for the equilibrium payoffs and a condition for rent dissipation.

This note explores how to evaluate an agent's performance in standard incentive contracts. We show that the MPS criterion proposed by Kim (1995) becomes a tight condition for one performance measurement system to be more informative than another, as long as the first-order approach can be justified. In the one-signal case obeying the monotone likelihood ratio property, the MPS criterion is equivalent to the way of ordering signals developed by Lehmann (1988), establishing a link to statistical decision theory. Our results demonstrate that depending on the agent's potential deviations, ideal performance measures can be different. JEL CLASSIFICATION: D86.