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Contract Theory

Paper Session

Saturday, Jan. 4, 2025 2:30 PM - 4:30 PM (PST)

Hilton San Francisco Union Square, Union Square 13
Hosted By: Econometric Society
  • Chair: Franz Ostrizek, Sciences Po

The Limits of Repeated Nonlinear Pricing

Heng Liu
,
Rensselaer Polytechnic Institute

Abstract

This paper studies repeated nonlinear pricing problems between a long-lived buyer who privately observes her marginal willingness to pay, which can take arbitrarily finitely many possible values, and a sequence of short-lived sellers who offer menus of contracts that consist of quantity and price pairs. The main result characterizes the equilibrium outcome when the time horizon is finite but arbitrarily long and the buyer is patient enough. In equilibrium, almost all sellers offer a menu containing only the efficient contract for the lowest type of buyer, which is accepted by all buyer types. Technically, the paper applies relative entropy methods to deal with the multidimensionality of the sellers' beliefs about the buyer's type.

Tournaments with a Standard

Mikhail Drugov
,
New Economic School
Dmitry Ryvkin
,
RMIT University
Jun Zhang
,
University of Technology Sydney

Abstract

We study tournaments where winning a rank-dependent prize requires passing a minimum performance standard. We show that, for any prize allocation, the optimal standard is always at a mode of performance that is weakly higher than the global mode and identify a necessary and sufficient condition for it to be at the global mode. When the prize scheme can be designed as well, the winner-take-all prize scheme is optimal for noise distributions with an increasing failure rate; and awarding equal prizes to all qualifying agents is optimal for noise distributions with a decreasing failure rate. For distributions with monotone likelihood ratios---log-concave and log-convex, respectively---these pay schemes are also optimal in a larger class of anonymous, monotone contracts that may depend on cardinal performance.

Bilateral Trade with Costly Information Acquisition

Daniil Larionov
,
University of Muenster
Takuro Yamashita
,
Osaka School of International Public Policy

Abstract

We study a bilateral trade problem with flexible but costly information acquisition. There is a buyer and a seller who can trade a single unit of a good through an intermediary who designs a mechanism to facilitate their trade. In the beginning, the buyer, the seller and the intermediary share a common prior over a finite set of states of the world. The intermediary proposes a mechanism to the players, who can then acquire information about the true state by privately designing a signal device. Assuming that the information acquisition cost is proportional to the expected reduction in entropy, we characterize the set of implementable allocations. Using the implementability conditions, given by a finite-dimensional system of equations and inequalities, we maximize the intermediary’s revenue over all implementable allocationally efficient mechanisms. Under certain symmetry conditions, our revenue maximization problem can be solved in closed form.

Vague by Design: Performance Evaluation and Learning from Wages

Franz Ostrizek
,
Sciences Po

Abstract

We study a dynamic principal-agent setting in which both sides learn about the importance of effort. The quality of the agent’s output is not observed directly. Instead, the principal jointly designs an evaluation and wage schedule. More precise performance evaluation reduces current agency costs but promotes learning, which can increase future agency costs. The optimal evaluation technology is noisy. Information that is purely informative about effort is revealed, while the principal optimally shrouds information about the agent's ability. Under strong complementarities, the optimal evaluation features lower-censorship. In the binary case, it is imprecise and tough: a bad performance is always sanctioned, but a good one not always recognized.
JEL Classifications
  • D8 - Information, Knowledge, and Uncertainty