Unique equilibrium in contests with incomplete information

Area of Science:

• Game Theory
• Mechanism Design
• Industrial Organization

Background:

• Contests with imperfect discrimination are common in economic and social settings.
• Players often have private information regarding contest parameters like costs and valuations.
• Understanding equilibrium behavior in such settings is crucial for policy and strategy.

Purpose of the Study:

• To establish general conditions for the existence and uniqueness of pure-strategy Nash equilibria in incomplete information contests.
• To explore the implications of various information structures on equilibrium properties.
• To analyze the impact of player characteristics, such as budget constraints and activity, on contest outcomes.

Main Methods:

• Analysis of imperfectly discriminating contests with private information.
• Derivation of conditions for a unique pure-strategy Nash equilibrium.
• Examination of diverse information structures including independent private values, correlated values, and common values.

Main Results:

• General conditions are found for a unique pure-strategy Nash equilibrium in incomplete information contests.
• Existence of equilibrium is guaranteed by standard concavity/convexity assumptions when players have positive budgets.
• The framework accommodates various information structures and complexities like inactive types and population uncertainty.

Conclusions:

• The study provides a robust framework for analyzing contests with incomplete information.
• Positive budgets simplify equilibrium analysis, requiring only standard regularity conditions.
• Active players in these contests are shown to achieve positive net rents.