Bertrand Menu Competition

2025-04-23

AI Summary

This paper investigates the equilibrium properties of a Bertrand price competition model under monotonicity constraints—such as wage schedules that must increase with worker productivity to comply with equal-pay regulations. The institutional setting requires firms to offer contract menus satisfying a global monotonicity condition. Methodologically, the authors formulate a game-theoretic model integrating mechanism design and equilibrium analysis, thereby extending the classic Bertrand framework to legally mandated menu-based contracting for the first time. Their results establish that, despite monotonicity restricting price discrimination and aggressive undercutting, a pure-strategy Nash equilibrium exists; firm profits are driven to zero, and resource allocation is both non-rationing and Pareto efficient. This finding relaxes the conventional Bertrand assumption of unconstrained pricing, substantially broadening the model’s theoretical applicability to regulated labor markets and other settings where legal or institutional constraints impose structure on contractual offers.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We study a variation of the price competition model a la Bertrand, in which firms must offer menus of contracts that obey monotonicity constraints, e.g., wages that rise with worker productivity to comport with equal pay legislation. While such constraints limit firms' ability to undercut their competitors, we show that Bertrand's classic result still holds: competition drives firm profits to zero and leads to efficient allocations without rationing. Our findings suggest that Bertrand's logic extends to a broader variety of markets, including labor and product markets that are subject to real-world constraints on pricing across workers and products.

Problem

• Bertrand competition with menu constraints
• Zero profits under pricing constraints
• Efficient allocations without rationing

Innovation

• Bertrand competition with menu constraints
• Monotonicity constraints ensure wage fairness
• Zero profits and efficient allocations result