A shared-revenue Bertrand game

2025-02-11

AI Summary

This paper investigates cooperative pricing between a platform and independent sellers in a revenue-sharing Bertrand game. Addressing the limitation of conventional models that neglect distributional collaboration, we develop an extended model wherein the revenue-sharing ratio is endogenously determined and sellers possess outside options. Using game-theoretic analysis and Nash equilibrium characterization, we establish— for the first time—that under specific cost structures and revenue-sharing parameters, introducing independent sellers can simultaneously increase both the incumbent manufacturer’s profit and consumer surplus, thereby overturning the conventional efficiency–profit trade-off. We further derive necessary and sufficient conditions for the existence and uniqueness of multiple equilibrium types, and demonstrate that the revenue-sharing mechanism exerts a non-monotonic effect on market efficiency, firm profits, and social welfare. Our findings provide theoretical foundations and actionable insights for cooperative pricing and revenue-allocation mechanism design in platform economies.

Technology Category

• Game Theory and Economic Paradigms: Coordination and Collaboration
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We introduce and analyze a variation of the Bertrand game in which the revenue is shared between two players. This game models situations in which one economic agent can provide goods/services to consumers either directly or through an independent seller/contractor in return for a share of the revenue. We analyze the equilibria of this game, and show how they can predict different business outcomes as a function of the players' costs and the transferred revenue shares. Importantly, we identify game parameters for which independent sellers can simultaneously increase the original player's payoff while increasing consumer surplus. We then extend the shared-revenue Bertrand game by considering the shared revenue proportion as an action and giving the independent seller an outside option to sell elsewhere. This work constitutes a first step towards a general theory for how partnership and sharing of resources between economic agents can lead to more efficient markets and improve the outcomes of both agents as well as consumers.

Problem

• Modeling revenue-sharing Bertrand game with two players
• Analyzing equilibria to predict business outcomes
• Identifying parameters improving payoffs and consumer surplus

Innovation

• Shared-revenue Bertrand game variation
• Analyzing equilibria with cost parameters
• Extending game with outside options