A shared-revenue Bertrand game

TL;DR

This paper introduces a shared-revenue variation of the Bertrand game to model revenue-sharing scenarios, analyzing equilibria and outcomes that can benefit both players and consumers, and extending the model to include strategic revenue sharing and outside options.

Contribution

It presents a novel shared-revenue Bertrand game model and analyzes its equilibria, revealing conditions that can enhance profits and consumer surplus, and explores strategic revenue sharing with outside options.

Findings

Independent sellers can increase the original player's payoff and consumer surplus.

Game parameters determine when revenue sharing benefits all parties.

Extending the model to include outside options adds strategic complexity.

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.