Reputational Spillovers

TL;DR

This paper studies a multi-party reputational bargaining game where spillovers influence outcomes, showing that reputation effects can reverse traditional incentives and depend on initial reputation standings.

Contribution

It introduces a model with multiple players and reputation spillovers, providing a unique equilibrium analysis and contrasting it with bilateral bargaining results.

Findings

Spillovers are relevant only if a peripheral is initially most reputable.

Spillovers can make the central player worse off, contrary to bilateral predictions.

The weakest peripheral can benefit from spillovers, especially in high-stakes disputes.

Abstract

We analyze a reputational bargaining game in which a central player negotiates simultaneously with two peripheral players. Each player is either rational or a commitment type who never concedes and insists on a fixed share, and concessions are publicly observed. The central player's type is global, so actions in one dispute update beliefs in the other and generate reputational spillovers. The game admits a unique equilibrium, enabling a sharp comparison with the bilateral benchmark of Abreu and Gul (2000). Spillovers are payoff-relevant if and only if a peripheral is uniquely the most reputable player initially. In that case, spillovers overturn the bilateral prediction that toughness pays: the central player is never strictly better off and can be strictly worse off; the strongest peripheral loses; and the weakest peripheral can benefit, especially when the center's higher-stakes dispute is with the other peripheral.