The strategy of conflict and cooperation

TL;DR

This paper presents a unified framework for cooperative extensive form games, introducing the cooperative equilibrium system (CES), which accounts for complex coalition dynamics and strategic adjustments, extending beyond traditional Nash equilibrium concepts.

Contribution

It develops a novel solution concept, CES, that generalizes Nash equilibrium by incorporating coalition formation and strategic regrouping, with proofs of existence for all cooperative extensive form games.

Findings

CES is immune to credible deviations.

Every cooperative extensive form game has a CES.

Constructive proof for perfect information games.

Abstract

This paper introduces a unified framework called cooperative extensive form games, which (i) generalizes standard non-cooperative games, and (ii) allows for more complex coalition formation dynamics than previous concepts like coalition-proof Nash equilibrium. Central to this framework is a novel solution concept called cooperative equilibrium system (CES). CES differs from Nash equilibrium in two important respects. First, a CES is immune to both unilateral and multilateral `credible' deviations. Second, unlike Nash equilibrium, whose stability relies on the assumption that the strategies of non-deviating players are held fixed, CES allows for the possibility that players may regroup and adjust their strategies in response to a deviation. The main result establishes that every cooperative extensive form game, possibly with imperfect information, possesses a CES. For games with perfect information, the proof is constructive. This framework is broadly applicable in contexts such as oligopolistic markets and dynamic political bargaining.