Cooperative oligopoly games: a probabilistic approach

TL;DR

This paper investigates the core stability of cooperative oligopoly games using a probabilistic approach, demonstrating non-emptiness of the core for large markets and its relation to the b3-core.

Contribution

It introduces a probabilistic framework for analyzing the core in cooperative Cournot games and establishes conditions for core non-emptiness in large markets.

Findings

Core is non-empty when the number of firms is large

The core is a subset of the b3-core

Probabilistic coalition formation impacts core stability

Abstract

We analyze the core of a cooperative Cournot game. We assume that when contemplating a deviation, the members of a coalition assign positive probability over all possible coalition structures that the non-members can form. We show that when the number of firms in the market is sufficiently large then the core of the underlying cooperative game is non-empty. Moreover, we show that the core of our game is a subset of the \gamma - core.