Coalition Formation in Constant Sum Queueing Games

TL;DR

This paper studies a constant sum queueing game among service providers, revealing that stable outcomes are duopolies rather than grand coalitions due to competition over market share and resource pooling benefits.

Contribution

It introduces a novel constant sum game model for coalition formation in congestible services, highlighting the instability of grand coalitions and the emergence of stable duopolies.

Findings

Grand coalition is generally unstable due to competition.

Stable configurations are typically duopolies exploiting economies of scale.

Analysis includes a dynamic variant of the game.

Abstract

We analyse a coalition formation game between strategic service providers of a congestible service. The key novelty of our formulation is that it is a constant sum game, i.e., the total payoff across all service providers (or coalitions of providers) is fixed, and dictated by the total size of the market. The game thus captures the tension between resource pooling (to benefit from the resulting statistical economies of scale) and competition between coalitions over market share. In a departure from the prior literature on resource pooling for congestible services, we show that the grand coalition is in general not stable, once we allow for competition over market share. Instead, the stable configurations are duopolies, where the dominant coalition exploits its economies of scale to corner a disproportionate market share. We analyse the stable duopolies that emerge from this interaction, and also study a dynamic variant of this game.