Nash Equilibria of The Multiplayer Colonel Blotto Game on Arbitrary Measure Spaces

TL;DR

This paper extends the classical multiplayer Colonel Blotto game to arbitrary measure spaces, providing algorithms for equilibrium sampling and characterizing fair symmetric equilibria over continuous battlegrounds.

Contribution

It introduces a generalized framework for multiplayer Blotto games on arbitrary measure spaces and offers methods to find and analyze symmetric equilibria.

Findings

Algorithm for sampling equilibria in symmetric games

Characterization of symmetric fair equilibria over the unit interval

Extension of Blotto game theory to continuous measure spaces

Abstract

The Colonel Blotto Problem proposed by Borel in 1921 has served as a widely applicable model of budget-constrained simultaneous winner-take-all competitions in the social sciences. Applications include elections, advertising, R&D and more. However, the classic Blotto problem and variants limit the study to competitions over a finite set of discrete battlefields. In this paper, we extend the classical theory to study multiplayer Blotto games over arbitrary measurable battlegrounds, provide an algorithm to efficiently sample equilibria of symmetric "equipartionable" Generalized Blotto games, and characterize the symmetric fair equilibria of the Blotto game over the unit interval.