Proportional resource allocation in dynamic n-player Blotto games

TL;DR

This paper introduces a dynamic n-player Blotto game model with asymmetric resources and heterogeneous prizes, demonstrating a proportional resource allocation equilibrium that remains stable under resource shocks.

Contribution

It develops a general dynamic n-player Blotto game framework and proves the existence of a proportional allocation equilibrium that is robust to resource shocks.

Findings

Existence of a subgame perfect equilibrium with proportional resource allocation.

Equilibrium remains stable despite exogenous resource shocks.

Applicable to diverse social, economic, and political contest scenarios.

Abstract

A variety of social, economic, and political interactions have long been modelled after Blotto games. In this paper, we introduce a general model of dynamic $n$-player Blotto contests. The players have asymmetric resources, and the battlefield prizes are not necessarily homogeneous. Each player's probability of winning the prize in a battlefield is governed by a contest success function and players' resource allocation on that battlefield. We show that there exists a subgame perfect equilibrium in which players allocate their resources proportional to the battlefield prizes for every history. This result is robust to exogenous resource shocks throughout the game.