Blotto Games with Costly Winnings

TL;DR

This paper introduces a sequential multi-stage Colonel Blotto game where players must allocate resources for both winning battles and maintaining their wins, establishing a unique Nash equilibrium under certain conditions.

Contribution

It models a new sequential variant of the asymmetric Colonel Blotto game with maintenance costs and proves the existence of a unique Nash equilibrium.

Findings

Existence of a unique Nash equilibrium under certain resource conditions.

Equilibrium strategies guarantee specific expected payoffs.

Game dynamics incorporate maintenance costs for winning battles.

Abstract

We introduce a new variation of the m-player asymmetric Colonel Blotto game, where the n battles occur as sequential stages of the game, and the winner of each stage needs to spend resources for maintaining his win. The limited resources of the players are thus needed both for increasing the probability of winning and for the maintenance costs. We show that if the initial resources of the players are not too small, then the game has a unique Nash equilibrium, and the given equilibrium strategies guarantee the given expected payoff for each player.