A General Lotto game with asymmetric budget uncertainty

TL;DR

This paper analyzes a variant of the Colonel Blotto game with asymmetric and incomplete information, providing equilibrium solutions and demonstrating that randomized resource allocations can significantly outperform deterministic ones.

Contribution

It introduces equilibrium characterizations for asymmetric information General Lotto games with Bernoulli-distributed private budgets and extends the analysis to randomized resource assignments.

Findings

Equilibrium strategies are characterized for games with Bernoulli-distributed private budgets.

Randomized resource assignments can quadruple the performance compared to deterministic strategies.

Optimal Bernoulli randomized assignments improve strategic outcomes in multi-stage resource allocation.

Abstract

The General Lotto game is a popular variant of the famous Colonel Blotto game, in which two opposing players allocate limited resources over many battlefields. In this paper, we consider incomplete and asymmetric information formulations regarding the resource budgets of the players. In particular, one of the player's resource budget is common knowledge while the other player's is private. We provide complete equilibrium characterizations in the scenario where the private resource budget is drawn from an arbitrary Bernoulli distribution. We then show that these characterizations can be used to analyze a multi-stage resource assignment problem where a commander must decide how to assign resources to sub-colonels that compete against opponents in separate General Lotto games. While optimal deterministic assignments have been characterized in the literature, we broaden the context by deriving optimal (Bernoulli) randomized assignments, which induce asymmetric information General Lotto games to be played. We demonstrate that randomizing can offer a four-fold improvement in the commander's performance over deterministic assignments.