Characterizing the interplay between information and strength in Blotto games

TL;DR

This paper analyzes how informational asymmetries affect equilibrium outcomes in Colonel Blotto and General Lotto games, revealing that information generally benefits the informed player and that the impact depends on game parameters and player strength.

Contribution

It provides a detailed characterization of equilibrium payoffs and strategies in asymmetric Blotto and Lotto games, highlighting the role of information and strength in strategic resource allocation.

Findings

Information improves the informed player's performance guarantee.

The magnitude of the benefit varies with player strength and game parameters.

Unique equilibrium payoffs are characterized for specific game setups.

Abstract

In this paper, we investigate informational asymmetries in the Colonel Blotto game, a game-theoretic model of competitive resource allocation between two players over a set of battlefields. The battlefield valuations are subject to randomness. One of the two players knows the valuations with certainty. The other knows only a distribution on the battlefield realizations. However, the informed player has fewer resources to allocate. We characterize unique equilibrium payoffs in a two battlefield setup of the Colonel Blotto game. We then focus on a three battlefield setup in the General Lotto game, a popular variant of the Colonel Blotto game. We characterize the unique equilibrium payoffs and mixed equilibrium strategies. We quantify the value of information - the difference in equilibrium payoff between the asymmetric information game and complete information game. We find information strictly improves the informed player's performance guarantee. However, the magnitude of improvement varies with the informed player's strength as well as the game parameters. Our analysis highlights the interplay between strength and information in adversarial environments.