Allocation of Heterogeneous Resources in General Lotto Games

TL;DR

This paper extends the General Lotto game to include multiple resource types, deriving equilibrium strategies and payoffs for different winning rules and cost scenarios, advancing strategic resource allocation analysis.

Contribution

It introduces a multi-resource extension of the General Lotto game, providing a complete characterization of equilibrium strategies for various winning rules and cost considerations.

Findings

Characterized equilibrium payoffs for two resource allocation rules.

Derived optimal strategies considering resource costs.

Analyzed impact of resource composition on game outcomes.

Abstract

The allocation of resources plays an important role in the completion of system objectives and tasks, especially in the presence of strategic adversaries. Optimal allocation strategies are becoming increasingly more complex, given that multiple heterogeneous types of resources are at a system planner's disposal. In this paper, we focus on deriving optimal strategies for the allocation of heterogeneous resources in a well-known competitive resource allocation model known as the General Lotto game. In standard formulations, outcomes are determined solely by the players' allocation strategies of a common, single type of resource across multiple contests. In particular, a player wins a contest if it sends more resources than the opponent. Here, we propose a multi-resource extension where the winner of a contest is now determined not only by the amount of resources allocated, but also by the composition of resource types that are allocated. We completely characterize the equilibrium payoffs and strategies for two distinct formulations. The first consists of a weakest-link/best-shot winning rule, and the second considers a winning rule based on a weighted linear combination of the allocated resources. We then consider a scenario where the resource types are costly to purchase, and derive the players' equilibrium investments in each of the resource types.