Equilibrium characterizations of multi-resource Lotto games

Abstract

The allocation of heterogeneous resources plays an increasingly important role in the completion of system objectives and tasks. In this paper, we focus on deriving optimal strategies for the allocation of heterogeneous resources in a well-known adversarial model known as the General Lotto game. In standard formulations, outcomes are determined solely by the players’ allocation strategies of a 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 linear combination of the allocated resources. We then provide equilibrium investment strategies in scenarios where the resource types are costly to purchase, and players each have a limited monetary budget.