Allocation of Heterogeneous Resources in General Lotto Games

2025-05-02

AI Summary

This paper investigates the optimal allocation of multiple heterogeneous resource types in generalized Lotto games under adversarial settings, departing from conventional single-resource assumptions by introducing a novel win-determination mechanism wherein resource-type combinations jointly influence contest outcomes. We formulate the first multi-resource Lotto model and characterize Nash equilibria under two new winning rules: weakest-link/best-shot and weighted linear aggregation. Crucially, we jointly optimize both resource allocation and procurement investment decisions. Leveraging game-theoretic analysis, noncooperative equilibrium theory, convex optimization, and symmetric construction of probabilistic strategy spaces, we derive closed-form equilibrium solutions for both models and rigorously establish their existence, uniqueness, and structural properties. Furthermore, we quantify resource cost sensitivity and derive universal laws governing cross-type investment proportions at equilibrium.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Search and Optimization: Adversarial Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Optimal allocation of heterogeneous resources in competitive General Lotto games
• Determining contest winners by resource amount and type composition
• Equilibrium strategies for costly multi-resource investments in adversarial settings

Innovation

• Extends General Lotto game with multi-resource allocation
• Introduces weakest-link/best-shot and weighted linear rules
• Derives equilibrium strategies for costly resource investments