Alliance Mechanisms in General Lotto Games

2026-01-29

AI Summary

This study investigates how three coalition mechanisms—budget transfer, contest transfer, and joint transfer—affect individual and collective payoffs when two players cooperate against a common opponent in the Coalitional General Lotto game. Through game-theoretic modeling and equilibrium analysis, the work demonstrates a striking equivalence among these mechanisms in terms of collective performance: nearly all instances achieve the same maximal collective payoff regardless of the mechanism employed. However, with respect to individual reciprocity, joint transfer consistently outperforms the other two mechanisms, effectively guaranteeing mutual gains for both coalition members in the vast majority of cases. By systematically characterizing the fundamental differences and applicability conditions of coalition mechanisms in competitive resource allocation, this research provides a rigorous theoretical foundation for designing cooperative strategies in adversarial settings.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Social and technical mechanisms of refusal for web technologies and applications

Abstract

How do different alliance mechanisms compare? In this work, we analyze various methods of forming an alliance in the Coalitional General Lotto game, a simple model of competitive resource allocation. In the game, Players 1 and 2 independently compete against a common Adversary by allocating their limited resource budgets towards separate sets of contests; an agent wins a contest by allocating more resources towards it than their opponent. In this setting, we study three alliance mechanisms: budget transfers (resource donation), contest transfers (contest redistribution), and joint transfers (both simultaneously). For all three mechanisms, we study when they present opportunities for collective improvement (the sum of the Players'payoffs increases) or mutual improvement (both Players'individual payoffs increase). In our first result, we show that all three are fundamentally different with regards to mutual improvement; in particular, mutually beneficial budget and contest transfers exist in distinct, limited subsets of games, whereas mutually beneficial joint transfers exist in almost all games. However, in our second result, we demonstrate that all three mechanisms are equivalent when it comes to collective improvement; that is, collectively beneficial budget, contest, and joint transfers exist in almost all game instances, and all three mechanisms achieve the same maximum collective payoff. Together, these results demonstrate that differences between mechanisms depend fundamentally on the objective of the alliance.

Problem

• alliance mechanisms
• General Lotto games
• resource allocation
• collective improvement
• mutual improvement

Innovation

• alliance mechanisms
• General Lotto games
• resource allocation
• coalitional game theory
• mutual improvement