Alliance Mechanisms in General Lotto Games

TL;DR

This paper compares three alliance mechanisms in the Coalitional General Lotto game, analyzing their potential for mutual and collective improvement, and finds that their effectiveness varies based on alliance objectives.

Contribution

It provides a theoretical comparison of budget, contest, and joint transfer mechanisms, revealing their differences and similarities in promoting improvements.

Findings

Mutually beneficial budget and contest transfers are limited to specific game subsets.

Mutually beneficial joint transfers exist in almost all games.

All three mechanisms are equivalent regarding collective improvement across most game instances.

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.