Problem
Research questions and friction points this paper is trying to address.
Alliance formation
General Lotto game
Uncertainty
Resource allocation
Coalitional games
Forming Alliances in the Fog of War: A General Lotto Perspective
🤖 AI Summary
This study addresses how resource transfer strategies in coalition formation can achieve robustness under budgetary uncertainty. By investigating the General Lotto game with coalitions under uncertainty, this work integrates applied game theory, coalition allocation theory, and robust optimization to characterize, for the first time, the set of robust budget transfers that are mutually beneficial to both parties across two distinct uncertainty models. The analysis demonstrates that even under conditions of high uncertainty, there exists a positive measure of games admitting room for mutually advantageous transfers. These findings validate the effectiveness and robustness of cooperative coalition mechanisms in environments characterized by ambiguous budgets, offering new theoretical insights into strategic resource allocation when precise budget information is unavailable.
📝 Abstract
Agents competing against a common opponent can often gain an edge by forming alliances, but deciding whether to do so is difficult when they lack precise knowledge about their opponent or ally. We study how uncertainty affects opportunities for alliance formation in the coalitional General Lotto game, in which two players compete aganist a shared adversary by allocating their resource budgets over separate sets of valued contests. When all agents know one another's budgets, it is known that a budget transfer from one player to the other can benefit both players. We ask whether such alliances survive when the players know the relevant budgets only up to a multiplicative factor. Under two models, one in which the players are uncertain about the adversary's budget and one in which they are uncertain about each other's budgets, we characterize exactly which games admit a transfer that benefits both players in every game consistent with what they conjecture to be possible. In both models, we show that such robust transfers exist in a set of games of positive measure for every level of uncertainty. These results suggest that alliances can remain worthwhile even when allies are largely in the dark.
Innovation
Methods, ideas, or system contributions that make the work stand out.
General Lotto game
alliance formation
uncertainty
robust budget transfer
coalitional game
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