Compound Attrition Games: A Unified Model for Inter- and Intra-Coalition Rivalry
Madjid Eshaghi Gordji, Mohamad Ali Berahman

TL;DR
This paper introduces the Compound Coalition-Attrition Game (CCAG), a unified model capturing both inter- and intra-coalition rivalry, revealing feedback effects and characterizing unique mixed-strategy equilibria.
Contribution
It develops a novel integrated game-theoretic framework that combines external and internal attrition processes, addressing limitations of previous separate models.
Findings
External competition increases internal conflict.
Internal discord weakens external performance.
The model characterizes a unique mixed-strategy Nash equilibrium.
Abstract
Strategic competitions in the real world, from wars to geopolitical rivalries, often involve coalitions competing against rival groups. These contests are not simple interactions between unified entities, but multilayered processes in which coalitions face external competition while dealing with internal conflicts over resources and strategy. Existing game-theoretic models typically treat inter-coalition rivalry and intra-coalition competition separately. This paper introduces the Compound Coalition-Attrition Game (CCAG), a unified framework that integrates a war of attrition between coalitions with a simultaneous war of attrition within each coalition. In this model, the endurance of a coalition in external competition is determined by the strategic choices of its members, who compete internally for shares of the outcome. We prove the nonexistence of pure-strategy equilibria and…
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