Multiplayer General Lotto Game
摘要
In this paper, we investigate the multiplayer General Lotto game – a significant extension of the classic Colonel Blotto game – in a setting involving competition across multiple battlefields. Under this framework, resources are allocated probabilistically by players, ensuring their expected expenditures remain within individual budgets. Our contributions begin by establishing the existence of Nash equilibrium for general scenarios, accommodating asymmetries in both player budgets and battlefield valuations. A detailed characterization of equilibrium strategies follows, specifically addressing the complexities arising when multiple players compete on a single battlefield, and culminating in a system of equations for computing equilibria. Furthermore, we identify conditions under which equilibrium uniqueness is guaranteed in single-battlefield game. Turning to multi-battlefield competition, our analysis reveals an upper bound on the average number of battlefields actively contested by each player. For symmetric scenarios, we provide explicit equilibrium solutions. Finally, equilibrium multiplicity is demonstrated concretely through an illustrative example involving multiple players and battlefields.