Equilibrium analysis of three-player General Lotto game with leader-follower framework

In this paper, we introduce the General Lotto game with a regulator (R-Lotto), a leader-follower extension of the classical two-player General Lotto game. The model captures regulatory interventions in competitive resource allocation, where a regulator first chooses an intervention parameter to influence the subsequent competition between two resource-constrained followers. The intervention parameter represents favoritism toward one of the followers, and the followers then play a general Lotto subgame with favoritism. We derive the followers' equilibrium payoff and characterize the Nash--Stackelberg equilibrium (NSE) intervention of the regulator. We further develop a multi-battlefield R-Lotto model with a regulator budget constraint. In this setting, the follower subgames on different battlefield is decoupled, while the regulator's intervention decisions are coupled through a common budget. Numerical simulations demonstrate the proposed equilibrium characterizations and provide practical decision-making guidance for the regulator.