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

2026-07-19

AI Summary

This study addresses equilibrium analysis in a three-player game involving resource competition with regulatory intervention. It proposes a Regulator-augmented Generalized Lotto model (R-Lotto) within a Nash–Stackelberg framework, where the regulator acts as the leader and two resource-constrained competitors serve as followers. For the first time, regulatory intervention is integrated into the generalized Lotto game, extended to multi-battlefield settings, and subjected to a regulatory budget constraint. The equilibrium strategies are derived through decoupling and coupling optimization techniques. Theoretical analysis fully characterizes the followers’ equilibrium payoffs and the regulator’s optimal intervention policy. Numerical experiments validate the model’s efficacy, offering both theoretical foundations and practical guidance for regulatory decision-making.

Abstract

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.

Problem

• General Lotto game
• leader-follower framework
• regulatory intervention
• resource allocation
• Nash-Stackelberg equilibrium

Innovation

• General Lotto game
• leader-follower framework
• regulatory intervention
• Nash-Stackelberg equilibrium
• budget-constrained multi-battlefield