Equilibrium analysis of three-player General Lotto game with leader-follower framework
Computer Science and Game Theory
Summary
The authors introduce a new version of a game called the General Lotto game, where a regulator leader first sets a rule to influence two players who compete for resources. This rule shows favoritism toward one player, and then the players compete under those conditions. The authors figure out how the players end up scoring and how the regulator should set their rule to get the best outcome. They also study a more complex version with many battlefields and a limited budget for the regulator's influence. Their simulations help show how these strategies work and guide decision-making for the regulator.
Authors
Yang Jiao, Dunbiao Niu, Yiguang Hong
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.