Interconnected Contests

2025-10-13

AI Summary

This paper investigates how spillover networks affect resource allocation and win-probability in two-player, multi-battlefield conflicts, where each player possesses an independent bidirectional spillover network enabling resource coordination across adjacent battlefields. The central questions concern characterizing win-probabilities and designing optimal network topologies to maximize total effort and aggregate utility. Method: We formulate an asymmetric contest game model and analyze it via Nash equilibrium computation, network centrality measures (e.g., eigenvector centrality), and multi-stage optimization. Contribution/Results: We introduce, for the first time, a bidirectional spillover network structure and analytically establish that battlefield win-probabilities are jointly determined by network centrality and the marginal effort cost ratio. We prove uniqueness of the Nash equilibrium and characterize the network topological features—such as degree of centralization and link symmetry—that maximize total effort and aggregate utility. Our results demonstrate that spillover network design serves as a critical regulatory instrument for both competitive efficiency and individual incentive alignment.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study a two-player model of conflict with multiple battlefields -- the novel element is that each of the players has their own network of spillovers so that resources allocated to one battle can be utilized in winning neighboring battles. There exists a unique equilibrium in which the relative probability of a player winning a battle is the product of the ratio of the centrality of the battlefield in the two respective competing networks and the ratio of the relative cost of efforts of the two players. We study the design of networks and characterize networks that maximize total efforts and maximize total utility. Finally, we characterize the equilibrium of a game in which players choose both networks and efforts in the battles.

Problem

• Modeling conflict with networked spillovers across multiple battlefields
• Analyzing equilibrium conditions using network centrality and cost ratios
• Optimizing network design to maximize total efforts and utility

Innovation

• Model uses networked spillovers between battlefields
• Equilibrium depends on network centrality and cost ratios
• Characterizes optimal network designs for maximizing outcomes