Finding optimal strategies for influencing social networks in two player games

Abstract

This thesis considers the problem of optimally influencing social networks in Afghanistan as part of ongoing counterinsurgency efforts. The social network is analyzed using a discrete time agent based model. Each agent has a belief [-0.5,0.5] and interacts stochastically pairwise with their neighbors. The network converges to a set of equilibrium beliefs in expectation. A 2-player game is formulated in which the players control a set of stubborn agents whose beliefs never change, and who wield significant influence in the network. Each player chooses how to connect their stubborn agents to maximally influence the network. Two different payoff functions are defined, and the pure Nash equilibrium strategy profiles are found in a series of test networks. Finding equilibrium strategy profiles can be difficult for large networks due to exponential increases in the strategy space but a simulated annealing heuristic is used to rapidly find equilibria using best response dynamics. We demonstrate through experimentation that the games formulated admit pure Nash equilibrium strategy profiles and that best response dynamics can be used to find them. We also test a scenario based on the author's experience in Afghanistan to show how nonsymmetric equilibria can naturally emerge if each player weights the value of agents in the network differently.