Essays on Integer Programming Approaches to Analyze Equilibrium Solutions in Games

In this dissertation, we present three applications of integer programming to analyze non-cooperative games. In a non-cooperative game, players of the game act selfishly and choose the best response given every other player\u27s decision. The game reaches a Nash equilibrium when no player can benefit by changing its decisions. Our goal is to create an integer program that can identify these Nash equilibriums by modeling the best response of the game\u27s players in the constraints. We prove a one-to-one correspondence between the game\u27s Nash equilibrium and the feasible solution of a corresponding integer program. The one-to-one correspondence allows us to analyze the game and the equilibriums from multiple perspectives; we can identify equilibriums that are best for each player, compare the best and the worst equilibrium solutions with a centrally optimal solution, compare the loss in the objective for one player when the game reaches an equilibrium that is best for another player, and find an equilibrium that is optimal for society\u27s goals. We identify games that arise in industry and public sectors, including the Platform Based Scheduling Game, the Arctic Infrastructure Game, and the Multiple Arctic Port Game. The Platform Based Scheduling Game is inspired by an online freelancer platform, which the clients choose a freelancer that they wish to work with. We analyze how the clients\u27 selfish behaviors impact the equilibrium that is optimized for the freelancers, clients, and the platform. In the Arctic Infrastructure Game, we analyze whether the stakeholders are capable of constructing and maintaining a costly infrastructure in a remote region in the Arctic and the Multiple Arctic Port Game extends the Arctic Infrastructure Game where multiple ports are operating across several remote locations in the Arctic. In the last two games, our formulation can identify equilibrium\u27s the resulting stakeholders\u27 optimal monetary contribution that would yield the highest net benefit. The models also answer key questions that the government, local communities, and private industry would like to ask before venturing into a costly project