Two-person Investment Game

In this thesis, we design and study a new game for investment consideration. Two investors, each with an individual budget, bid on a common pool of potential projects. Due to the economic development consideration, these projects are packed into multiple sets for investors to select. Associated with each project, there is a potential market profit that can be taken by the only investor or shared proportionally between both of them. The objective function for each investor is assumed to be a linear combination of two investors' profits. In the game, both investors act in a selfish manner with the best-response to each other to optimize their own objective functions by choosing portfolios under the budget constraints. We show that a pure Nash equilibrium exists under certain conditions. In this case, no investor can improve the objective by changing individual strategy unilaterally. A dynamic programming algorithm is presented to generate a pure Nash equilibrium in special cases. For general situations, we design a genetic-based algorithm to find pure Nash equilibrium solutions. Also, we investigate the price of anarchy associated with a simplified two-person investment game.