Game theory for decision-making

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Many real-world decision*processes involve the interaction of competing decision makers. Such situations*fall in two fields: (1) Game Theory, with decision makers being called players;*and (2) Mathematical Programming, with players aiming to optimize their individual*outcome (payoff). Integer programming*games (IPGs) is a recently defined class of games that brings together these two fields: it models situations*where each player's goal is described through a mathematical optimization program*whose payoff depends on the competitors. Furthermore, this framework allows one*to encode discrete decisions that are inherent to practical problems.******There is a striking difference between IPGs and most*of the game theory literature. In general, the literature focus in games where: (1) each player's optimization problem*is convex, or (2) all possible game outcomes are explicitly enumerated in the*input, the so-called normal-form games. ******The goal of our research is to*tackle non-cooperative IPGs. In specific, we aim to determine what are the most*rational strategies that the players can select, the so-called equilibrium*strategies. ******Understanding integer programming*games is of crucial importance as this class enables us to properly mirror*practical situations where different self-interested entities interact. For*example, defender-attacker interactions in the context of homeland security, transplant*programs (markets) across countries that aim to optimize the benefit of their*own patients, production planning of different firms competing in the same*market, to name a few.******By investigating the development*of algorithms to compute the games' equilibria one can: (1) classify the problem*complexity and, consequently, establish hypothesis on the realism of players*adopting an equilibrium; (2) generalize game theory results to this broader*class of games and, simultaneously, advance on mathematical programming tools;*(3) propose policy changes to repair ongoing games, by re-designing games with*more “convenient equilibria”.******The ultimate goal of this*research is to study beyond static games and move forward to dynamic and*incomplete-information games. Such investigation has the potential to suggest*more transparent policies, incentive progress through adequate game rules for*competition, and accomplish social benefits.