Precision game engineering through reshaping strategic payoffs

Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, with applications in diverse fields such as economics, political science, and biology. However, the Nash equilibrium may not always align with desired outcomes within the broader system. This article introduces a novel game engineering framework that tweaks strategic payoffs within a game to achieve a pre-defined desired Nash equilibrium while averting undesired ones. Leveraging mixed-integer linear programming, this framework identifies intricate combinations of players and strategies and optimal perturbations to their payoffs that enable the shift from undesirable Nash equilibria to more favorable ones. We demonstrate the effectiveness and scalability of our approach on games of varying complexity, ranging from simple prototype games such as the Prisoner's Dilemma and Snowdrift games with two or more players to complex game configurations with up to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow> <mml:mn>6</mml:mn></mml:msup> </mml:math> entries in the payoff matrix. These studies showcase the capability of this framework in efficiently identifying the alternative ways of reshaping strategic payoffs to secure desired Nash equilibria and preclude undesired equilibrium states. Our game engineering framework offers a versatile toolkit for precision strategic decision-making with far-reaching implications across diverse domains.