(319f) Gibbsian Game Theory for Tragedy of the Commons Problems in Food-Energy-Water Sustainability

Sustainability problems in the food-energy-water nexus often involve "tragedy of the commons" (TOC) problems. TOC challenges are often modeled in game theory using n-player Prisoner's Dilemma (NPD) games and other games. However, classical solutions to game theory problems â?? here called â??Nashian gamesâ? â?? have a number of shortcomings, and do not always conform to experimental data. In this talk we treat strategic games as a set of chemical reactions, and we treat choices as types of reactive molecules. Thus, this model provides new solutions to classical games. By using the usual Gibbsian approach to chemical reaction equilibrium, we are able to employ entropic considerations and minimize a type of Gibbs free energy to find game theory equilibria, overcoming the usual shortcomings in game theory. We solve classical games, including the 2-player PD game and the NPD game, using the â??Gibbsian game theoryâ? approach, which accounts for â??entropic choicesâ?. We then show how treating strategic games as a set of chemical reactions can be used to represent decision situations more accurately than typical games, and we solve for the equilibrium of sets of reactions. Then, we apply Gibbsian solutions to NPD games to problems in sustainability. By quantifying concepts like "trust", "power", and "corruption", we explore opportunities for nudging outcomes of contested decisions in sustainability decisions. When overlapping considerations occur, as in the food-energy-water nexus, the NPD games reveal fundamental political conditions that increase the probabilities for when genuine human solutions can advance. In this talk we describe Gibbsian game solutions for NPD problems, and show how they apply to sustainability problems in the food-energy-water nexus.