(243e) Gibbsian Game Theory for Competitive Decisions

Optimization problems involve finding parameters that minimize a given optimization function.  However, in many competitive decisions involving conflict or cooperation, the optimization function for one person or group is often very different from the optimization function for another person or group, giving rise to power and political considerations.  Over the past half century, competitive decision problems have been represented and solved by game theory, originated by John von Neumann.  Later developments by John Nash showed that strategic games always have one or more “Nash equilibria”.  However, current solutions to game theory problems – here called “Nashian games” – have a number of shortcomings, and do not always conform to experimental data.  For example, in the classical “Battle of the Sexes” game, three distinct equilibria arise, but no guidance is provided on how often each of the equilibria will apply.  In this talk we treat strategic games as a series of chemical reactions, and so are able to use entropic considerations and minimize a type of Gibbs free energy.  We solve classical games like a Prisoners’ Dilemma, Battle of the Sexes, and Chicken using the “Gibbsian game theory” approach, which accounts for “entropic choices”.  We then show how treating strategic games as a set of chemical reactions can be used to represent situations more accurately than typical games, and solve these sets of reactions.  This new way of treating social, economic, and political data in situations of conflict, power, and contested decisions could produce new possibilities for mechanistic design.