A semantical approach to equilibria and rationality

TL;DR

This paper explores a semantical, computational perspective on game theoretic equilibria, emphasizing the role of fixed points and formal semantics in understanding rationality across biological and economic systems.

Contribution

It introduces a novel semantical framework based on computation and fixed point semantics to analyze equilibria and rationality in diverse systems.

Findings

Fixed points as fundamental to equilibria

Semantical methods offer new reasoning tools

Application to biological and economic models

Abstract

Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and with the environment. Rational behaviors are achieved not only through conscious reasoning, but also through spontaneous stabilization at equilibrium points. Formal theories of rationality are usually guided by informal intuitions, which are acquired by observing some concrete economic, biological, or network processes. Treating such processes as instances of computation, we reconstruct and refine some basic notions of equilibrium and rationality from the some basic structures of computation. It is, of course, well known that equilibria arise as fixed points; the point is that semantics of computation of fixed points seems to be providing novel methods, algebraic and coalgebraic, for reasoning about them.