Natural games

TL;DR

This paper models behavior in game theory as a thermodynamic process driven by entropy increase, linking physical principles to strategic decision-making and explaining unpredictability and stability in games.

Contribution

It introduces a thermodynamic formalism to describe game behavior, connecting physical energy flows to strategic interactions and equilibrium concepts.

Findings

Behavior follows entropy increase, akin to physical energy consumption.

Game equilibrium corresponds to entropy maximization with Lyapunov stability.

Unpredictability arises when multiple degrees of freedom influence future motives.

Abstract

Behavior in the context of game theory is described as a natural process that follows the 2nd law of thermodynamics. The rate of entropy increase as the payoff function is derived from statistical physics of open systems. The thermodynamic formalism relates everything in terms of energy and describes various ways to consume free energy. This allows us to associate game theoretical models of behavior to physical reality. Ultimately behavior is viewed as a physical process where flows of energy naturally select ways to consume free energy as soon as possible. This natural process is, according to the profound thermodynamic principle, equivalent to entropy increase in the least time. However, the physical portrayal of behavior does not imply determinism. On the contrary, evolutionary equation for open systems reveals that when there are three or more degrees of freedom for behavior, the course of a game is inherently unpredictable in detail because each move affects motives of moves in the future. Eventually, when no moves are found to consume more free energy, the extensive-form game has arrived at a solution concept that satisfies the minimax theorem. The equilibrium is Lyapunov-stable against variation in behavior within strategies but will be perturbed by a new strategy that will draw even more surrounding resources to the game. Entropy as the payoff function also clarifies motives of collaboration and subjective nature of decision making.