Natural games

Physics Letters A (Impact Factor: 1.63). 03/2011; 375(43). DOI: 10.1016/j.physleta.2011.08.056
Source: arXiv

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.