Betting on dynamics

• We first consider a game whose results represent the type of dynamics that the system exhibits.
• By introducing a second game, we show that different games can be defined to focus on different aspects of the physics of a system.
• Different winning strategies and Nash equilibrium points, related to distinct physical properties, emerge in each game.
• Special emphasis is made on Nash points, which add a new conceptual perspective, to analyze a physical system.

A physical system in game-theoretic terms is represented in this work. We first consider an abstract game between a classical and a quantum player, whose results represent the two different kinds of non-linear dynamics that the system exhibits. The existence of winning strategies shows that the dynamics can be fully determined through a game theory analysis. Moreover by considering a second game, we show that different games can be defined to focus on different aspects of the physics of a system. Different winning strategies and Nash equilibrium points, emerge in each game. These games theory tools are related to physical properties, so distinct physical information is obtained for each game. In this work, special emphasis is made on Nash points, which add a new conceptual perspective, to analyze a physical system.