Doing some computer experiments on learning algorithms in the context of wireless systems, I had some thought on the role of memory (another thing that trigged my interest was a paper I saw on
magnetic holographic memory and also my on-off reading of "In Search of Lost Times" .
The computer experiments were on sequential games, and we were looking at a two-agent system, where each agent could make a move followed by a move by the other one. The very naive strategy that we first used was that at every move each agent would choose the action that would maximize its instantaneous pay-off. In this case the system just "flip-flopped"
1st agent chooses its best move according to the above strategy
This resultss in the worse outcome for the second agent
Subsequently, the 2nd agent try to improve the situation by choosing the best move available
This would then result in the worst outcome for the 1st agent
And the above cycle goes on without the system ever settling into any kind of equilibrium.
Obviously, none of the agents had memory so could not forecast/predict that chosing the action with the best immediate payoff would result in the next timestep in a bad payoff due to the oponent's response. Introducing memory can help the agents reach a compromise solution (at least if this exists, which was the case in our experiments) .
This made me think about one of the previous blogs that I posted quite a while ago about the parallels with game theory and theory of interacting many-particle systems in physics. If one starts from a game theory context/background the postulate that the motion of particles is governed by rules that would guarantee minimization (or maximization) a global function, like energy or action, may seem a bit peculiar. Since in non-cooperative game theory every agent is supposed to attempt to maximize its own utility.
Would it be possible to derive the equations of motion of particles in an interacting system without the need to first postulate the existence of such a global function? I.e. that minimization of energy, or action, is an emerging behaviour of a many-particle system (e.g. an electron gas) rather than a property that is already built-in to the theory through a postulate.
The idea is to replace the strong assumption of the existence of a global function by a much weaker assumption that each particle's movements are governed by "local optimization" rules. Nevertheless, the execution of these local rules by each particle would result in a global minimum to be achieved.
Looking again into game theory, one way this could be achieved is if we could assume that particles have some form of memory that guides them to equilibrium solutions through repeated games.
This may require that particles (e.g. electrons) have some internal degrees of freedom (states) that can act as memory storage.
