Department of Mathematics, UCI

A long-running difficulty with conventional game theory is how to modify it to accommodate bounded rationality. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. A major problem in control theory is how to implement control on (massively) distributed systems, especially in an adaptive manner, with mixed types of control variables.

This talk shows that the same information-theoretic structure, known as Probability Collectives (PC), underpins all three issues. This means that statistical physics, game theory, and distributed control are fundamentally identical. Accordingly techniques and insights from one of those fields can be applied to the others. One example of this, presented here, is the use of the grand canonical ensemble of statistical physics to elaborate game theory in which the number of players is not pre-determined, but varies stochastically. Another example is how to apply steepest descent techniques to optimize/control systems of discrete variables.