Game-theoretic management of interacting adaptive systems

Joint work with Nilesh V. Kulkarni

Say we have a set of players engaged in a non-cooperative game, with y being a parameter of that game. So the joint behavior of the players, q, is given by the equilibrium of the game specified by y. In other words, q is a function of y. We consider a ''manager'' who controls y but whose utility function U depends on q. So the manager's problem is to find the y whose associated q optimizes U. This problem can be viewed as an extension of mechanism design, to allow bounded rational players, to exploit knowledgeconcerning players not directly affected by y, and to allow arbitrary types of variable y. We introduce a solution to this problem based on using gradient descent to move a fixed point, and illustrate this solution with computer experiments.