Solving Games Forwards and Backwards

Computing equilibria in games is a problem of great interest in both economics and computer science. We present a min-max formulation of this problem, in which the minimizer seeks an equilibrium solution for the game, while the maximizer seeks to find fault with the proposed solutions. We call this problem the “forward” problem. In the “backwards” problem, we are instead given an equilibrium and a parameterized game, and we are interested in inferring a game from that equilibrium: i.e., identifying the game parameters that induce the observed equilibrium.

We consider the backwards problem under weaker and weaker assumptions, ranging from inverse multiagent planning to inverse multiagent learning and beyond, for each of which we present min-max formulations. We apply our backwards method to Spanish electricity market time-series price data, and then push the inferred game forward to predict future prices.