Computing Sensible Nash Equilibria

概要

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A simplicial algorithm is developed to compute a robust stationary point of a continuous function on a simplotope. The concept of a robust stationary point is a refinement of that of a stationary point. It is shown that every continuous function on the simplotope has a robust stationary point but a stationary point need not be a robust one. The algorithm can be briefly stated as follows. Starting with an arbitrarily chosen interior point of the simplotope, the algorithm generates a piecewise linear path which leads to an approximate robust stationary point of any a priori chosen accuracy within a finite number of steps. A primary application of the algorithm concerns the computation of a proper Nash equilibrium of a non-cooperative finite game, where the simplotope is the strategy space of the game. The path of points, traced by the algorithm admits a game-theoretically natural interpretation. A few numerical examples are given.
横浜国立大学の論文