A 'Pencil Sharpening' Algorithm for Two Player Stochastic Games with Perfect Monitoring

79 Pages Posted: 24 Feb 2016

See all articles by Dilip Abreu

Dilip Abreu

Princeton University - Department of Economics

Benjamin A. Brooks

Princeton University - Department of Economics

Yuliy Sannikov

Princeton University

Date Written: February 11, 2016

Abstract

We study the subgame perfect equilibria of two player stochastic games with perfect monitoring and geometric discounting. A novel algorithm is developed for calculating the discounted payoffs that can be attained in equilibrium. This algorithm generates a sequence of tuples of payoffs vectors, one payoff for each state, that move around the equilibrium payoff sets in a clockwise manner. The trajectory of these "pivot" payoffs asymptotically traces the boundary of the equilibrium payoff correspondence. We also provide an implementation of our algorithm, and preliminary simulations indicate that it is more efficient than existing methods. The theoretical results that underlie the algorithm also yield a bound on the number of extremal equilibrium payoffs.

Keywords: Stochastic game, perfect monitoring, algorithm, computation

JEL Classification: C63, C72, C73, D90

Suggested Citation

Abreu, Dilip and Brooks, Benjamin A. and Sannikov, Yuliy, A 'Pencil Sharpening' Algorithm for Two Player Stochastic Games with Perfect Monitoring (February 11, 2016). Princeton University William S. Dietrich II Economic Theory Center Research Paper No. 078_2016, Available at SSRN: https://ssrn.com/abstract=2736574 or http://dx.doi.org/10.2139/ssrn.2736574

Dilip Abreu (Contact Author)

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States

Benjamin A. Brooks

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States

Yuliy Sannikov

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544-0708
United States

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