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Noisy Stochastic Games

Author

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  • John Duggan

    (W. Allen Wallis Institute of Political Economy, 107 Harkness Hall, University of Rochester, Rochester, NY 14627-0158)

Abstract

This paper establishes existence of a stationary Markov perfect equilibrium in general stochastic games with noise—a component of the state that is nonatomically distributed and not directly affected by the previous period’s state and actions. Noise may be simply a payoff-irrelevant public randomization device, delivering known results on existence of correlated equilibrium as a special case. More generally, noise can take the form of shocks that enter into players’ stage payoffs and the transition probability on states. The existence result is applied to a model of industry dynamics and to a model of dynamic electoral competition.

Suggested Citation

  • John Duggan, 2012. "Noisy Stochastic Games," RCER Working Papers 570, University of Rochester - Center for Economic Research (RCER).
  • Handle: RePEc:roc:rocher:570
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    File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_570.pdf
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    References listed on IDEAS

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    1. Mertens, J.-F. & Parthasarathy, T., 1987. "Equilibria for discounted stochastic games," LIDAM Discussion Papers CORE 1987050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Herings, P. Jean-Jacques & Peeters, Ronald J. A. P., 2004. "Stationary equilibria in stochastic games: structure, selection, and computation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 32-60, September.
    3. Barro, Robert J & Gordon, David B, 1983. "A Positive Theory of Monetary Policy in a Natural Rate Model," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 589-610, August.
    4. , & ,, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
    5. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    6. Bergin, James & Bernhardt, Dan, 1992. "Anonymous sequential games with aggregate uncertainty," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 543-562.
    7. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
    8. James Bergin & Dan Bernhardt, 2008. "Industry dynamics with stochastic demand," RAND Journal of Economics, RAND Corporation, vol. 39(1), pages 41-68, March.
    9. Herings, P. J. J. & Polemarchakis, H., 2002. "Equilibrium and arbitrage in incomplete asset markets with fixed prices," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 133-155, April.
    10. Alberto Alesina, 1987. "Macroeconomic Policy in a Two-Party System as a Repeated Game," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(3), pages 651-678.
    11. Parthasarathy, T & Sinha, S, 1989. "Existence of Stationary Equilibrium Strategies in Non-zero Sum Discounted Stochastic Games with Uncountable State Space and State-Independent Transitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 189-194.
    12. Rabah Amir, 2002. "Complementarity and Diagonal Dominance in Discounted Stochastic Games," Annals of Operations Research, Springer, vol. 114(1), pages 39-56, August.
    13. Horst, Ulrich, 2005. "Stationary equilibria in discounted stochastic games with weakly interacting players," Games and Economic Behavior, Elsevier, vol. 51(1), pages 83-108, April.
    14. Avinash Dixit & Gene M. Grossman & Faruk Gul, 2000. "The Dynamics of Political Compromise," Journal of Political Economy, University of Chicago Press, vol. 108(3), pages 531-568, June.
    15. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
    16. Hopenhayn, Hugo A, 1992. "Entry, Exit, and Firm Dynamics in Long Run Equilibrium," Econometrica, Econometric Society, vol. 60(5), pages 1127-1150, September.
    17. Andrzej Nowak, 2007. "On stochastic games in economics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 513-530, December.
    18. A. S. Nowak & T. E. S. Raghavan, 1992. "Existence of Stationary Correlated Equilibria with Symmetric Information for Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 519-526, August.
    19. Andrzej Nowak, 2003. "On a new class of nonzero-sum discounted stochastic games having stationary Nash equilibrium points," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 121-132, December.
    20. Harris, Christopher & Reny, Philip & Robson, Arthur, 1995. "The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Case for Public Randomization," Econometrica, Econometric Society, vol. 63(3), pages 507-544, May.
    21. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-491, June.
    22. Alesina, Alberto, 1988. "Credibility and Policy Convergence in a Two-Party System with Rational Voters," American Economic Review, American Economic Association, vol. 78(4), pages 796-805, September.
    23. Yannelis, Nicholas C., 1990. "On the upper and lower semicontinuity of the Aumann integral," Journal of Mathematical Economics, Elsevier, vol. 19(4), pages 373-389.
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