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On stochastic games in economics

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Abstract

In this paper we show that many results on equilibria in stochastic games arising from economic theory can be deduced from the theorem on the existence of a correlated equilibrium due to Nowak and Raghavan. Some new classes of nonzero-sum Borel state space discounted stochastic games having stationary Nash equilibria are also presented. Three nontrivial examples of dynamic stochastic games arising from economic theory are given closed form solutions.

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References

  • Amir R (1996) Continuous stochastic games of capital accumulation with convex transitions. Games Econ Behav 15:111–131

    Article  MATH  MathSciNet  Google Scholar 

  • Bertsekas DP, Shreve SE (1978) Stochastic optimal control: the discrete time case. Academic, New York

    MATH  Google Scholar 

  • Blackwell D (1965) Discounted dynamic programming. Ann Math Stat 36:226–235

    MathSciNet  MATH  Google Scholar 

  • Chakrabarti SK (1999) Markov equilibria in discounted stochastic games. J Econ Theory 85:294–327

    Article  MATH  MathSciNet  Google Scholar 

  • Cooper R, John A (1988) Coordinating coordination failures in Keynesian models. Quart J Econ CIII:441–464

    Google Scholar 

  • Curtat LO (1996) Markov equilibria of stochastic games with complementarities. Games Econ Behav 17:177–199

    Article  MATH  MathSciNet  Google Scholar 

  • Diamond P (1982) Aggregate demand management in search equilibrium. J Polit Econ 90:881–894

    Article  Google Scholar 

  • Dutta PK, Sundaram RK (1992) Markovian equilibrium in a class of stochastic games: existence theorems for discounted and undiscounted models. Econ Theory 2:197–214

    Article  MATH  MathSciNet  Google Scholar 

  • Gabay D, Moulin H (1980) On the uniqueness and stability of Nash equilibria in noncooperative games. In: Bensoussan A, Kleindorfer P, Tapiero C (eds) Applied stochastic control in econometrics and management science. North-Holland, Amsterdam, pp 271–293

    Google Scholar 

  • Filar JA, Schultz TA, Thuijsman F, Vrieze OJ (1991) Nonlinear programming and stationary equilibria in stochastic games. Math Program 50:227–237

    Article  MATH  MathSciNet  Google Scholar 

  • Filar J, Vrieze K (1997) Competitive Markov decision processes. Springer, New York

    MATH  Google Scholar 

  • Horst U (2004) Stability of linear stochastic difference equations in strategically controlled random environments. Adv Appl Probab 35:961–981

    Article  MathSciNet  Google Scholar 

  • Horst U (2005) Stationary equilibria in discounted stochastic games with weakly interacting players. Games Econ Behav 51:83–108

    Article  MATH  MathSciNet  Google Scholar 

  • Klein E, Thompson AC (1984) Theory of correspondences. Wiley, New York

    MATH  Google Scholar 

  • Milgrom P, Roberts J (1990) Rationalizability, learning, and equilibrium in games with strategic complementarities. Econometrica 58:1255–1277

    Article  MATH  MathSciNet  Google Scholar 

  • Nash J (1951) Non-cooperative games. Ann Math 54:286–295

    Article  MathSciNet  Google Scholar 

  • Neveu J (1965) Mathematical foundations of the calculus of probability. Holden-Day, San Francisco

    MATH  Google Scholar 

  • Nowak AS (2003a) On a new class of nonzero-sum discounted stochastic games having stationary Nash equilibrium points. Int J Game Theory 32:121–132

    Article  MATH  Google Scholar 

  • Nowak AS (2003b) N-person stochastic games: extensions of the finite state space case and correlation. In: Neyman A, Sorin S (eds) Stochastic games and applications, NATO science series, series C: mathematical and physical sciences, vol 570. Kluwer, Dordrecht, pp 93–106

    Google Scholar 

  • Nowak AS, Jaśkiewicz A (2005) Nonzero-sum semi-Markov games with the expected average payoffs. Math Meth Oper Res 62:23–40

    Article  MATH  Google Scholar 

  • Nowak AS, Raghavan TES (1992) Existence of stationary correlated equilibria with symmetric information for discounted stochastic games. Math Oper Res 17:519–526

    MATH  MathSciNet  Google Scholar 

  • Rieder U (1979) Equilibrium plans for non-zero-sum Markov games. In: Moeschlin O, Pallaschke D (eds) Game theory and related topics. North-Holland, Amsterdam, pp 91–102

    Google Scholar 

  • Topkis DM (1978) Minimizing a submodular function on a lattice. Oper Res 26:305–321

    Article  MATH  MathSciNet  Google Scholar 

  • Topkis DM (1979) Equilibrium points in nonzero-sum n-person submodular games. SIAM J Control Optim 17:773–787

    Article  MATH  MathSciNet  Google Scholar 

  • Topkis DM (1998) Supermodularity and complementarity. Princeton University Press, Princeton

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics, Computer Science, and Econometrics, University of Zielona Góra, Podgórna 50, 65-246, Zielona Góra, Poland

    Andrzej S. Nowak

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  1. Andrzej S. Nowak
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Correspondence to Andrzej S. Nowak.

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Research partially supported by MNSW grant 1 P03A 01030.

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Nowak, A.S. On stochastic games in economics. Math Meth Oper Res 66, 513–530 (2007). https://doi.org/10.1007/s00186-007-0167-8

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  • DOI: https://doi.org/10.1007/s00186-007-0167-8

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