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Complementarity and Diagonal Dominance in Discounted Stochastic Games

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  • Rabah Amir

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Abstract

We consider discounted stochastic games characterized by monotonicity, supermodularity and diagonal dominance assumptions on the reward functions and the transition law. A thorough novel discussion of the scope and limitations of this class of games is provided. Existence of a Markov-stationary equilibrium for the infinite-horizon game, proved by Curtat (1996), is summarized. Uniqueness of Markov equilibrium and dominance solvability of the finite-horizon game are established. In both cases, the equilibrium strategies and the corresponding value functions are nondecreasing Liptschitz-continuous functions of the state vector. Some specific economic applications are discussed. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • Rabah Amir, 2002. "Complementarity and Diagonal Dominance in Discounted Stochastic Games," Annals of Operations Research, Springer, vol. 114(1), pages 39-56, August.
  • Handle: RePEc:spr:annopr:v:114:y:2002:i:1:p:39-56:10.1023/a:1021097716583
    DOI: 10.1023/A:1021097716583
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    Cited by:

    1. He, Wei & Sun, Yeneng, 2017. "Stationary Markov perfect equilibria in discounted stochastic games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 35-61.
    2. Łukasz Balbus & Łukasz Woźny, 2016. "A Strategic Dynamic Programming Method for Studying Short-Memory Equilibria of Stochastic Games with Uncountable Number of States," Dynamic Games and Applications, Springer, vol. 6(2), pages 187-208, June.
    3. Pawel Dziewulski & John Quah, 2016. "Supermodular value functions and supermodular correspondences," Economics Series Working Papers 795, University of Oxford, Department of Economics.
    4. Piotr Więcek, 2017. "Total Reward Semi-Markov Mean-Field Games with Complementarity Properties," Dynamic Games and Applications, Springer, vol. 7(3), pages 507-529, September.
    5. Sachin Adlakha & Ramesh Johari, 2013. "Mean Field Equilibrium in Dynamic Games with Strategic Complementarities," Operations Research, INFORMS, vol. 61(4), pages 971-989, August.

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