Abstract
We present a generalization of Amir’s continuous model of nonsymmetric infinite-horizon discounted stochastic game of capital accumulation. We show that the game has a pure-strategy equilibrium in strategies that are nondecreasing and have Lipschitz property. To prove that, we use a technique based on an approximation of continuous model by the analogous discrete one.
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References
Amir R. (1996) Continuous Stochastic Games of Capital Accumulation with Convex Transitions. Games Econ. Behavior 15, 111–131.
Bartle R. (1976) The Elements of Real Analysis. Wiley, New York.
Billingsley P. (1968) Convergence of Probability Measures. Wiley, New York.
Dutta P.K., Sundaram R.K. (1992) Markovian Equilibrium in a Class of Stochastic Games: Existence Theorems for Discounted and Undiscounted Models. Econ. Theory 2, 197–214.
Levhari D., Mirman L. (1980) The Great Fish War: An Example Using a Dynamic Cournot-Nash Solution. Bell J. Econ 11, 322–334.
Majumdar M., Sundaram R.K. (1991) Symmetric Stochastic Games of Resource Extraction: Existence of Nonrandomized Stationary Equilibrium. in Stochastic Games and Related Topics (Raghavan et. al. Eds.). Kluwer, Dordrecht.
Nowak A.S. (2003) On a New Class of Nonzero-sum Discounted Stochastic Games Having Stationary Nash Equilibrium Points. Internat. J. Game Theory 32: 121–132.
Nowak A.S. (2003) N-person Stochastic Games: Extensions of the Finite State Space Case and Correlation. In: Stochastic Games and Applications (Neyman A., Sorin S. Eds.). Kluwer, Dordrecht, pp. 93–106.
Nowak A.S., Szajowski P. (2003) On Nash Equilibria in Stochastic Games of Capital Accumulation. Game Theory Appl. 9: 118–129.
Sundaram R.K. (1989) Perfect Equilibrium in Non-Randomized Strategies in a Class of Symmetric Dynamic Games. J. Econ. Theory 47, 153–177.
Więcek P. (2003) Convex Stochastic Games of Capital Accumulation with Nondivisible Money Unit. Scientiae Mathematicae Japonicae 57, 397–411.
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© 2005 Birkhäuser Boston
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Więcek, P. (2005). Continuous Convex Stochastic Games of Capital Accumulation. In: Nowak, A.S., Szajowski, K. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 7. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4429-6_6
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DOI: https://doi.org/10.1007/0-8176-4429-6_6
Publisher Name: Birkhäuser Boston
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