(s,S) Equilibria in Stochastic games with an Application to Product Innovations
We study a class of two-player continuous time stochastic games in which agents can make (costly) discrete or discontinuous changes in the variables that affect their payoffs. It is shown that in these games there are Markov perfect equilibria of the two-sided (s,S) rule type. In such equilibria at a critical low state (resp. high state) player 1 (resp. 2) effects a discrete change in the environment. In some of these equilbria either or both players may be passive. On account of the presence of fixed costs (to discrete changes) the payoffs are non-convex and hence standard existence arguments fail. We prove that the best response map satisfies a surprisingly strong monotonicity condition and use this to establish the existence of Markov perfect equilibria. The first-best solution is also a two-sided (s,S) rule but the symmetric first-best solution has a wider s-S band than the symmetric Markovian equilibria. A further contribution of this paper is the development of a framework for continuous time games, which allows players to react instantaneously to their opponent's moves. We mention various applications of the theory and discuss in detail an application to product innovations.
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|Date of creation:||1991|
|Date of revision:|
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dixit, Avinash K, 1989.
"Entry and Exit Decisions under Uncertainty,"
Journal of Political Economy,
University of Chicago Press, vol. 97(3), pages 620-38, June.
- Boyan Jovanovic & Rafael Rob, 1990.
"Long Waves and Short Waves: Growth Through Intensive and Extensive Search,"
Levine's Working Paper Archive
2082, David K. Levine.
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- Lee, Tom & Wilde, Louis L, 1980. "Market Structure and Innovation: A Reformulation," The Quarterly Journal of Economics, MIT Press, vol. 94(2), pages 429-36, March.
- Mansfield, Edwin & Schwartz, Mark & Wagner, Samuel, 1981. "Imitation Costs and Patents: An Empirical Study," Economic Journal, Royal Economic Society, vol. 91(364), pages 907-18, December.
- Stinchcombe, Maxwell B., 1992. "Maximal strategy sets for continuous-time game theory," Journal of Economic Theory, Elsevier, vol. 56(2), pages 235-265, April.
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- Prajit K. Dutta, 1990. "Innovation and Product Differentiation," Discussion Papers 894, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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