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Ergodic Equilibria in Stochastic Sequential Games

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  • Jeremy Large
  • Thomas Norman

Abstract

Many dynamic economic situations, including certain markets, can be fruitfully modeled as binary-action stochastic sequential games. Such games have a state variable, which in the case of a market might be the inventory of the good waiting for sale. Conditional on the state, players choose in sequence whether to subtract from it (buy) or add to it (sell). Under two assmptions - called Self-Regulation and Separable Preferences - we can derive the existence of a stationary, sequential equilibrium where the state is geometrically ergodic and stationary, and the two actions are played in the ratio required to avoid drift. We solve for the equilibrium strategies of a particular class of uninformed player. In equilibrium, players must solve a potentially complicated forecasting problem, but our analysis used stationarity to bypass the details of this problem, thus avoiding the (often intractable) dynamic programming usually required to solve stochastic games. This simplification allows us to develop powerful invariance and welfare results, and to provide a microfoundation for market-clearing price adjustment.

Suggested Citation

  • Jeremy Large & Thomas Norman, 2008. "Ergodic Equilibria in Stochastic Sequential Games," Economics Series Working Papers 405, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:405
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    File URL: http://www.economics.ox.ac.uk/materials/working_papers/paper405.pdf
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    References listed on IDEAS

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    1. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
    2. Large, Jeremy, 2009. "A market-clearing role for inefficiency on a limit order book," Journal of Financial Economics, Elsevier, vol. 91(1), pages 102-117, January.
    3. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832 Elsevier.
    4. Rubinstein, Ariel & Wolinsky, Asher, 1985. "Equilibrium in a Market with Sequential Bargaining," Econometrica, Econometric Society, vol. 53(5), pages 1133-1150, September.
    5. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-968, October.
    6. Hassin, Refael, 1986. "Consumer Information in Markets with Random Product Quality: The Case of Queues and Balking," Econometrica, Econometric Society, vol. 54(5), pages 1185-1195, September.
    7. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    8. Edelson, Noel M & Hildebrand, David K, 1975. "Congestion Tolls for Poisson Queuing Processes," Econometrica, Econometric Society, vol. 43(1), pages 81-92, January.
    9. Gale, Douglas, 1987. "Limit theorems for markets with sequential bargaining," Journal of Economic Theory, Elsevier, vol. 43(1), pages 20-54, October.
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    Cited by:

    1. Large, Jeremy, 2009. "A market-clearing role for inefficiency on a limit order book," Journal of Financial Economics, Elsevier, vol. 91(1), pages 102-117, January.

    More about this item

    Keywords

    Stochastic Games; Sequential Games; Ergodicity; Market Games;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition

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