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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.

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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 405.

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Date of creation: 01 Oct 2008
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Handle: RePEc:oxf:wpaper:405

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Keywords: Stochastic Games; Sequential Games; Ergodicity; Market Games;

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  1. Rubinstein, Ariel & Wolinsky, Asher, 1985. "Equilibrium in a Market with Sequential Bargaining," Econometrica, Econometric Society, vol. 53(5), pages 1133-50, September.
  2. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  3. 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.
  4. MERTENS, Jean-François, . "Stochastic games," CORE Discussion Papers RP -1587, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Hassin, Refael, 1986. "Consumer Information in Markets with Random Product Quality: The Case of Queues and Balking," Econometrica, Econometric Society, vol. 54(5), pages 1185-95, September.
  6. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July.
  7. Edelson, Noel M & Hildebrand, David K, 1975. "Congestion Tolls for Poisson Queuing Processes," Econometrica, Econometric Society, vol. 43(1), pages 81-92, January.
  8. 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 937-68, October.
  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. Jeremy Large, 2006. "A Market-Clearing Role for Inefficiency on a Limit Order Book," Economics Papers 2006-W08, Economics Group, Nuffield College, University of Oxford.

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