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Finite State Dynamic Games with Asymmetric Information: A Framework for Applied Work

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  • Fershtman, Chaim
  • Pakes, Ariel

Abstract

We present a framework for the applied analysis of dynamic games with asymmetric information. The framework consists of a definition of equilibrium, and an algorithm to compute it. Our definition of Applied Markov Perfect equilibrium is an extension of the definition of Markov Perfect equilibrium for games with asymmetric information; an extension chosen for its usefulness to applied research. Each agent conditions its strategy on the payoff or informationally relevant variables that are observed by that particular agent. The strategies are optimal given the beliefs on the evolution of these observed variables, and the rules governing the evolution of the observables are consistent with the equilibrium strategies. We then provide a simple algorithm for computing this equilibrium. The algorithm is easy to program and does not require computation of posterior distributions, explicit integration over possible future states, or information from all possible points in the state space. For specificity, we present our results in the context of a dynamic oligopoly game with collusion in which the outcome of firms’ investments are random and only observed by the investing agent. We then use this example to illustrate the computational properties of the algorithm.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 5024.

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Date of creation: Apr 2005
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Handle: RePEc:cpr:ceprdp:5024

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Keywords: cartels; collusive behaviour; dynamic games; numerical analysis;

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  1. Ariel Pakes & Michael Ostrovsky & Steve Berry, 2004. "Simple Estimators for the Parameters of Discrete Dynamic Games (with Entry/Exit Samples)," NBER Working Papers 10506, National Bureau of Economic Research, Inc.
  2. Paul Ellickson & Beresteanu Arie, 2005. "The Dynamics of Retail Oligopolies," 2005 Meeting Papers 829, Society for Economic Dynamics.
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Cited by:
  1. Weintraub, Gabriel Y. & Benkard, C. Lanier & Van Roy, Benjamin, 2007. "Computational Methods for Oblivious Equilibrium," Research Papers 1969, Stanford University, Graduate School of Business.
  2. Lewis, Greg & Backus, Matthew, 2009. "An Estimable Demand System for a Large Auction Platform Market," Department of Economics, Working Paper Series qt8vk5j2kr, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  3. Weintraub, Gabriel Y. & Benkard, C. Lanier & Van Roy, Benjamin, 2007. "Markov Perfect Industry Dynamics with Many Firms," Research Papers 1919r, Stanford University, Graduate School of Business.
  4. Luís Cabral, 2005. "Collusion Theory: Where to Go Next?," Journal of Industry, Competition and Trade, Springer, vol. 5(3), pages 199-206, December.
  5. Bernard Caillaud & Romain De Nijs, 2011. "Strategic loyalty reward in dynamic price Discrimination," Working Papers halshs-00622291, HAL.

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