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Algorithms for Finding Repeated Game Equilibria

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Abstract

This paper describes computational techniques for finding all equilibria in infinitely repeated games with discounting and perfect monitoring. It illustrates these techniques with a three player Cournot game. This is the first infinitely repeated three player game ever solved. The paper also presents the solution for the set of equilibria in a two country tariff war. In both games the set of equilibria is large even when the players are not patient.

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References

  1. Abreu, D. 1983, On the theory of infinitely repeated games with discounting. Ph.D. Thesis, Princeton University.

  2. Abreu, D. 1988, On the theory of infinitely repeated games with discounting. Econometrica, 56, 383–396.

    Google Scholar 

  3. Abreu, D. 1986, Extremal equilibria of oligopolistic supergames. Journal of Economic Theory, 39, 191–225.

    Google Scholar 

  4. Abreu, D., Pearce, D. and Stacchetti, E. 1986, Optimal cartel equilibria with imperfect monitoring. Journal of Economic Theory, 39, 251–269.

    Google Scholar 

  5. Abreu, D., Pearce, D. and Stacchetti, E. 1990, Toward a theory of discounted repeated games with imperfect monitoring. Econometrica, 58 1041–1064.

    Google Scholar 

  6. Conklin, J. and Judd, K. 1993, Computing Supergame Equilibria. mimeo, Stanford.

  7. Cronshaw, M.B. and Luenberger, D.G. 1994, Strongly symmetric subgame perfect equilibria in infinitely repeated games with perfect monitoring and discounting. Games and Economic Behavior, 6, 220–237.

    Google Scholar 

  8. Cronshaw, M.B. and Rutherford, T.F. 1993, (Even Impatient) Small countries can win tariff wars. mimeo, University of Colorado.

  9. Drud, A. 1985, A GRG code for large sparse dynamic nonlinear optimization problems. Mathematical Programming, 31, 153–191.

    Google Scholar 

  10. Friedman, J.W. 1977, Oligopoly and the theory of games. North Holland.

  11. Fudenberg, D. and Maskin, E. 1986, The Folk theorem in repeated games with discounting and incomplete information. Econometrica, 54, 533–554.

    Google Scholar 

  12. Fudenberg, D. and Maskin, E. 1991, On the dispensability of public randomization in discounted repeated games. Journal of Economic Theory, 53, 428–438.

    Google Scholar 

  13. Kennan, J. and Riezman, R. 1988, Do big countries win tariff wars? International Economic Review, 29, 81–85.

    Google Scholar 

  14. Gasiorek, M., Smith, A. and Venables, A.J. 1989, Tariffs, subsidies and retaliation. European Economic Review, 33, 480–489.

    Google Scholar 

  15. Harrison, G. and Rutström, E.E. 1991, Trade wars, trade negotiations and applied game theory. The Economic Journal, 101, 420–435.

    Google Scholar 

  16. Markusen, J.R. and Wigle, R.M. 1989, Nash equilibrium tariffs for the United States and Canada: The roles of country size, scale economies and capital mobility. Journal of Political Economy, 97, 368–386.

    Google Scholar 

  17. Riezman, R. 1991, Dynamic tariffs with asymmetric information. Journal of International Economics, 30, 267–283.

    Google Scholar 

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CRONSHAW, M.B. Algorithms for Finding Repeated Game Equilibria. Computational Economics 10, 139–168 (1997). https://doi.org/10.1023/A:1008670607684

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  • DOI: https://doi.org/10.1023/A:1008670607684

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