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Finite Automata in Undiscounted Repeated Games with Private Monitoring

  • Julian Romero

I study two-player undiscounted repeated games with imperfect private monitoring. When strategies are restricted to those implementable by nite automata, fewer equilibrium outcomes are possible. When only two-state automata are allowed, a simple strategy, "Win-Stay, Lose-Shift," leads to cooperation. WSLS has the nice property that it is able to endogenously recoordinate back to cooperation after an incorrect signal. I show that WSLS is essentially the only equilibrium that leads to cooperation in the in nitely repeated Prisoner's Dilemma game. In addition, it is also an equilibrium for a wide range of 2 x 2 games. I also give necessary and sucient conditions on the structure of equilibrium strategies when players can use strategies implementable by fnite automata.

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Paper provided by Purdue University, Department of Economics in its series Purdue University Economics Working Papers with number 1260.

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Length: 38 pages
Date of creation: Mar 2011
Date of revision:
Handle: RePEc:pur:prukra:1260
Contact details of provider: Postal: Krannert Building, West Lafayette, IN 47907
Web page: http://www.krannert.purdue.edu/programs/phd

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  1. Pedro Dal Bo & Guillaume R. Frechette, . "The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence," Working Papers 2007-7, Brown University, Department of Economics.
  2. Olivier Compte & Andrew Postlewaite, 2007. "Effecting Cooperation," PIER Working Paper Archive 09-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 29 May 2009.
  3. Lehrer, Ehud, 1992. "On the Equilibrium Payoffs Set of Two Player Repeated Games with Imperfect Monitoring," International Journal of Game Theory, Springer, vol. 20(3), pages 211-26.
  4. Obara, Ichiro, 2009. "Folk theorem with communication," Journal of Economic Theory, Elsevier, vol. 144(1), pages 120-134, January.
  5. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  6. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 2058, David K. Levine.
  7. Sabourian, Hamid, 1998. "Repeated games with M-period bounded memory (pure strategies)," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 1-35, August.
  8. Reinhard Selten & Thorsten Chmura, 2008. "Stationary Concepts for Experimental 2x2-Games," American Economic Review, American Economic Association, vol. 98(3), pages 938-66, June.
  9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  10. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
  11. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  12. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
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