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Uncertain Information Structures and Backward Induction

  • Zuazo Garín, Peio

In everyday economic interactions, it is not clear whether sequential choices are visible or not to other participants: agents might be deluded about opponents'capacity to acquire,interpret or keep track of data, or might simply unexpectedly forget what they previously observed (but not chose). Following this idea, this paper drops the assumption that the information structure of extensive-form games is commonly known; that is, it introduces uncertainty into players' capacity to observe each others' past choices. Using this approach, our main result provides the following epistemic characterisation: if players (i) are rational,(ii) have strong belief in both opponents' rationality and opponents' capacity to observe others' choices, and (iii) have common belief in both opponents' future rationality and op-ponents' future capacity to observe others' choices, then the backward induction outcome obtains. Consequently, we do not require perfect information, and players observing each others' choices is often irrelevant from a strategic point of view. The analysis extends {from generic games with perfect information to games with not necessarily perfect information{the work by Battigalli and Siniscalchi (2002) and Perea (2014), who provide different sufficient epistemic conditions for the backward induction outcome.

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Paper provided by Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I in its series IKERLANAK with number Ikerlanak;2014-79.

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Date of creation: 25 Mar 2014
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Handle: RePEc:ehu:ikerla:12097
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Order Information: Postal: Dpto. de Fundamentos del Análisis Económico I, Facultad de CC. Económicas y Empresariales, Universidad del País Vasco, Avda. Lehendakari Aguirre 83, 48015 Bilbao, Spain
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  1. Akerlof, George A, 1970. "The Market for 'Lemons': Quality Uncertainty and the Market Mechanism," The Quarterly Journal of Economics, MIT Press, vol. 84(3), pages 488-500, August.
  2. Antonio Penta, 2012. "Higher Order Uncertainty and Information: Static and Dynamic Games," Econometrica, Econometric Society, vol. 80(2), pages 631-660, 03.
  3. Spence, A Michael, 1973. "Job Market Signaling," The Quarterly Journal of Economics, MIT Press, vol. 87(3), pages 355-74, August.
  4. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
  5. Samet, Dov, 1996. "Hypothetical Knowledge and Games with Perfect Information," Games and Economic Behavior, Elsevier, vol. 17(2), pages 230-251, December.
  6. Samet, Dov, 2013. "Common belief of rationality in games of perfect information," Games and Economic Behavior, Elsevier, vol. 79(C), pages 192-200.
  7. Battigalli, Pierpaolo & Friedenberg, Amanda, 2012. "Forward induction reasoning revisited," Theoretical Economics, Econometric Society, vol. 7(1), January.
  8. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
  9. Pierpaolo Battigalli, . "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Working Papers 111, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  10. Jeffrey Ely & Drew Fudenberg & David K. Levine, 2002. "When is Reputation Bad?," Harvard Institute of Economic Research Working Papers 1962, Harvard - Institute of Economic Research.
  11. Pierpaolo Battigalli & Alfredo Di Tillio & Dov Samet, 2011. "Strategies and interactive beliefs in dynamic games," Working Papers 375, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  12. Jeffrey Ely & Jusso Valimaki, 2002. "Bad Reputation," NajEcon Working Paper Reviews 391749000000000514, www.najecon.org.
    • Jeffrey C. Ely & Juuso Valimaki, 2002. "Bad Reputation," Discussion Papers 1348, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
  14. Giacomo Bonanno, 2012. "A dynamic epistemic characterization of backward induction without counterfactuals," Working Papers 122, University of California, Davis, Department of Economics.
  15. Paul Milgrom & John Roberts, 1980. "Predation, Reputation, and Entry Deterrence," Discussion Papers 427, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  16. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, June.
  17. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2007. "Interactive epistemology in games with payoff uncertainty," Research in Economics, Elsevier, vol. 61(4), pages 165-184, December.
  18. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  19. Aumann, Robert J., 1998. "On the Centipede Game," Games and Economic Behavior, Elsevier, vol. 23(1), pages 97-105, April.
  20. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
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