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Compactification of Extensive Game Structures and Backward Dominance Procedure

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  • Shuige Liu

Abstract

We study the relationship between invariant transformations on extensive game structures and backward dominance procedure (BD), a generalization of the classical backward induction introduced in Perea (2014). We show that behavioral equivalence with unambiguous orderings of information sets, a critical property that guarantees BD's applicability, can be characterized by the classical Coalescing and a modified Interchange/Simultanizing in Battigalli et al. (2020). We also give conditions on transformations that improve BD's efficiency. In addition, we discuss the relationship between transformations and Bonanno (2014)'s generalized backward induction.

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  • Shuige Liu, 2019. "Compactification of Extensive Game Structures and Backward Dominance Procedure," Papers 1905.00355, arXiv.org, revised Nov 2020.
    • Handle: RePEc:arx:papers:1905.00355
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    References listed on IDEAS

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    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. Kreps, David M., 1990. "Game Theory and Economic Modelling," OUP Catalogue, Oxford University Press, number 9780198283812.
    3. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
    4. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396.
    5. Elmes Susan & Reny Philip J., 1994. "On the Strategic Equivalence of Extensive Form Games," Journal of Economic Theory, Elsevier, vol. 62(1), pages 1-23, February.
    6. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    7. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    8. Perea, Andrés, 2014. "Belief in the opponentsʼ future rationality," Games and Economic Behavior, Elsevier, vol. 83(C), pages 231-254.
    9. Reny Philip J., 1993. "Common Belief and the Theory of Games with Perfect Information," Journal of Economic Theory, Elsevier, vol. 59(2), pages 257-274, April.
    10. Krzysztof R. Apt, 2011. "Direct proofs of order independence," Economics Bulletin, AccessEcon, vol. 31(1), pages 106-115.
    11. Philip J. Reny, 1992. "Rationality in Extensive-Form Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 103-118, Fall.
    12. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    13. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915.
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