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The Deception of the Greeks: Generalizing the Information Structure of Extensive Form Games

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Oliver Board

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Abstract

The standard model of an extensive form game rules out an important phenomenon in situations of strategic interaction: deception. Using examples from the world of ancient Greece and from modern-day Wall Street, we show how the model can be generalized to incorporate this phenomenon. Deception takes place when the action observed by a player is different from the action actually taken. The standard model does allow imperfect information (modeled by non-singleton information sets), but not deception: the actual action taken is never ruled out. Our extension of extensive form games relaxes the assumption that the information sets partition the set of nodes, so that the set of nodes considered possible after a certain action is taken might not include the actual node. We discuss the implications of this relaxation, and show that in certain games deception is inconsistent with common knowledge of rationality even along the backward induction path. `You are to hear now how the Greeks tricked us. From this one proof of their perfidy you may understand them all` (Aeneas).

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 137.

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Date of creation: 2002
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Handle: RePEc:oxf:wpaper:137

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Keywords: deception extensive form games information

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Reny, Philip J, 1992. "Rationality in Extensive-Form Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 103-18, Fall. [Downloadable!] (restricted)
  2. Vincent P. Crawford, 2001. "Lying for Strategic Advantage: Rational and Boundedly Rational Misrepresentation of Intentions," University of California at San Diego, Economics Working Paper Series 2001-16, Department of Economics, UC San Diego. [Downloadable!]
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  3. Piccione, Michele & Rubinstein, Ariel, 1997. "On the Interpretation of Decision Problems with Imperfect Recall," Games and Economic Behavior, Elsevier, vol. 20(1), pages 3-24, July. [Downloadable!] (restricted)
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  4. Aumann, Robert J. & Hart, Sergiu & Perry, Motty, 1997. "The Absent-Minded Driver," Games and Economic Behavior, Elsevier, vol. 20(1), pages 102-116, July. [Downloadable!] (restricted)
  5. Sobel, Joel, 1985. "A Theory of Credibility," Review of Economic Studies, Blackwell Publishing, vol. 52(4), pages 557-73, October. [Downloadable!] (restricted)
  6. Benabou, Roland & Laroque, Guy, 1992. "Using Privileged Information to Manipulate Markets: Insiders, Gurus, and Credibility," The Quarterly Journal of Economics, MIT Press, vol. 107(3), pages 921-58, August. [Downloadable!] (restricted)
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  7. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-51, November. [Downloadable!] (restricted)
  8. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Oliver Board, 2003. "The Not-So-Absent-Minded Driver," Economics Series Working Papers 147, University of Oxford, Department of Economics. [Downloadable!]
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  2. Oliver Board, 2002. "Dynamic Interactive Epistemology," Economics Series Working Papers 125, University of Oxford, Department of Economics. [Downloadable!]
    Other versions:
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