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A Decision Analysis Approach to Solving the Signaling Game

Author

Listed:
  • Barry R. Cobb

    (Department of Economics and Business, Virginia Military Institute, Lexington, Virginia 24450)

  • Atin Basuchoudhary

    (Department of Economics and Business, Virginia Military Institute, Lexington, Virginia 24450)

Abstract

Decision analysis has traditionally been applied to choices under uncertainty involving a single decision maker. Game theory has been applied to solving games of strategic interaction between two or more players. Building upon recent work of van Binsbergen and Marx (van Binsbergen, J. H., L. M. Marx. 2007. Exploring relations between decision analysis and game theory. Decision Anal . 4 (1) 32--40), this paper defines a modified decision-theoretic approach to solving games of strategic interaction between two players. Using this method, the choices of the two players are modeled with separate decision trees comprised entirely of chance nodes. Optimal policies are reflected in the probabilities in the decision trees of each player. In many cases, the Nash equilibrium strategy for each player can be obtained by rolling back the opponent's decision tree. Results are demonstrated for the multistage signaling game, which is difficult to model using decision nodes to represent strategies, as in the approach of van Binsbergen and Marx.

Suggested Citation

  • Barry R. Cobb & Atin Basuchoudhary, 2009. "A Decision Analysis Approach to Solving the Signaling Game," Decision Analysis, INFORMS, vol. 6(4), pages 239-255, December.
    • Handle: RePEc:inm:ordeca:v:6:y:2009:i:4:p:239-255
    DOI: 10.1287/deca.1090.0148
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    References listed on IDEAS

    as
    1. Koller, Daphne & Milch, Brian, 2003. "Multi-agent influence diagrams for representing and solving games," Games and Economic Behavior, Elsevier, vol. 45(1), pages 181-221, October.
    2. Jules H. van Binsbergen & Leslie M. Marx, 2007. "Exploring Relations Between Decision Analysis and Game Theory," Decision Analysis, INFORMS, vol. 4(1), pages 32-40, March.
    3. Huseyin Cavusoglu & Srinivasan Raghunathan, 2004. "Configuration of Detection Software: A Comparison of Decision and Game Theory Approaches," Decision Analysis, INFORMS, vol. 1(3), pages 131-148, September.
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    Cited by:

    1. Jason R. W. Merrick & Fabrizio Ruggeri & Refik Soyer & L. Robin Keller, 2012. "From the Editors---Games and Decisions in Reliability and Risk," Decision Analysis, INFORMS, vol. 9(2), pages 81-85, June.
    2. L. Robin Keller & Ali Abbas & Manel Baucells & Vicki M. Bier & David Budescu & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Ahti Salo & George Wu, 2010. "From the Editors..," Decision Analysis, INFORMS, vol. 7(4), pages 327-330, December.
      • L. Robin Keller & Manel Baucells & Kevin F. McCardle & Gregory S. Parnell & Ahti Salo, 2007. "From the Editors..," Decision Analysis, INFORMS, vol. 4(4), pages 173-175, December.
      • L. Robin Keller & Manel Baucells & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Gregory S. Parnell & Ahti Salo, 2008. "From the Editors..," Decision Analysis, INFORMS, vol. 5(4), pages 173-176, December.
      • L. Robin Keller & Manel Baucells & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Gregory S. Parnell & Ahti Salo, 2009. "From the Editors ..," Decision Analysis, INFORMS, vol. 6(4), pages 199-201, December.
    3. Jie Xu & Jun Zhuang, 2016. "Modeling costly learning and counter-learning in a defender-attacker game with private defender information," Annals of Operations Research, Springer, vol. 236(1), pages 271-289, January.
    4. L. Robin Keller, 2012. "From the Editor---Decisions over Time (Exploding Offers or Purchase Regret), in Game Settings (Embedded Nash Bargaining or Adversarial Games), and in Influence Diagrams," Decision Analysis, INFORMS, vol. 9(1), pages 1-5, March.
    5. L. Robin Keller & Kelly M. Kophazi, 2012. "From the Editors ---Copulas, Group Preferences, Multilevel Defenders, Sharing Rewards, and Communicating Analytics," Decision Analysis, INFORMS, vol. 9(3), pages 213-218, September.
    6. L. Robin Keller & Kelly M. Kophazi, 2011. "From the Editors---Deterrence, Multiattribute Utility, and Probability and Bayes' Updating," Decision Analysis, INFORMS, vol. 8(2), pages 83-87, June.
    7. Rakesh K. Sarin & L. Robin Keller, 2013. "From the Editors: Probability Approximations, Anti-Terrorism Strategy, and Bull's-Eye Display for Performance Feedback," Decision Analysis, INFORMS, vol. 10(1), pages 1-5, March.
    8. Jesus Rios & David Rios Insua, 2012. "Adversarial Risk Analysis for Counterterrorism Modeling," Risk Analysis, John Wiley & Sons, vol. 32(5), pages 894-915, May.
    9. L. Robin Keller & Ali Abbas & J. Eric Bickel & Vicki M. Bier & David V. Budescu & John C. Butler & Philippe Delquié & Kenneth C. Lichtendahl & Jason R. W. Merrick & Ahti Salo & George Wu, 2011. "From the Editors ---Probability Scoring Rules, Ambiguity, Multiattribute Terrorist Utility, and Sensitivity Analysis," Decision Analysis, INFORMS, vol. 8(4), pages 251-255, December.
    10. L. Robin Keller, 2011. "Investment and Defense Strategies, Heuristics, and Games: From the Editor ..," Decision Analysis, INFORMS, vol. 8(1), pages 1-3, March.
    11. Du, Shaofu & Peng, Jing & Nie, Tengfei & Yu, Yugang, 2020. "Pricing strategies and mechanism choice in reward-based crowdfunding," European Journal of Operational Research, Elsevier, vol. 284(3), pages 951-966.

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    More about this item

    Keywords

    decision analysis; decision tree; game theory; mixed strategy; Nash equilibrium; signaling game;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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