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Games with Espionage

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  • Eilon Solan
  • Leeat Yariv

Abstract

"There is no place where espionage is not possible." -Sun Tzu, The Art of War, approximately 500BC We consider extensive form games in which players decide on their strategies before the start of play and can purchase noisy information about their opponents' decisions concerning future response policies (i.e., spy on their opponents' decisions). This addition to the agent's optimization problem naturally changes the set of subgame perfect equilibria (SPE). For example, in the chain-store model, for sufficiently small costs of espionage, the population of Incumbents splits into a positive fraction that accommodates and a positive fraction that fights. For general 2x2 games in extensive form, the existence of equilibria with espionage turns out to depend on the difference between the Stackelberg equilibrium payoffs and the SPE payoffs. We characterize the set of equilibria with espionage as a sunset of the set of correlated equilibria. Welfare and Pareto properties of such equilibria are also explored.

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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1257.

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Date of creation: Jul 1998
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Handle: RePEc:nwu:cmsems:1257

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Keywords: Espionage; subgame perfect equilibria; information; timing.;

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References

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  1. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-85, November.
  2. Drew Fudenberg & David K. Levine, 1995. "Reputation and Equilibrium Selection in Games with a Patient Player," Levine's Working Paper Archive 103, David K. Levine.
  3. Robert Townsend, 1979. "Optimal contracts and competitive markets with costly state verification," Staff Report 45, Federal Reserve Bank of Minneapolis.
  4. Fudenberg, D., 1991. "Maintaining a Reputation when Strategies are Imperfectly Observed," Working papers 589, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. S. Sorin, 1998. "Distribution equilibrium I : Definition and examples," THEMA Working Papers 98-35, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  6. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-51, November.
  7. Damme, E.E.C. van & Hurkens, J.P.M., 1997. "Games with imperfectly observable commitment," Open Access publications from Tilburg University urn:nbn:nl:ui:12-74216, Tilburg University.
  8. Sadanand, Asha & Sadanand, Venkatraman, 1996. "Firm Scale and the Endogenous Timing of Entry: a Choice between Commitment and Flexibility," Journal of Economic Theory, Elsevier, vol. 70(2), pages 516-530, August.
  9. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  10. Akihiko Matsui, 1988. "Information Leakage Forces Cooperation," Discussion Papers 786, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Van Damme, E. & Hurkens, S., 1993. "Commitment Robust Equilibria and Endogenous Timing," Papers 9356, Tilburg - Center for Economic Research.
  12. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
  13. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  14. Kamien, Morton I. & Tauman, Yair & Zamir, Shmuel, 1990. "On the value of information in a strategic conflict," Games and Economic Behavior, Elsevier, vol. 2(2), pages 129-153, June.
  15. Mookherjee, Dilip & Png, Ivan, 1989. "Optimal Auditing, Insurance, and Redistribution," The Quarterly Journal of Economics, MIT Press, vol. 104(2), pages 399-415, May.
  16. Mailath George J., 1993. "Endogenous Sequencing of Firm Decisions," Journal of Economic Theory, Elsevier, vol. 59(1), pages 169-182, February.
  17. Hirshleifer, Jack, 1971. "The Private and Social Value of Information and the Reward to Inventive Activity," American Economic Review, American Economic Association, vol. 61(4), pages 561-74, September.
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Citations

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Cited by:
  1. Alex Barrachina & Yair Tauman & Amparo Urbano Salvador, 2013. "Entry and espionage with noisy signals," Discussion Papers in Economic Behaviour 0113, University of Valencia, ERI-CES.
  2. D. Thorleuchter & D. Van Den Poel, 2012. "Protecting Research and Technology from Espionage," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 12/824, Ghent University, Faculty of Economics and Business Administration.
  3. repec:ebl:ecbull:v:3:y:2005:i:18:p:1-4 is not listed on IDEAS
  4. Van Gorder, Robert A. & Caputo, Michael R., 2010. "Envelope theorems for locally differentiable open-loop Stackelberg equilibria of finite horizon differential games," Journal of Economic Dynamics and Control, Elsevier, vol. 34(6), pages 1123-1139, June.
  5. S. Ho, 2008. "Extracting the information: espionage with double crossing," Journal of Economics, Springer, vol. 93(1), pages 31-58, February.

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