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Assessing Strategic Risk

  • R. J. Aumann
  • J. H. Dreze

In recent decades, subjective probabilities have been increasingly applied to an adversary's choices in strategic games (SGs). In games against nature (GANs), the subjective probability of a state can be elicited from lotteries yielding utility 1 if that state obtains, 0 otherwise. But in SGs, making such a lottery available changes the game, and so the players' incentives. Here, we propose a definition of subjective probabilities in SGs that uses actually available strategies only. The definition applies also to GANs where the decision maker's options are restricted. The probabilities that emerge need not be unique, but expected utilities are unique. (JEL D81)

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Article provided by American Economic Association in its journal American Economic Journal: Microeconomics.

Volume (Year): 1 (2009)
Issue (Month): 1 (February)
Pages: 1-16

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Handle: RePEc:aea:aejmic:v:1:y:2009:i:1:p:1-16
Note: DOI: 10.1257/mic.1.1.1
Contact details of provider: Web page: https://www.aeaweb.org/aej-micro
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  1. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
  2. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  3. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, June.
  4. O'Neill, Barry, 1994. "Game theory models of peace and war," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 29, pages 995-1053 Elsevier.
  5. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
  6. Joseph B. Kadane & Patrick D. Larkey, 1982. "Subjective Probability and the Theory of Games," Management Science, INFORMS, vol. 28(2), pages 113-120, February.
  7. Mariotti, Marco, 1995. "Is Bayesian Rationality Compatible with Strategic Rationality?," Economic Journal, Royal Economic Society, vol. 105(432), pages 1099-1109, September.
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