Non-Additive Beliefs in Solvable Games

Springer Science and Business Media LLC - Tập 49 - Trang 313-338 - 2000
Hans Haller1
1Department of Economics, Virginia Polytechnic Institute andState University, Blacksburg, USA

Tóm tắt

This paper studies how the introduction of non-additive probabilities (capacities) affects the solvability of strategic games.

Tài liệu tham khảo

Aumann, R.J. (1987), Correlated Equilibrium as an Expression of Bayesian Rationality, Econometrica 55: 1–18. Ben-Porath, E., Gilboa, I. and Schmeidler, D. (1997), On the Measurement of Inequality under Uncertainty, Journal of Economic Theory 75: 194–204. Billingsley, P. (1968), Convergence of Probability Measures, John Wiley & Sons, Inc., New York. Camerer, C. and Weber, M. (1992), Recent Developments in Modeling Preferences: Uncertainty and Ambiguity, Journal of Risk and Uncertainty 5: 325–370. Denneberg, D. (1994a), Conditioning (Updating) Non-Additive Probability Measures, Annals of Operations Research 52: 21–42. Denneberg, D. (1994b), Non-Additive Measure and Integral, Kluwer, Dordrecht. Denneberg, D. (1995), Extensions of a Measurable Space and Linear Representation of the Choquet Integral, Universität Bremen, Mathematische Arbeitspapiere Nr. 45. Dow, J., and Werlang, S.R.C. (1992a), Uncertainty Aversion, Risk Aversion and the Optimal Choice of Portfolio, Econometrica 60: 197–204. Dow, J. and Werlang, S.R.C. (1992b), Excess Volatility of Stock Prices and Knightian Uncertainty, European Economic Review 36: 631–638. Dow, J. and Werlang, S.R.C. (1994), Equilibrium under Knightian Uncertainty: Breaking Down Backward Induction, Journal of Economic Theory 64: 305–324. Dow, J., Orioli, S. and Werlang, S.R.C. (1996), The Centipede Game under Knightian Uncertainty, mimeo. Eichberger, J. and Kelsey, D. (1995), Signalling Games with Uncertainty, mimeo. Eichberger, J. and Kelsey, D. (1996a), Free Riders Do Not Like Uncertainty, mimeo. Eichberger, J., and Kelsey, D. (1996b), Uncertainty Aversion and Preference for Randomisation, Journal of Economic Theory 71: 31–43. Eichberger, J., and Kelsey, D. (1996c), Uncertainty Aversion and Dynamic Consistency, International Economic Review 37: 625–640. Eichberger, J. and Kelsey, D. (1999), E-Capacities and the Ellsberg Paradox, Theory and Decision 46: 107–140. Eichberger, J. and Kelsey, D. (2000), Non-Additive Beliefs and Strategic Equilibria, Games and Economic Behavior 30: 183–215. Epstein, L.G. (1997), Preference, Rationalizability and Equilibrium, Journal of Economic Theory 73: 1–29. Ghirardato, P. (1994a), Agency Theory with Non-Additive Uncertainty, mimeo. Ghirardato, P. (1994b), Coping with Ignorance: Unforeseen Contingencies and Non-Additive Uncertainty, mimeo. Ghirardato, P. (1997), On Independence for Non-Additive Measures, with a Fubini Theorem, Journal of Economic Theory 73: 261–291. Ghirardato, P., and Le Breton, M. (2000), Choquet Rationalizability, Journal of Economic Theory 90: 277–285. Ghirardato, P., and Marinacci, M. (1997), Ambiguity Made Precise: A Comparative Foundation and Some Implications, California Institute of Technology, Social Science Working Paper 1026. Gilboa, I. (1987), Expected Utility with Purely Subjective Non-Additive Probabilities, Journal of Mathematical Economics 16: 65–88. Gilboa, I. and Schmeidler, D. (1989), Maxmin Expected Utility with a Non-Unique Prior, Journal of Mathematical Economics 18: 141-153. Gilboa, I. and Schmeidler, D. (1993), Updating Ambiguous Beliefs, Journal of Economic Theory 59: 33–49. Groes, E., Jacobsen, H.J., Sloth, B. and Tranæs, T. (1998), Nash Equilibrium in Lower Probabilities, Theory and Decision 44: 37–66. Harsanyi, J.C. (1973), Games with Randomly Disturbed Payoffs: A New Rationale for Mixed Strategy Equilibrium Points, International Journal of Game Theory 2: 1–23. Hendon, E., Jacobsen, H.J., Sloth, B. and Tranæs, T. (1994), Expected Utility with Lower Probabilities, Journal of Risk and Uncertainty 8: 197–216. Hendon, E., Jacobsen, H.J., Sloth, B. and Tranæs, T. (1996), The Product of Capacities and Belief Functions, Mathematical Social Sciences 32: 177–202. Hougaard, J.L. and Keiding, H. (1996), Representation of Preferences on Fuzzy Measures by a Fuzzy Integral, Mathematical Social Sciences 31: 1–17. Jaffrey, Y. (1992) Bayesian Updating and Belief Functions, IEEE Transactions on Systems, Man and Cybernetics 22: 1144–1152. Kelsey, D. (1994), Maxmin Expected Utility and Weight of Evidence, Oxford Economic Papers 46: 425–444. Kelsey, D., and Quiggin, J. (1992), Theories of Choice under Ignorance and Uncertainty, Journal of Economic Surveys 6: 133–153. Klibanoff, P. (1996a), Uncertainty, Decision, and Normal Form Games, mimeo. Klibanoff, P. (1996b), Characterizing Uncertainty Aversion Through Preference for Mixture, mimeo, forthcoming in Social Choice and Welfare. Lehrer, E. (1996), An Approach to the Conditional Expectation with Non-Additive Probabilities, mimeo. Lo, K.C. (1996), Equilibrium in Beliefs Under Uncertainty, Journal of Economic Theory 71: 443–484. Lo, K.C. (1999), Extensive Form Games with Uncertainty Averse Players, Games and Economic Behavior 28: 256–270. Machina, M. (1982), Expected Utility Analysis Without the Independence Axiom, Econometrica 50: 277–323. Machina, M. (1989), Dynamic Consistency and Non-Expected Utility Models of Choice Under Uncertainty, Journal of Economic Literature 27: 1622–1668. Marinacci, M. (2000), Ambiguous Games, Games and Economic Behavior 31: 191–219. Moulin, H. (1979), Dominance Solvable Voting Schemes, Econometrica 47: 1337–1351. Mukerji, S. (1997), Understanding the Non-Additive Probability Decision Model, Economic Theory 9: 23–46. Mukerji, S. (1998), Ambiguity and Incompleteness of Contractual Form, American Economic Review 88: 1207–1231. Nash, J. (1951), Non-Cooperative Games, Annals of Mathematics 54: 286–295. Nehring, K. (1999), Capacities and Probabilistic Beliefs: A Precarious Coexistence, Mathematical Social Sciences 38: 197–213. Nehring, K. (1999), Preference for Flexibility in a Savage Framework, Econometrica 67: 101–119. Parthasarathy, K.R. (1967), Probability Measures on Metric Spaces, Academic Press: New York and London. Quiggin, J. (1982), A Theory of Anticipated Utility, Journal of Economic Behavior and Organization 3: 323–343. Ritzberger, K. (1996), On Games under Expected Utility with Rank Dependent Probabilities, Theory and Decision 40: 1–27. Rosenmüller, J. (1982), L.P.-Games with Sufficiently Many Players, International Journal of Game Theory 11: 129–149. Rosenmüller, J. and Weidner, H.G. (1973), A Class of Extreme Convex Set Functions with Finite Carrier, Advances in Mathematics 10: 1–38. Rosenmüller, J. and Weidner, H.G. (1974), Extreme Convex Set Functions with Finite Carrier: General Theory, Discrete Mathematics 10: 343–382. Ryan, M.J. (1998a), Supports and the Updating of Capacities, University of Auckland. Ryan, M. (1998b), A Refinement of Dempster-Shafer Equilibrium, University of Auckland. Sarin, R. and Wakker, P. (1992), A Simple Axiomatisation of Non-Additive Expected Utility, Econometrica 60: 1255–1272. Schmeidler, D. (1989), Subjective Probability and Expected Utility without Additivity, Econometrica 57: 571–587. Sundberg, C. and Wagner, C. (1992), Generalized Finite Differences and Bayesian Conditioning of Choquet Capacities, Advances in Applied Mathematics 13: 262–272. Wakker, P. (1987), From Decision Making under Uncertainty to Game Theory, pp. 163-180, in H.J.M. Peters and O.J. Vrieze (eds.), Surveys of Game Theory and Related Topics, CWI Tract 39, Centre for Mathematics and Computer Science, Amsterdam. Wasserman, L.A., and Kadane, J.B. (1990), Bayes' Theorem for Choquet Capacities, Annals of Statistics 18: 1328–1339.