Game theory without partitions, and applications to speculation and consensus. (English) Zbl 1508.91142
Summary: Decision theory and game theory are extended to allow for information processing errors. This extended theory is then used to reexamine market speculation and consensus, both when all actions (opinions) are common knowledge and when they may not be. Five axioms of information processing are shown to be especially important to speculation and consensus. They are called nondelusion, knowing that you know (KTYK), nested, balanced, and positively balanced. We show that it is necessary and sufficient that each agent’s information processing errors be (1) nondeluded and balanced so that the agents cannot agree to disagree, (2) nondeluded and positively balanced so that it cannot be common knowledge that they are speculating, and (3) nondeluded and KTYK and nested so that agents cannot speculate in equilibrium. Each condition is strictly weaker than the next one, and the last is strictly weaker than partition information.
References:
| [1] | Aumann, R. 1976. “Agreeing to Disagree.” The Annals of Statistics 4: 1236-39, doi:10.1214/aos/1176343654. · Zbl 0379.62003 · doi:10.1214/aos/1176343654 |
| [2] | Bacharach, M. 1985. “Some extensions of a claim of Aumann in an axiomatic model of knowledge.” Journal of Economic Theory 37: 167-90, doi:10.1016/0022-0531(85)90035-3. · Zbl 0597.90003 · doi:10.1016/0022-0531(85)90035-3 |
| [3] | Brandenburger, A., E. Dekel, and J. Geanakoplos. 1992. Correlated Equilibrium with Generalized Information Structures, 4, 182-201. Games and Economic Behavior. doi:10.1016/0899-8256(92)90014-J. · Zbl 0765.90091 · doi:10.1016/0899-8256(92)90014-J |
| [4] | Brandenburger, A., J. Geanakoplos, R. McKelvey, L. Nielson, and T. Page. 1990. “Common Knowledge of an Aggregate of Expectations.” Econometrica 58: 1235-9, doi:10.2307/2938308. · Zbl 0728.90005 · doi:10.2307/2938308 |
| [5] | Brown, D., and J. Geanakoplos. 1988. Common Knowledge without Partitions. Unpublished. |
| [6] | Cave, J. 1983. “Learning to Agree.” Economic Letters 12: 147-52, doi:10.1016/0165-1765(83)90126-x. · Zbl 1273.91282 · doi:10.1016/0165-1765(83)90126-x |
| [7] | Doyle, Arthur Conan. 1901. The Adventure of Silver Blaze: The Strand Magazine. |
| [8] | Dubey, P., J. Geanakoplos, and M. Shubik. 1987. “The Revelation of Information in Strategic Market Games: A Critique of Rational Expectations Equilibrium.” Journal of Mathematical Economics 16(2): 105-38, doi:10.1016/0304-4068(87)90002-4. · Zbl 0637.90016 · doi:10.1016/0304-4068(87)90002-4 |
| [9] | Geanakoplos, J. 1987. Common Knowledge of Actions Negates Asymmetric Information: mimeo, Yale University. |
| [10] | Geanakoplos, J. 1988. Common Knowledge, Bayesian Learning, and Market Speculation with Bounded Rationality: mimeo, Yale University. |
| [11] | Geanakoplos, J., and H. Polemarchakis. 1982. “We Can’t Disagree Forever.” Journal of Economic Theory 28 (1): 192-200, doi:10.1016/0022-0531(82)90099-0. · Zbl 0486.90031 · doi:10.1016/0022-0531(82)90099-0 |
| [12] | Kreps, D. 1977. “A Note on Fulfilled Expectations Equilibrium.” Journal of Economic Theory 14 (1): 32-43, doi:10.1016/0022-0531(77)90083-7. · Zbl 0351.90011 · doi:10.1016/0022-0531(77)90083-7 |
| [13] | Lewis, D. 1969. Conventions: A Philosophical Study. Cambridge: Harvard University Press. |
| [14] | McKelvey, R., and T. Page. 1986. “Common Knowledge, Consensus, and Aggregate Information.” Econometrica 54: 109-27, doi:10.2307/1914160. · Zbl 0578.90019 · doi:10.2307/1914160 |
| [15] | Milgrom, P., and N. Stokey. 1982. “Information, Trade, and Common Knowledge.” Journal of Economic Theory 26: 17-27, doi:10.1016/0022-0531(82)90046-1. · Zbl 0485.90018 · doi:10.1016/0022-0531(82)90046-1 |
| [16] | Monderer, D., and D. Samet. 1988. Approximating Common Knowledge with Common Beliefs, 1, 2nd ed., 170-190. The Journal of Games and Economic Behavior. doi:10.1016/0899-8256(89)90017-1. · Zbl 0755.90110 · doi:10.1016/0899-8256(89)90017-1 |
| [17] | Samet, D. 1987. Ignoring Ignorance and Agreeing to Disagree. MEDS Discussion Paper: Northwestern University. · Zbl 0719.90022 |
| [18] | Sebenius, J., and J. Geanakoplos. 1983. “Don’t Bet On It: Contingent Agreements with Asymmetric Information.” Journal of the American Statistical Association 78: 424-6, doi:10.1080/01621459.1983.10477988. · Zbl 0971.62500 · doi:10.1080/01621459.1983.10477988 |
| [19] | Shin, H. 1987. Logical Structure of Common Knowledge, I and II. unpublished. Oxford: Nuffield College. |
| [20] | Strotz, R. H. 1955-6. “Myopia and Inconsistency in Dynamic Utility Maximization.” Review of Economic Studies 23: 165-80, doi:10.2307/2295722. · doi:10.2307/2295722 |
| [21] | Tirole, J. 1982. “On the Possibility of Speculation under Rational Expectations.” Econometrica 50 (5): 1163-81, doi:10.2307/1911868. · Zbl 0488.90026 · doi:10.2307/1911868 |
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