Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-17T04:20:17.470Z Has data issue: false hasContentIssue false
  • English
  • Français

Information in Continuous Time Decision Models with Many Agents

Published online by Cambridge University Press:  27 July 2009

Bruno Bassan ,
Monica Brezzi  and
Marco Scarsini
Bruno Bassan
Affiliation:
Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 1-20133 Milano. Italy
Monica Brezzi
Affiliation:
Dipartimento di Scienze Statistiche, Università di Padova, Via San Francesco 33, 1-35127 Padova, Italy
Marco Scarsini
Affiliation:
Dipartimento di Scienze, Università D'Annunzio, Viale Pindaro 42, 1-65127 Pescara, Italy
Get access Rights & Permissions [Opens in a new window]

Extract

Several agents with different subjective probabilities make a binary decision at a time determined by a planner. Each agent chooses the action that has the highest probability of success. Given that their probabilities differ, so will their choices. From time 0 until decision time, all the agents are entitled to access the same increasing flow of information. The planner, who gains from having as many agents as possible making the right choice, faces the following tradeoff: the more information she feeds to the agents, the better off they will be in making their decisions, but the less likely they will be to diversify their actions, so the more difficult it will be for her to hedge her positions. The model gives rise to a continuous time optimal stopping problem.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 4 , October 1996 , pp. 543 - 555
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Aumann, R.J. (1974). Subjectivity and correlation in randomized strategies. Journal of Mathematical Economics 1: 67–96.CrossRefGoogle Scholar
2.Aumann, R.J. (1987). Correlated equilibrium as an expression of bounded rationality. Econometrica 55: 1–19.CrossRefGoogle Scholar
3.Bassan, B. & Scarsini, M. (1995). On the value of information in multi-agent decision theory. Journal of Mathematical Economics 24: 557–576.CrossRefGoogle Scholar
4.Bassan, B. & Scarsini, M. (1995). Sequential decisions with several agents. Dipartimento di Matematica, Politecnico di Milano.Google Scholar
5.Bassan, B. & Scarsini, M. (1995). The social value of withholding information. Dipartimento di Matematica, Politecnico di Milano.Google Scholar
6.Blackwell, D. & Dubins, L. (1962). Merging of opinions with increasing information. Annals of Mathematical Statistics 33: 882–886.CrossRefGoogle Scholar
7.Erev, I., Wallsten, T.S., & Neal, M.M. (1991). Vagueness, ambiguity, and the cost of mutual understanding. Psychological Science 2: £321–324.CrossRefGoogle Scholar
8.Fudenberg, D. & Kreps, D.M. (1995). Learning in extensive-form games I. Self-confirming equilibria. Games and Economic Behavior 8: 20–55.CrossRefGoogle Scholar
9.Harrison, J.M. & Kreps, D.M. (1978). Speculative investor behavior in a stock market with heterogeneous expectations. Quarterly Journal of Economics 92: 323–336.CrossRefGoogle Scholar
10.Kalai, E. & Lehrer, E. (1993). Rational learning leads to Nash equilibrium. Econometrica 61: 1019–1045.CrossRefGoogle Scholar
11.Kalai, E. & Lehrer, E. (1993). Subjective equilibrium in repeated games. Econometrica 61: 1231–1240.CrossRefGoogle Scholar
12.Kalai, E. & Lehrer, E. (1994). Weak and strong merging of opinions. Journal of Mathematical Economics 23: 73–86.CrossRefGoogle Scholar
13.Kalai, E. & Lehrer, E. (1995). Subjective games and equilibria. Games and Economic Behavior 8: 123–163.CrossRefGoogle Scholar
14.Karlin, S. & Taylor, H.M. (1975). A first course in stochastic processes, 2nd ed.New York: Academic Press.Google Scholar
15.Lehrer, E. & Smorodinsky, R. (1993). Compatible measures and merging. School of Mathematical Sciences, Tel Aviv University.Google Scholar
16.Mertens, J.F. & Zamir, S. (1985). Formalization of Bayesian analysis for games with incomplete information. International Journal of Game Theory 14: 1–29.CrossRefGoogle Scholar
17.Shiryayev, A.N. (1978). Optimal stopping rules. New York: Springer-Verlag.Google Scholar