Asymptotic agreement among communicating decisionmakers. (English) Zbl 0578.60005
Summary: This paper studies asymptotic agreement among communicating decision- makers in terms of the evolution of a dynamical system defined on the lattice of information \(\sigma\)-algebras. This approach focuses on the concept of decisions based on common knowledge introduced earlier by R. J. Aumann [Ann. Stat. 4, 1236-1239 (1976; Zbl 0379.62003)] but it extends the investigation to general decision rules.
We obtain conditions for asymptotic agreement in cases of direct, indirect, and random communications. We also present several examples to illustrate disagreement when the agreement conditions are not satisfied.
We obtain conditions for asymptotic agreement in cases of direct, indirect, and random communications. We also present several examples to illustrate disagreement when the agreement conditions are not satisfied.
MSC:
| 60A99 | Foundations of probability theory |
| 91A35 | Decision theory for games |
| 60F99 | Limit theorems in probability theory |
Citations:
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