Meet meets join: the interaction between pooled and common knowledge
| Autor: | Áron Tóbiás |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Economics and Econometrics Theoretical computer science Computer science Duality (mathematics) Pooling Joins Mathematics (miscellaneous) Distributive property Common knowledge State space Join (sigma algebra) Statistics Probability and Uncertainty Social Sciences (miscellaneous) Information exchange |
| Zdroj: | International Journal of Game Theory. 50:989-1019 |
| ISSN: | 1432-1270 0020-7276 |
| DOI: | 10.1007/s00182-021-00778-w |
| Popis: | This paper explores the lattice-theoretic properties of the family of all partitions of an arbitrary state space. I discuss a duality correspondence connecting meets (finest common coarsening) and joins (coarsest common refinement) of families of partitions, which conforms to the natural order-theoretic representations of these two operations. The partition lattice turns out to fail to be a distributive, or even a modular, lattice. I provide intuitive interpretations of these negative results in terms of the interaction between common knowledge and pooling multiple sources of private information, with applications to information exchange within and between different populations and to criminal-procedure law. |
| Databáze: | OpenAIRE |
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