Putting all eggs in one basket: some insights from a correlation inequality
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909321554558976 |
|---|---|
| author | Dubey, Pradeep Sahi, Siddhartha Wang, Guanyang |
| author_facet | Dubey, Pradeep Sahi, Siddhartha Wang, Guanyang |
| contents | We give examples of situations -- stochastic production, military tactics, corporate merger -- where it is beneficial to concentrate risk rather than to diversify it, that is, to put all eggs in one basket. Our examples admit a dual interpretation: as optimal strategies of a single player (the `principal') or, alternatively, as dominant strategies in a non-cooperative game with multiple players (the `agents').
The key mathematical result can be formulated in terms of a convolution structure on the set of increasing functions on a Boolean lattice (the lattice of subsets of a finite set). This generalizes the well-known Harris inequality from statistical physics and discrete mathematics; we give a simple self-contained proof of this result, and prove a further generalization based on the game-theoretic approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15957 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Putting all eggs in one basket: some insights from a correlation inequality Dubey, Pradeep Sahi, Siddhartha Wang, Guanyang Probability Theoretical Economics Optimization and Control 60E15, 91A10, 91A18, 91B43 We give examples of situations -- stochastic production, military tactics, corporate merger -- where it is beneficial to concentrate risk rather than to diversify it, that is, to put all eggs in one basket. Our examples admit a dual interpretation: as optimal strategies of a single player (the `principal') or, alternatively, as dominant strategies in a non-cooperative game with multiple players (the `agents'). The key mathematical result can be formulated in terms of a convolution structure on the set of increasing functions on a Boolean lattice (the lattice of subsets of a finite set). This generalizes the well-known Harris inequality from statistical physics and discrete mathematics; we give a simple self-contained proof of this result, and prove a further generalization based on the game-theoretic approach. |
| title | Putting all eggs in one basket: some insights from a correlation inequality |
| topic | Probability Theoretical Economics Optimization and Control 60E15, 91A10, 91A18, 91B43 |
| url | https://arxiv.org/abs/2403.15957 |