2024/03/23 by Pradeep Dubey, Siddhartha Sahi, Dubey, Pradeep +3
Agricultural and Biological Sciences · #60E15 #91A10 #91A18 #91B43 #Agricultural Economics and Policy #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2403.15957
openalex publication_date 2024/03/23 · openalex created_date 2024/03/27 · openalex updated_date 2026/07/28
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.