@article{b247cd91b7714e2b9edcf1985e290e5b,

title = "Decomposition-integral: Unifying Choquet and the concave integrals",

abstract = "This paper introduces a novel approach to integrals with respect to capacities. Any random variable is decomposed as a combination of indicators. A prespecified set of collections of events indicates which decompositions are allowed and which are not. Each allowable decomposition has a value determined by the capacity. The decomposition-integral of a random variable is defined as the highest of these values. Thus, different sets of collections induce different decomposition-integrals. It turns out that this decomposition approach unifies well-known integrals, such as Choquet, the concave and Riemann integral. Decomposition-integrals are investigated with respect to a few essential properties that emerge in economic contexts, such as concavity (uncertainty-aversion), monotonicity with respect to stochastic dominance and translation-covariance. The paper characterizes the sets of collections that induce decomposition-integrals, which respect each of these properties.",

keywords = "Capacity, Choquet integral, Concave integral, Decision making, Decomposition-integral, Non-additive probability",

author = "Yaarit Even and Ehud Lehrer",

note = "Funding Information: The authors acknowledge the helpful comments of Salvatore Greco, Radko Mesiar, Roee Teper and Peter Wakker and two anonymous referees of Economic Theory whose comments and suggestions greatly contributed to the paper. This research was supported in part by the Google Inter-university center for Electronic Markets and Auctions. Lehrer acknowledges the support of the Israel Science Foundation, Grant #538/11. ",

year = "2014",

month = may,

doi = "10.1007/s00199-013-0780-0",

language = "אנגלית",

volume = "56",

pages = "33--58",

journal = "Economic Theory",

issn = "0938-2259",

publisher = "Springer New York",

number = "1",

}