Values of vector measure market games and their representations

Abstract

We offer a representation result for values of vector measure market games, proving that the value of a game is an "average of marginals". As a direct result we obtain that the Mertens value is the unique continuous value on the space of vector measure market games, and the unique value on the space of Lipschitz vector measure market games.

A note on $L^p_{w}(ν,X,Y)$ spaces of vector-valued functions with respect to vector measures

“…Furthermore the study of vector measures has contributed to other disciplines such as control theory, game theory, stochastic differential equations and statistics. See [EO16] and [GL17].…”