Values of Non - Atomic Vector Measure Games
نویسنده
چکیده
Consider non-atomic vector measure games; i.e., games u of the form u = f o(pI.. . ,p.), where (pIr.. .,p.) is a vector of non-atomic non-negative measures and f is a real-valued function defined on the range of (pi,. . .,pi.). Games of this form arise, for example, from production models and from finite-type markets. We show that the value of such a game need not be a linear combination of the measures p,, , pn (this is in contrast to all the values known to date). Moreover, this happens even for market games in pNA. In the economic models, this means that the value allocations are not necessarily generated by prices. All the examples we present are special cases of a new class of values.
منابع مشابه
Construction of Haar Measure on Projective Limit Group and Random Order Values of Non-atomic Games 1
By superimposing a group structure on a sequence of projective probability spaces of Lebesgue measure preserving (l.m.p.) automorphisms of unit interval, the paper extends the Daniel-Kolmogorov consistency theorem that enables the construction of a measurable group structure with invariant Haar probability measure on an uncountably large projective limit space. The projective limit group is the...
متن کاملCONTINUOUS VALUES OF MARKET GAMES ARE CONIC By
We prove that every continuous value on a space of vector measure market games Q, containing the space of nonatomic measures NA, has the conic property, i.e., if a game v ∈ Q coincides with a nonatomic measure ν on a conical diagonal neighborhood then φ(v) = ν. We deduce that every continuous value on the linear spaceM, spanned by all vector measure market games, is determined by its values on ...
متن کاملNot-Quite Non-Atomic Games: Values and Cores of Large Games
Non-atomic games were first introduced in several articles by Aumann and Shapley, which eventually culminated in their definitive book [1974, here denoted A/S]. We note that this was not the first treatment of games with a continuum of players; other articles, notably by Shapley et al., had done so. It is in A/S, however, that a rigorous definition of such games, and their meaning, first appear...
متن کاملA TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS
In this paper, we deal with games with fuzzy payoffs. We proved that players who are playing a zero-sum game with fuzzy payoffs against Nature are able to increase their joint payoff, and hence their individual payoffs by cooperating. It is shown that, a cooperative game with the fuzzy characteristic function can be constructed via the optimal game values of the zero-sum games with fuzzy payoff...
متن کاملThe Hebrew University of Jerusalem Asymptotic Values of Vector Measure Games
The asymptotic value, introduced by Kannai in 1966, is an asymptotic approach to the notion of the Shapley value for games with infinitely many players. A vector measure game is a game v where the worth v(S) of a coalition S is a function f of μ(S) where μ is a vector measure. Special classes of vector measure games are the weighted majority games and the two-house weighted majority games where...
متن کامل