Scarcity, competition, and value
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We suggest a value for finite coalitional games with transferable utility that are enriched by non-negative weights for the players. In contrast to other weighted values, players stand for types of agents and weights are intended to represent the population sizes of these types. Therefore, weights do not only affect individual payoffs but also the joint payoff. Two principles guide the behavior of this value. Scarcity: the generation of worth is restricted by the scarcest type. Competition: only scarce types are rewarded. We find that the types’ payoffs for this value coincide with the payoffs assigned by the Mertens value to their type populations in an associated infinite game.
KeywordsTU game Shapley value Lovász extension Strong monotonicity Partnership Vector measure game Mertens value
Mathematics Subject Classification91A12 91A13 91B15
JEL ClassificationC71 D60
We are grateful to Frank Huettner, Michael Kramm, and Philippe Solal as well as two anonymous rerefees for valuable comments on this paper. Financial support by the Deutsche Forschungsgemeinschaft for André Casajus (Grant CA 266/4-1) is gratefully acknowledged.
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