International Journal of Game Theory

, Volume 46, Issue 2, pp 295–310 | Cite as

Scarcity, competition, and value

  • André Casajus
  • Harald Wiese
Original Paper


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.


TU game Shapley value Lovász extension Strong monotonicity Partnership Vector measure game Mertens value 

Mathematics Subject Classification

91A12 91A13 91B15 

JEL Classification

C71  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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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.HHL Leipzig Graduate School of ManagementLeipzigGermany
  2. 2.Institut für Theoretische Volkswirtschaftslehre, Wirtschaftswissenschaftliche FakultätUniversität LeipzigLeipzigGermany

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