This paper analyzes bankruptcy problems with nontransferable utility as a generalization of bankruptcy problems with monetary estate and claims. Following the classical axiomatic theory of bankruptcy, we formulate some appropriate properties for NTU-bankruptcy rules and study their implications. We explore duality of bankruptcy rules and we derive several characterizations of the generalized proportional rule and the constrained relative equal awards rule.
In this paper we introduce and analyze the procedural egalitarian solution for transferable utility games. This new concept is based on the result of a coalitional bargaining procedure in which egalitarian considerations play a central role. The procedural egalitarian solution is the first single-valued solution which coincides with the constrained egalitarian solution of Dutta and Ray (1989) on the class of convex games and which exists for any TU-game.
This paper analyzes bankruptcy games with nontransferable utility as a generalization of bankruptcy games with monetary payoffs. Following the game theoretic approach to NTU-bankruptcy problems, we study some appropriate properties and the core of NTU-bankruptcy games. Generalizing the core cover and the reasonable set to the class of NTU-games, we show that NTU-bankruptcy games are compromise stable and reasonable stable. Moreover, we derive a necessary and sufficient condition for an NTU-bankruptcy rule to be game theoretic.
Given the ranking of competitors, how should the prize endowment be allocated? This paper introduces and axiomatically studies the prize allocation problem. We focus on consistent prize allocation rules satisfying elementary solidarity and fairness principles. In particular, we derive several families of rules satisfying anonymity, order preservation, and endowment monotonicity, which all fall between the equal division rule and the winner-takes-all rule. Our results may help organizers to select the most suitable prize allocation rule for rank-order competitions. This paper was accepted by Manel Baucells, behavioral economics and decision analysis.
This paper axiomatically studies the equal split-off set (cf. Branzei et al. (2006)) as a solution for cooperative games with transferable utility. This solution extends the well-known Dutta and Ray (1989) solution for convex games to arbitrary games. By deriving several characterizations, we explore the relation of the equal split-off set with various consistency notions.1 Dutta (1990) obtained two characterizations of the Dutta and Ray (1989) solution for convex games. The main axioms in these characterizations are based on the consistency principle. Imagine a group of cooperating players agreeing on applying a certain solution concept for the allocation of their joint revenues. Suppose that some players leave with their assigned payoffs and that the remaining players reevaluate their payoffs by applying the solution to a reduced game. The solution is consistent if it prescribes for this reduced game the same allocation as for the original game. Thomson (2011) provides a general introduction to the consistency principle.The exact interpretation of the consistency principle in cooperative games depends on the axiomatic formulation, which is mainly determined by the specific definition of reduced games. The results of Dutta (1990) involve the formulations proposed by Davis and Maschler (1965) and Hart and Mas-Colell (1989), to which we refer as max-consistency and selfconsistency, respectively. Klijn et al. (2000) obtained similar results using weak variants of these axioms which only require consistent allocations in situations where the richest players leave with their assigned payoffs, to which we refer as rich-restricted consistency. Moreover, they derived a third characterization based on an alternative consistency formulation which closely resembles the definition of the equal split-off set, to which we refer as rich-restricted marginal-consistency.Recently, Llerena and Mauri (2017) introduced the class of exact partition games and wondered whether the characterizations of Klijn et al. (2000) on convex games can be extended to this larger class. We show that the class of exact partition games is exactly the class of games for which the equal split-off set intersects the core and we provide a full answer to this open question. In particular, we show that the characterizations based on max-consistency and marginal-consistency can be extended to exact partition games, but the characterization based on self-consistency cannot. Moreover, we weaken the rather specific rich-restricted marginal-consistency to the rich-restricted version of the well-known consistency notion introduced by Moulin (1985), to which we refer as complement-consistency. Both max-consistency and complement-consistency have been used in axiomatizations of the core, respectively by Peleg (1986) and Tadenuma (1992). We show that rich-restricted complement-consistency can also play a similar role as rich-restricted max-consistency in the extended characterization of Klijn et al. (2000) on the class of exact partition games. As a by-product, we ...
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