Bas Dietzenbacher

Maastricht University | UM · Department of Quantitative Economics

This paper introduces and studies the equal split-off set for cooperative games with nontransferable utility. We illustrate the new solution for the well-known Roth-Shafer examples and present two axiomatic characterizations based on different consistency properties on the class of exact partition games, i.e. the class of games where it intersects...

This paper studies axiomatic characterizations of the constrained equal awards rule for bankruptcy problems. We show that many results apply in a much more general context than for which they are originally formulated. In particular, we generalize several axiomatic characterizations based on symmetry, sustainability, and consistency to the domain o...

This paper studies Davis–Maschler reduced games of two-bound core games and shows that all these reduced games with respect to core elements are two-bound core games with the same pair of bounds. Based on associated reduced game properties, we axiomatically characterize the core, the nucleolus, and the egalitarian core for two-bound core games. Mor...

This paper introduces the new class of two-bound core games, where the core can be described by a lower bound and an upper bound on the payoffs of the players. Many classes of games turn out to be two-bound core games. We show that the core of each two-bound core game can be described equivalently by the pair of exact core bounds, and study to what...

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 preservati...

This paper introduces and studies a random arrival rule for bankruptcy problems with nontransferable utility. This bankruptcy rule generalizes the random arrival rule for bankruptcy problems with transferable utility which assigns the unique efficient allocation proportional to the sum of marginal vectors. We provide two axiomatic characterizations...

This paper formally introduces Hart–Mas-Colell consistency for general (possibly multi-valued) solutions for cooperative games with transferable utility. This notion is used to axiomatically characterize the core on the domain of convex games. Moreover, we characterize all nonempty solutions satisfying individual rationality, anonymity, scale covar...

This paper studies the nucleolus of graph-restricted games as an alternative for the Shapley value to evaluate communication situations. We focus on the inheritance of properties of cooperative games related to the nucleolus: strong compromise admissibility and compromise stability. These two properties allow for a direct, closed formula for the nu...

A solution for transferable utility games is self-antidual if it assigns to each game the set of payoff allocations that it assigns to the antidual game with opposite sign. Well-known examples of self-antidual solutions are the core, the Shapley value, the prenucleolus, and the Dutta-Ray solution. To evaluate the extent to which a solution violates...

Given the final ranking of a competition, how should the total prize endowment be allocated among the competitors? We study consistent prize allocation rules satisfying elementary solidarity and fairness principles. In particular, we axiomatically characterize several families of rules satisfying anonymity, order preservation, and endowment monoton...

This paper studies bankruptcy problems with nontransferable utility as a generalization of bankruptcy problems with monetary estate and claims. Following the theory on TU-bankruptcy, we introduce a duality notion for NTU-bankruptcy rules and derive several axiomatic characterizations of the proportional rule and the constrained relative equal award...

This paper identifies the maximal domain of transferable utility games on which aggregate monotonicity (no player is worse off when the worth of the grand coalition increases) and egalitarian core selection (no other core allocation can be obtained by a transfer from a richer to a poorer player) are compatible, which turns out to be the class of ga...

This paper axiomatically studies the equal split-off set (cf. Branzei et al. (Banach Center Publ 71:39–46, 2006)) as a solution for cooperative games with transferable utility which extends the well-known Dutta and Ray (Econometrica 57:615–635, 1989) solution for convex games. By deriving several characterizations, we explore consistency of the equ...

This paper takes an axiomatic bargaining approach to bankruptcy problems with nontransferable utility, by using properties from bargaining theory in order to characterize bankruptcy rules. In particular, we derive new axiomatic characterizations of the proportional rule, the truncated proportional rule, and the constrained relative equal awards rul...

This paper formally introduces Hart-Mas-Colell consistency for general (possibly multi-valued) solutions for cooperative games with transferable utility. This notion is used to axiomatically characterize the core on the domain of convex games. Moreover, we characterize all nonempty solutions satisfying individual rationality, anonymity, scale covar...

This paper studies independence of higher claims and independence of irrelevant claims on the domain of bargaining problems with claims. Independence of higher claims requires that the payoff of an agent does not depend on the higher claim of another agent. Independence of irrelevant claims states that the payoffs should not change when the claims...

This paper axiomatically studies bankruptcy problems with nontransferable utility by focusing on generalizations of consistency and the contested garment principle. On the one hand, we discuss several consistency notions and introduce the class of parametric bankruptcy rules which contains the proportional rule, the constrained relative equal award...

This note shows that the egalitarian Dutta and Ray (1989) solution for transferable utility games is self-antidual on the class of exact partition games. By applying a careful antiduality analysis, we derive several new axiomatic characterizations. Moreover, we point out an error in earlier work on antiduality and repair and strengthen several rela...

This paper introduces and analyzes a procedural egalitarian solution for nontransferable utility games. This concept is based on an egalitarian procedure in which egalitarian opportunities of coalitions are explicitly taken into account. We formulate conditions under which the new solution prescribes a core element and derive a direct expression on...

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...

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...

Using network control structures, this paper introduces a general class of network communication games and studies their decomposition into unanimity games. We obtain a relation between the dividends in any network communication game and its underlying transferable utility game, which depends on the structure of the communication network. Moreover,...

We consider the problem of computing the influence of a neuronal structure in a brain network. Abraham et al. (2006) computed this influence by using the Shapley value of a coalitional game corresponding to a directed network as a rating. Kötter et al. (2007) applied this rating to large-scale brain networks, in particular to the macaque visual cor...

Using network control structures this paper introduces network communication games as a generalization of vertex games and edge games corresponding to communication situations and studies their decomposition into unanimity games. We obtain a relation between the dividends of the network communication game and the underlying transferable utility gam...