Bas Dietzenbacher

Bankruptcy games with nontransferable utility

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.

Proportionality, Equality, and Duality in Bankruptcy Problems with Nontransferable Utility

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.

Egalitarianism in Nontransferable Utility Games

This paper studies egalitarianism in the context of nontransferable utility games by introducing and analyzing the egalitarian value. This new solution concept is based on an egalitarian negotiation procedure in which egalitarian opportunities of coalitions are explicitly taken into account. We formulate conditions under which it leads to a core element and discuss the egalitarian value for the well-known Roth-Shafer examples. Moreover, we characterize the new value on the class of bankruptcy games and bargaining games.

NTU-Bankruptcy Problems: Consistency and the Relative Adjustment Principle

This paper axiomatically studies bankruptcy problems with nontransferable utility by adequately generalizing and analyzing properties for bankruptcy rules. In particular, we discuss several consistency notions and introduce the class of parametric bankruptcy rules. Moreover, we introduce the class of adjusted bankruptcy rules and study the relative adjustment principle based on relative symmetry, truncation invariance, and minimal rights first.

The procedural egalitarian solution

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.

Bankruptcy Games with Nontransferable Utility

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.

The Procedural Egalitarian Solution

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.

A Note on Shapley Ratings in Brain Networks

We consider the problem of computing the in uence of a neuronal structure in a brain network. Abraham, Kotter, Krumnack, and Wanke (2006) computed this influence by using the Shapley value of a coalitional game corresponding to a directed network as a rating. Kotter, Reid, Krumnack, Wanke, and Sporns (2007) applied this rating to large-scale brain networks, in particular to the macaque visual cortex and the macaque prefrontal cortex. We introduce an alternative coalitional game that is more intuitive from a game theoretical point of view. We use the Shapley value of this game as an alternative rating to analyze the macaque brain networks and corroborate the findings of Kotter et al. (2007). Moreover, we show how missing information on the existence of certain connections can readily be incorporated into this game and the corresponding Shapley rating.

On Shapley Ratings in Brain Networks

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 cortex and the macaque prefrontal cortex. Our aim is to improve upon the above technique by measuring the importance of subgroups of neuronal structures in a different way. This new modeling technique not only leads to a more intuitive coalitional game, but also allows for specifying the relative influence of neuronal structures and a direct extension to a setting with missing information on the existence of certain connections.

Decomposition of Network Communication Games

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 introduce a new class of network control values which contains both the Myerson value and the position value. The decomposition results are used to explicitly express these values in terms of dividends.