A comparison of the average prekernel and the prekernel

We propose positive and normative foundations for the average prekernel of NTU games, and compare them with the existing ones for the prekernel. In our non-cooperative analysis, the average prekernel is approximated by the set of equilibrium payoffs of a game where each player faces the possibility of bargaining at random against any other player. In the cooperative analysis, we characterize the average prekernel as the unique solution that satisfies a set of Nash-like axioms for two-person games, and versions of average consistency and its converse for multilateral setting

Robert Aumann's and Thomas Schelling's Contributions to Game Theory: Analyses of Conflict and Cooperation

Advanced information on the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel 2005.Game Theory;

A COMPARISON OF THE AVERAGE PREKERNEL AND THE PREKERNEL

We propose positive and normative foundations for the average prekernel of NTU games, and compare them with the existing ones for the prekernel. In our non-cooperative analysis, the average prekernel is approximated by the set of equilibrium payoffs of a game where each player faces the possibility of bargaining at random against any other player. In the cooperative analysis, we characterize the average prekernel as the unique solution that satisfies a set of Nash-like axioms for two-person games, and versions of average consistency and its converse for multilateral settings

A comparison of the average prekernel and the prekernel.

We propose positive and normative foundations for the average prekernel of NTU games, and compare them with the existing ones for the prekernel. In our non-cooperative analysis, the average prekernel is approximated by the set of equilibrium payoffs of a game where each player faces the possibility of bargaining at random against any other player. In the cooperative analysis, we characterize the average prekernel as the unique solution that satisfies a set of Nash-like axioms for two-person games, and versions of average consistency and its converse for multilateral settings

Leximals, the Lexicore and the Average Lexicographic Value

The lexicographic vectors of a balanced game, called here leximals, are used to define a new solution concept, the lexicore, on the cone of balanced games. Properties of the lexicore and its relation with the core on some classes of games are studied. It is shown that on cones of balanced games where the core is additive, the leximals, the lexicore and the Average Lexicographic (AL-)value are additive, too. Further, it turns out that the leximals satisfy a consistency property with respect to a reduced game `a la Davis and Maschler, which implies an average consistency property of the AL-value. Explicit formulas for the AL-value on the class of k-convex games and on the class of balanced almost convex games are provided.cooperative games;the core;the AL-value;the Shapley value

Consistency, converse consistency, and aspirations in TU-games

In problems of choosing ‘aspirations’ for TU-games, we study two axioms, ‘MW-consistency’ and ‘converse MW-consistency.’ In particular, we study which subsolutions of the aspiration correspondence satisfy MW-consistency and/or converse MW-consistency. We also provide axiomatic characterizations of the aspiration kernel and the aspiration nucleolus

Tree enterprises and bankruptcy ventures: a game theoretic similarity due to a graph theoretic proof

In a tree enterprise, users reside at the nodes of the tree and their aim is to connect themselves, directly or indirectly, to the root of the tree. The construction costs of arcs of the tree are given by means of the arc-cost-function associated with the tree. Further the bankruptcy venture is described in terms of the estate of the bankrupt firm and the claims of the various creditors. The first objective of the paper is to provide conditions (on the claims and the surplus of the claims in the bankruptcy venture) which are sufficient and necessary for the bankruptcy venture to agree with some tree enterprise. It is established that the bankruptcy venture agrees with some tree enterprise if and only if the surplus of claims in the bankruptcy venture is at most the size of the second smallest claim (in the weak sense). For that purpose, both the tree enterprise as well as the bankruptcy venture are modelled as a cooperative game with transferable utility. Within the framework of cooperative game theory, the proof of the equivalence theorem concerning the tree enterprise game and the bankruptcy game, under the given circumstances, is based on graph-theoretic tools in a tree structure. As an adjunct to the proof of the equivalence theorem, the solution concept of the nucleolus for specific tree enterprises is determine

Compensatory Transfers in Two-Player Decision Problems

This paper presents an axiomatic characterization of a family of solutions to two-player quasi-linear social choice problems. In these problems the players select a single action from a set available to them. They may also transfer money between themselves. The solutions form a one-parameter family, where the parameter is a nonnegative number, t. The solutions can be interpreted as follows: Any efficient action can be selected. Based on this action, compute for each player a "best claim for compensation". A claim for compensation is the difference between the value of an alternative action and the selected efficient action, minus a penalty proportional to the extent to which the alternative action is inefficient. The coefficient of proportionality of this penalty is t. The best claim for compensation for a player is the maximum of this computed claim over all possible alternative actions. The solution, at the parameter value t, is to implement the chosen efficient action and make a monetary transfer equal to the average of these two best claims. The characterization relies on three main axioms. The paper presents and justifies these axioms and compares them to related conditions used in other bargaining contexts. In Nash Bargaining Theory, the axioms analagous to these three are in conflict with each other. In contrast, in the quasi-linear social choice setting of this paper, all three conditions can be satisfied simultaneously.