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- Tijs, S. H. [x] 11 (%)
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## On the axiomatization of the τ-value

### Top (1995-06-01) 3: 35-46 , June 01, 1995

### Summary

The τ-value is a solution concept for a subclass of games with transferable utility introduced and axiomatized by Tijs (1981, 1987). In this note an alternative characterization of the τ-value by means of five axioms is offered. Two of them are well-known: efficiency and translation equivalence; the other three relate the solution of a game with the minimal and maximal aspiration vectors involved in the definition of the τ-value.

## On the existence of values for arbitration games

### International Journal of Game Theory (1982-06-01) 11: 87-104 , June 01, 1982

Two-person games in normal form are considered, where the players may use correlated strategies and where the problem arises, which Pareto optimal point in the payoff region to choose. We suppose that the players solve this problem with the aid of an arbitration function, which is continuous and profitable, and for which the inverse image of each Pareto point is a convex set. Then the existence of values and defensive ε-optimal strategies is discussed. Existence theorems are derived, using families of suitable dummy zero-sum games. The derived existence theorems contain all known existence results as special cases.

## Theτ-value for games on matroids

### Top (2002-06-01) 10: 67-81 , June 01, 2002

In the classical model of games with transferable utility one assumes that each subgroup of players can form and cooperate to obtain its value. However, we can think that in some situations this assumption is not realistic, that is, not all coalitions are feasible. This suggests that it is necessary to raise the whole question of generalizing the concept of transferable utility game, and therefore to introduce new solution concepts. In this paper we define games on matroids and extend the*τ*-value as a compromise value for these games.

## OnS-equivalence and isomorphism of games in characteristic function form

### International Journal of Game Theory (1976-12-01) 5: 209-210 , December 01, 1976

In this note an example is given of two superadditive games which are isomorphic and not*S*-equivalent.

## Continuity of bargaining solutions

### International Journal of Game Theory (1983-06-01) 12: 91-105 , June 01, 1983

Upper semicontinuous solutions of the bargaining problem are studied and also lower semicontinuous weak solutions of that problem are considered. Though mainly compact bargaining pairs are investigated, extensions to non-compact bargaining pairs are indicated. The continuity properties of some well known bargaining solutions are discussed.

## The general nucleolus and the reduced game property

### International Journal of Game Theory (1992-03-01) 21: 85-106 , March 01, 1992

The nucleolus of a TU game is a solution concept whose main attraction is that it always resides in any nonempty ɛ-core. In this paper we generalize the nucleolus to an arbitrary pair (Π,*F*), where Π is a topological space and*F* is a finite set of real continuous functions whose domain is Π. For such pairs we also introduce the “least core” concept. We then characterize the nucleolus for*classes* of such pairs by means of a set of axioms, one of which requires that it resides in the least core. It turns out that different classes require different axiomatic characterizations.

One of the classes consists of TU-games in which several coalitions may be nonpermissible and, moreover, the space of imputations is required to be a certain “generalized” core. We call these games*truncated games*. For the class of truncated games, one of the axioms is a new kind of*reduced game property*, in which consistency is achieved even if some coalitions leave the game, being promised the nucleolus payoffs. Finally, we extend Kohlberg's characterization of the nucleolus to the class of truncated games.

## Characterization of all individually monotonic bargaining solutions

### International Journal of Game Theory (1985-12-01) 14: 219-228 , December 01, 1985

A description is given of the class of all individually monotonic bargaining solutions by associating with each of these solutions a monotonic curve in the triangle of*R*^{2} with vertices (1, 0), (0, 1) and (1, 1). Also the family of globally individually monotonic bargaining solutions is characterized with the aid of monotonic curves in the unit square of*R*^{2}.

## The τ-value, The core and semiconvex games

### International Journal of Game Theory (1985-12-01) 14: 229-247 , December 01, 1985

The*τ*-value for cooperative*n*-person games is central in this paper. Conditions are given which guarantee that the*τ*-value lies in the core of the game. A full-dimensional cone of semiconvex games is introduced. This cone contains the cones of convex and exact games and there is a simple formula for the*τ*-value for such games. The subclass of semiconvex games with constant gap function is characterized in several ways. It turns out to be an (*n*+1)-dimensional cone and for all games in this cone the Shapley value, the nucleolus and the*τ*-value coincide.

## On the structure of the set of perfect equilibria in bimatrix games

### Operations-Research-Spektrum (1993-03-01) 15: 17-20 , March 01, 1993

### Summary

In this paper attention is focussed on the structure of the set of perfect equilibria. It turns out that the structure of this set resembles the structure of the Nash equilibrium set. Maximal Selten subsets are introduced to take the role of maximal Nash subsets. It is found that the set of perfect equilibria is the finite union of maximal Selten subsets. Furthermore it is shown that the dimension relation for maximal Nash subsets can be extended to faces of such sets. As a result a dimension relation for maximal Selten subsets is derived.

## Fictitious play applied to sequences of games and discounted stochastic games

### International Journal of Game Theory (1982-06-01) 11: 71-85 , June 01, 1982

In this paper, we show that the iterative method of Brown and Robinson, for solving a matrix game, is also applicable to a converging sequence of matrices, where the players choose at stage*t* a row and a column of the*t*-th matrix in the sequence. As an application of this result, we describe a new solution method for discounted stochastic games with finite state and action spaces.