The purpose of this paper is to discuss the properties of a new solution of the 2-person bargaining problem as formulated by Nash, the so-called Average Pay-off solution. This solution of a very simple form has a natural interpretation based on the center of gravity of the feasible set, and it is "more sensitive" to changes of feasible sets than any other standard bargaining solution. It satisfies the standard axioms: Pareto-Optimality, Symmetry, Scale Invariance, Continuity and Twisting. Moreover,...
Praca jest artykułem wspomnieniowym o prof. Stanisławie Trybule.Wprowadza ona czytelnika w tematykę tzw. gier czasowych (gamet of timing), będących w kręgu jego głównych zainteresowań w ostatnich dwudziestu latach. Gry czasowe stanowią jeden z istotnych działów studiowanych w teorii gier. Opisują one pewien szczególny rodzaj sytuacji konfliktowych między dwiema antagonistycznymi stronami, gdziekażda z nich musi zdecydować, w jakich momentach pewnego „przedziału czasowego” należy podjąć konieczne...
We study values for cooperative TU-games which are convex combinations of the Shapley value and the solidarity value, introduced in our recent paper [1]. First, we axiomatize the convex combination of the two values in the case when the coefficients are given exogenously. Next, we give an axiomatic description of the whole family of such values.
We study a generalization of bimatrix games in which not all pairs of players' pure strategies are admissible. It is shown that under some additional convexity assumptions such games have equilibria of a very simple structure, consisting of two probability distributions with at most two-element supports. Next this result is used to get a theorem about the existence of Nash equilibria in bimatrix games with a possibility of payoffs equal to -∞. The first of these results is a discrete counterpart...
This review paper gives a characterization of non-coalitional zero-sum and non-zero-sum games with finite strategy spaces and payoff functions having some concavity or convexity properties. The characterization is given in terms of the existence of two-point Nash equilibria, that is, equilibria consisting of mixed strategies with spectra consisting of at most two pure strategies. The structure of such simple equilibria is discussed in various cases. In particular, many of the results discussed can...
The book under review presents the serious theoretical development of the game models in an easy-to-follow style and provides computer methodology to solve a broad class of problems. It includes a wide range of game modeling applications in many different areas. The authors have focused on integration the fundamentals, methodology, and major application fields of non-cooperative and cooperative games including conflict resolution. The topics addressed in the book are discrete and continuous games...
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