ﻻ يوجد ملخص باللغة العربية
Partially defined cooperative games are a generalisation of classical cooperative games in which the worth of some of the coalitions is not known. Therefore, they are one of the possible approaches to uncertainty in cooperative game theory. The main focus of this paper is the class of 1-convex cooperative games under this framework. For incomplete cooperative games with minimal information, we present a compact description of the set of 1-convex extensions employing its extreme points and its extreme rays. Then we investigate generalisations of three solution concepts for complete games, namely the $tau$-value, the Shapley value and the nucleolus. We consider two variants where we compute the centre of gravity of either extreme games or of a combination of extreme games and extreme rays. We show that all of the generalised values coincide for games with minimal information and we call this solution concept the emph{average value}. Further, we provide three different axiomatisations of the average value and outline a method to generalise several axiomatisations of the $tau$-value and the Shapley value into an axiomatisation of the average value. We also briefly mention a similar derivation for incomplete games with defined upper vector and indicate several open questions.
Partially defined cooperative games are a generalisation of classical cooperative games in which payoffs for some of the coalitions are not known. In this paper we perform a systematic study of partially defined games, focusing on two important class
In some games, additional information hurts a player, e.g., in games with first-mover advantage, the second-mover is hurt by seeing the first-movers move. What properties of a game determine whether it has such negative value of information for a par
We investigate a class of weighted voting games for which weights are randomly distributed over the standard probability simplex. We provide close-formed formulae for the expectation and density of the distribution of weight of the $k$-th largest pla
An average-time game is played on the infinite graph of configurations of a finite timed automaton. The two players, Min and Max, construct an infinite run of the automaton by taking turns to perform a timed transition. Player Min wants to minimise t
Cooperative interval game is a cooperative game in which every coalition gets assigned some closed real interval. This models uncertainty about how much the members of a coalition get for cooperating together. In this paper we study convexity, core