R. Brânzei

On Cores and Stable Sets for Fuzzy Games

In this paper, cores and stable sets for games with fuzzy coalitions are introduced and their relations studied. For convex fuzzy games it turns out that all cores coincide and that the core is the unique stable set. Also relations between cores and stable sets of fuzzy clan games are discussed.

Tree-connected peer group situations and peer group games

Abstract. A class of cooperative games arising from economic and operations research situations in which agents with potential individual possibilities are connected via a hierarchy within an organization is introduced. It is shown that the games in this class form a cone which lies in the intersection of convex games and monotonic veto-rich games with the leader of the organization as veto-player. Different economic situations like auctions, communication situations, sequencing situations and flow situations are related to peer group games. For peer group games classical solution concepts have nice computational properties.

Cores and Stable Sets for Interval-Valued Games

In this paper, interval-type solution concepts for interval-valued cooperative games like the interval core, the interval dominance core and stable sets are introduced and studied. The notion of I-balancedness is introduced, and it is proved that the interval core of an interval-valued cooperative game is nonempty if and only if the game is I-balanced. Relations between the interval core, the dominance core and stable sets of an interval-valued game are established.

How to Cope with Division Problems under Interval Uncertainty of Claims

The paper deals with division situations where individual claims can vary within closed intervals.Uncertainty of claims is removed by compromising in a consistent way the upper and lower bounds of the claim intervals.Deterministic division problems with compromise claims are then considered and classical division rules from the bankruptcy literature are used to generate several procedures leading to e .cient and reasonable rules for division problems under interval uncertainty of claims.

Two Approaches to the Problem of Sharing Delay Costs in Joint Projects

This paper concentrates on cost sharing situations which arise when delayed joint projects involve joint delay costs. The problem here is to determine “fair” shares for each of the agents who contribute to the delay of the project such that the total delay cost is cleared. We focus on the evaluation of the responsibility of each agent in delaying the project based on the activity graph representation of the project and then on solving the important problem of the delay cost sharing among the agents involved. Two approaches, both rooted in cooperative game theory methods are presented as possible solutions. In the first approach delay cost sharing rules are introduced which are based on the delay of the project and on the individual delays of the agents who perform activities. This approach is inspired by the bankruptcy and taxation literature and leads to five rules: the (truncated) proportional rule, the (truncated) constrained equal reduction rule and the constrained equal contribution rule. By introducing two coalitional games related to delay cost sharing problems, which we call the pessimistic delay game and the optimistic delay game, also game theoretical solutions as the Shapley value, the nucleolus and the τ-value generate delay cost sharing rules. In the second approach the delays of the relevant paths in the activity graph together with the delay of the project play a role. A two-stage solution is proposed. The first stage can be seen as a game between paths, where the delay cost of the project has to be allocated to the paths. Here serial cost sharing methods play a role. In the second stage the allocated costs of each path are divided proportionally to the individual delays among the activities in the path.

COLLECTING INFORMATION TO IMPROVE DECISION-MAKING

In this paper, we consider information collecting (IC) situations where an action taker in an uncertain situation can improve his action choices by gathering information from some players who are more informed about the situation. Then the problem of sharing the gains when cooperating with informants is tackled by constructing an appropriate game, the IC-game corresponding to the IC-situation. It turns out that the cone of IC-games, given a fixed set of players, coincides with the cone of 0-normalized monotonic games with a veto player. Also special classes of convex IC-games and big boss IC-games are considered, for which more is known about the solution concepts.

Strongly Essential Coalitions and the Nucleolus of Peer Group Games

Most of the known efficient algorithms designed to compute the nucleolus for special classes of balanced games are based on two facts: (i) in any balanced game, the coalitions which actually determine the nucleolus are essential; and (ii) all essential coalitions in any of the games in the class belong to a prespecified collection of size polynomial in the number of players. We consider a subclass of essential coalitions, called strongly essential coalitions, and show that in any game, the collection of strongly essential coalitions contains all the coalitions which actually determine the core, and in case the core is not empty, the nucleolus and the kernelcore. As an application, we consider peer group games, and show that they admit at most 2n−1 strongly essential coalitions, whereas the number of essential coalitions could be as much as 2n−1. We propose an algorithm that computes the nucleolus of an n-player peer group game in time directly from the data of the underlying peer group situation.

A Simple Algorithm for the Nucleolus of Airport Profit Games

In this paper we present a procedure for calculating the nucleolus for airport profit games which are a generalization of the airport cost games.

Hypercubes and compromise values for cooperative fuzzy games

For cooperative fuzzy games with a non−empty core hypercubes catching the core, the Weber set and the path solution cover are introduced. Using the bounding vectors of these hypercubes, compromise values are defined. Special attention is given to the relations between these values for convex fuzzy games.

Information collecting situations and bi-monotonic allocation schemes

Abstract. This paper studies information collecting (IC) situations with the help of cooperative game theory. Relations are established between IC situations and IC games on one hand and information sharing (IS) situations and IS games on the other hand. Further, it is shown that IC games are convex combinations of so-called local games. Properties such as k-convexity and k-concavity are possessed by an IC game if all related local games have the respective properties. Special attention is paid to the classes of k-symmetric IC games and k-concave IC games. This last class turns out to consist of total big boss games. For the class of total big boss games a new solution concept is introduced: bi-monotonic allocation schemes. This solution takes the power of the big boss into account.