Uncertainty in Information Market Games

A new product can be produced and sold in a market thanks to the entrance of a patent holder into the market. This market is divided into submarkets controlled by only some firms and the profit attainable in each submarket is uncertain. In this paper, this situation is studied by means of cooperative games under interval uncertainty. We consider different ways of allocating the interval profit among the firms. One of these is the interval [Formula: see text]-value, which is defined for interval games satisfying some conditions. Efficient interval solutions in terms of the market data are provided.

On the Banzhaf-like Value for Cooperative Games with Interval Payoffs

By using Moore’s subtraction operator and a total order on the set of closed intervals, we introduce a new variation of the Banzhaf value for cooperative interval games called the interval Banzhaf-like value which may accommodate the shortcomings of the interval Banzhaf value. We first reveal the relation between this introduced value and the interval Banzhaf value. Then, we present two sets of properties that may be used to determine whether an interval value is median-indifferent to the interval Banzhaf-like value. Finally, in order to overcome the disadvantages of the interval Banzhaf-like value, we propose the contracted interval Banzhaf-like value and give an axiomatization of this proposed value.

The interval Shapley value of an M/M/1 service system

Service systems and their cooperation are one of the most important and hot topics in management and information sciences. To design a reasonable allocation mechanism of service systems is the key issue in the cooperation of service systems. In this paper, we systematically introduce the interval Shapley value as cost allocation of cooperative interval games 〈N,V〉 arising from cooperation in a multi-server service system, and provide an explicit expression for the interval Shapley value of cooperative interval games 〈N,V〉. We construct an interval game 〈N,W〉 of a service system which shares the same value for the grand coalition with the original interval game, by using the characteristic function which is dominated by the function of the original interval game. Finally, we prove that the interval game 〈N,W〉 is concave, which means that the interval Shapley value of the interval game 〈N,W〉 is in the interval core of this interval game, and illustrate this conclusion by using numerical examples.