Osman Palanci

Transportation interval situations and related games

Basically, uncertainty is present in almost every real-world situation, it is influencing and questioning our decisions. In this paper, we analyze transportation interval games corresponding to transportation interval situations. In those situations, it may affect the optimal amount of goods and consequently whether and how much of a product is transported from a producer to a retailer. Firstly, we introduce the interval Shapley value of a game arising from a transportation situation under uncertainty. Secondly, a one-point solution concept by using a one-stage producere depending on the proportional, the constrained equal awards and the constrained equal losses rule is given. We prove that transportation interval games are interval balanced (

Cooperative interval games: Mountain situations with interval data

\mathcal {I}

Alternative Axiomatic Characterizations of the Grey Shapley Value

I-balanced). Further, the nonemptiness of the interval core for the transportation interval games and some results on the relationship between the interval core and the dual interval optimal solutions of the underlying transportation situations are also provided. Moreover, we characterize the interval core using the square operator and addressing two scenarios such as pessimistic and optimistic.

Facility Location Situations and Related Games in Cooperation

This contribution is located in the common area of operational research and economics, with a close relation and joint future potential with optimization: game theory. We focus on collaborative game theory under uncertainty. This study is on a new class of cooperative games where the set of players is finite and the coalition values are interval grey numbers. An interesting solution concept, the grey Shapley value, is introduced and characterized with the properties of additivity, efficiency, symmetry and dummy player, which are straightforward generalizations of the corresponding properties in the classical cooperative game theory. The paper ends with a conclusion and an outlook to future studies.

Cooperative Grey Games: Grey Solutions and an Optimization Algorithm

In this paper, we extend mountain situations by using interval calculus. We define the interval Bird allocation and show that this allocation is a special core element of the interval cost game corresponding to an interval mountain situation. We deal with the interval cost sharing problem by introducing the cooperative interval cost game. Further, we consider a subset of the interval core of the related interval cost game. Each element of this set is extendable to a population monotonic interval allocation scheme or shortly pmias. Finally, we show that each interval core element of an interval connection game is extendable to bi-monotonic interval allocation scheme or shortly bi-mias.

On the Grey Equal Surplus Sharing Solutions

The allocation problem of rewards/costs is a basic question for players, namely, individuals and companies that are planning cooperation under uncertainty. The involvement of uncertainty in cooperative game theory is motivated by the real world in which noise in observation and experimental design, incomplete information and vagueness in preference structures and decision-making play an important role. In this study, a new class of cooperative games, namely, the cooperative bubbly games, where the worth of each coalition is a bubble instead of a real number, is presented. Furthermore, a new solution concept, the bubbly core, is defined. Finally, the properties and the conditions for the non-emptiness of the bubbly core are given. The paper ends with a conclusion and an outlook to related and future studies.

The grey Shapley value: an axiomatization

The Shapley value, one of the most common solution concepts of cooperative game theory is defined and axiomatically characterized in different game-theoretic models. Certainly, the Shapley value can be used in interesting sharing cost/reward problems in the Operations Research area such as connection, routing, scheduling, production and inventory situations. In this paper, we focus on the Shapley value for cooperative games, where the set of players is finite and the coalition values are interval grey numbers. The central question in this paper is how to characterize the grey Shapley value. In this context, we present two alternative axiomatic characterizations. First, we characterize the grey Shapley value using the properties of efficiency, symmetry and strong monotonicity. Second, we characterize the grey Shapley value by using the grey dividends.

On the interval game-theoretic solutions and their axiomatizations

In this paper, we study some of classical results in facility location games. Shapley value and equal surplus sharing rules are considered. It is seen that these rules do not have a population monotonic allocation schemes (PMAS). Further, we introduce facility location interval games and their properties. Finally, we conclude this paper.