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• Determining the urban critical infrastructures in the event of an earthquake. • Designing Location-Routing-Inventory decisions in humanitarian relief chain. • Simulation of interaction of urban infrastructure in earthquake conditions. • Using a cooperative game to examine the manner of cooperation of disaster relief supply chain players. • Application of the model to a real-world disaster relief logistic case study. This paper describes a new simulation based mathematical model for locating distribution centres, vehicle routing, and inventory problems under earthquake conditions. In this paper, the proposed network includes affected areas, suppliers, distribution centres, and hospitals. Additionally, the basic infrastructures of the city, which are very fragile at the time of the earthquake, are identified. Then, the demand of each relief commodity is calculated depending on the different earthquake scenarios using simulation. The estimated demand is incorporated into the mathematical model as an uncertain parameter. The proposed methodology is designed as a two-stage model so that in the first stage the location and inventory of distribution centres are addressed. Thereafter, in the second stage the routing decisions are taken for the distribution of relief commodities from the distribution centres and suppliers to the affected areas. Due to the NP-hardness of the second stage model, this model is solved using multi-objective stochastic fractal search. This algorithm is one of the population-based and stochastic optimization techniques and inspired by the natural phenomenon of fractal growth. It should be noted that in the second stage, a cooperative game theory of coalition type is considered, which resulted in synergies that minimize the relief golden time. The kind of cooperation is the use of potential of co-operators' vehicle. In this stage, the possibility for the players to cooperate by sharing people and commodities transportation requests is considered. Also, to validate the model, a real case study is provided for a possible earthquake in Tehran. Finally, the comparison between the simulation results and the values obtained from the real system evaluates the performance of the implemented model. Considering normality and a 95% confidence interval, it can be concluded that the proposed model provides a precise representation of the real system's performance. [ABSTRACT FROM AUTHOR]

In this paper, we present a general model in which mutually dependent negotiations are simultaneously conducted and define a solution concept for the model. We provide a sufficient condition for the solution to exist and show that the solutions approximately coincide with the equilibrium outcomes of extensive form games. We present a solution to the merger paradox as an application. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we investigate robustness and dynamics for coalitional games with transferable utilities (TU games). In particular we study sequences of TU games. These sequences model dynamic situations in which the values of coalitions of players are not known beforehand, and are subject to changes over time. An allocation rule assigns a payoff to each player in each time period. This payoff is bounded by external restrictions, for example due to contractual agreements. Our main questions are: (i) under which conditions do the allocations converge to a core-element of the game, and (ii) when do the allocations converge to some specific allocation, the so-called nominal allocation? The main contribution of this paper is a design method for allocation rules that return solutions in the core or -core of the game under delayed information on the coalitions’ values, and therefore the resulting allocation rule is called robust. [Copyright &y& Elsevier]

Abstract: Sharing damage that has been caused jointly by several tortfeasors is analyzed from a normative point of view. We show how damage can be apportioned on two distinct bases: causation and degree of misconduct. Our analysis uses the concept of potential damage on the basis of which we define a transferable utility game. Its core defines acceptable judgments as allocations of the total damage against which no group of tortfeasors can object. We show that weighted Shapley values define acceptable judgments and, vice versa, acceptable judgments reveal weights. Our paper illustrates how the cooperative approach may bring useful insights into legal questions. In particular, the Shapley value appears of special interest, being founded on axioms that are in line with fundamental principles of tort law. [Copyright &y& Elsevier]

Abstract: In the paper we study the asymptotic behavior of the solidarity value and the equal split value in different classes of cooperative games. In particular, we discuss three natural definitions of asymptotic equivalence of values for TU-games, and identify for each of them the classes of games for which the solidarity value and the equal split value are equivalent. Also, a computer illustration of the obtained results is given. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the notion of a bi-cooperative game with fuzzy bi-coalitions and discuss the related properties. In real game theoretic decision making problems, many criteria concerning the formation of coalitions have bipolar motives. Our model tries to explore such bipolarity in fuzzy environment. The corresponding Shapley axioms are proposed. An explicit form of the Shapley value as a possible solution concept to a particular class of such games is also obtained. Our study is supplemented with an illustrative example. [Copyright &y& Elsevier]