Convexity in stochastic cooperative situations

This paper introduces a new model concerning cooperative situations in which the payoffs are modeled by random variables. We analyze these situations by means of cooperative games with random payoffs. Special attention is paid to three types of convexity, namely coalitional-merge, individual-merge and marginal convexity. The relations between these types are studied and in particular, as opposed to their deterministic counterparts for TU games, we show that these three types of convexity are not equivalent. However, all types imply that the core of the game is nonempty. Sufficient conditions on the preferences are derived such that the Shapley value, defined as the average of the marginal vectors, is an element of the core of a convex game

A Nucleolus for Stochastic Cooperative Games

This paper extends the definition of the nucleolus to stochastic cooperative games, that is, to cooperative games with random payoffs to the coalitions. It is shown that the nucleolus is nonempty and that it belongs to the core whenever the core is nonempty. Furthermore, it is shown for a particular class of stochastic cooperative games that the nucleolus can be determined by calculating the traditional nucleolus introduced by Schmeidler (1969) of a specific deterministic cooperative game.Nucleolus;cooperative game theory;random variables;preferences

Stochastic Cooperative Games in Insurance and Reinsurance

This paper shows how problems in `non life'-insurance and `non life'-reinsurance can be modelled simultaneously as cooperative games with stochastic payoffs.Pareto optimal allocations of the risks faced by the insurers and the insureds are determined.It is shown that the core of the corresponding insurance games is nonempty.Moreover, it is shown that specific core allocations are obtained when the zero utility principle is used for calculating premiums. Finally, game theory is used to give a justification for subadditive premiums.insurance;stochastic processes;cooperative games

Convexity in Stochastic Cooperative Situations

AMS classification: 90D12.

A Nucleolus for Stochastic Cooperative Games

This paper extends the definition of the nucleolus to stochastic cooperative games, that is, to cooperative games with random payoffs to the coalitions. It is shown that the nucleolus is nonempty and that it belongs to the core whenever the core is nonempty. Furthermore, it is shown for a particular class of stochastic cooperative games that the nucleolus can be determined by calculating the traditional nucleolus introduced by Schmeidler (1969) of a specific deterministic cooperative game.

Stochastic Cooperative Games in Insurance and Reinsurance

This paper shows how problems in `non life'-insurance and `non life'-reinsurance can be modelled simultaneously as cooperative games with stochastic payoffs.Pareto optimal allocations of the risks faced by the insurers and the insureds are determined.It is shown that the core of the corresponding insurance games is nonempty.Moreover, it is shown that specific core allocations are obtained when the zero utility principle is used for calculating premiums. Finally, game theory is used to give a justification for subadditive premiums.

Price Uncertainty in Linear Production Situations

This paper analyzes linear production situations with price uncertainty, and shows that the corrresponding stochastic linear production games are totally balanced. It also shows that investment funds, where investors pool their individual capital for joint investments in financial assets, fit into this framework. For this subclass, the paper provides a procedure to construct an optimal investment portfolio. Furthermore it provides necessary and sufficient conditions for the proportional rule to result in a core-allocation.linear production;stochastic cooperative games;investment funds

Insurance Games

This paper generalizes the results of Suijs, De Waegenaere and Borm (1998) to arbitrary risks. It provides Pareto optimal allocations and shows that the zero utility premium calculation principle yields a core-allocation.