ABSTRACT. We present a well-defined generalisation of the core to coalitional games with externalities, where the value of a deviation is given by an endogenous response, the solution (if nonempty: the core) of the residual game.
Measuring risk can be axiomatized by the concept of coherent measures of risk. A risk environment specifies some individual portfolios' realization vectors and a coherent measure of risk. We consider sharing the risk of the aggregate portfolio by studying transferable utility cooperative games: risk allocation games. We show that the class of risk allocation games coincides with the class of totally balanced games. As a limit case the aggregate portfolio can have the same payoff in all states of nature. We prove that the class of risk allocation games with no aggregate uncertainty coincides with the class of exact games.
JEL: C 71Keywords: Abstract Measuring risk can be axiomatized by the concept of coherent measures of risk. A risk environment specifies some individual portfolios' realization vectors and a coherent measure of risk. We consider sharing the risk of the aggregate portfolio by studying transferable utility cooperative games: risk allocation games.We show that the class of risk allocation games coincides with the class of totally balanced games. As a limit case the aggregate portfolio can have the same payoff in all states of nature. We prove that the class of risk allocation games with no aggregate uncertainty coincides with the class of exact games.
Decision making has become slow in the 27-member European Union and the Treaty of Nice distributed power in a somewhat arbitrary way. The Lisbon Treaty makes decision making easier, and streamlines the process by removing the most controversial element: the voting weights. The new system relies entirely on population data. We look at the immediate impact of the reform as well as the long term effects of the different demographic trends across countries. We find that the Lisbon rules hurt medium sized countries, especially Central Eastern European countries with declining populations most, while the United Kingdom is the clear winner.
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