The thesis contains six independent papers with a common theme: Allocation problems and market design.

The first paper is concerned with fair allocation of risk capital where independent autonomous subunits have risky activities and together constitute the entity's total risk, whose associated risk capital has to be shared among the subunits. The problem is modeled as a TU game based on suitable measures of risk, which are applied to estimate the associated value of any possible coalition. The paper suggests the use of Lorenz undominated core selections for allocation of risk capital. It is argued that such a solution satisfies a number of desirable properties violated by the conventional alternatives.

The second paper is concerned with computational aspects of determining the set of Lorenz undominated core selections. The paper develops an algorithm.

The third paper uses the cooperative game theory approach with fractional players to allocate the common cost in an entity to the finite number of outputs. The paper is concerned with the computation of Aumann-Shapley prices when the cost function is estimated as a convex hull of a set of observed data points. It is discussed how to overcome certain problems related to non-differentiability of the cost function and inefficiency in production.

Staying within the theme of cost sharing a fourth paper analyzes a model for trading green energy in a grid where countries are characterized by stochastic demand and stochastic production. The gain is obtained by trading which at a certain point in time involves countries that have excess demand and countries that have surplus of green energy. The problem addressed here is how the gains from trade ought to influence the way that members of the grid share common costs.

The fifth paper extends the classical two-sided one-to-one matching model by including a set of objects, such that a matching consists of two agents from disjoint sets, and an object. Agents' preference lists consist of all possible pairs of objects and agents from the other set, and thus contain important information about agent-object tradeoffs. The notion of a blocking pair is defined for this setting and a certain class of matching mechanisms is suggested.

Finally, the sixth paper seeks to rationalize observed coalition formation in fish wars, in particular the so-called Mackerel crisis in the North Atlantic sea. The main idea here is to apply the concept of coalition proof Nash equilibrium to study stable patterns of cooperation.