Allocation in multi-agenda disputes: A set-valued games approach

We study allocation problems when agents negotiate across different agendas. Unlike existing papers on multi-agenda disputes, we consider environments in which resources are constrained and investing (time or effort) in one agenda reduces the ability to invest in other agendas. We introduce a class of cooperative games, referred to as set-valued games (SVG): The value of each coalition is a subset of payoff vectors. Each vector is associated with a distribution of the resources that the coalition may allocate across the agendas. In this environment we introduce and analyze the notion of the core. We show that the core allows for more cooperation opportunities and exchanging favors than existing cooperative multi-agenda models. Proving this relies on a general notion of a comparative advantage. It is shown that the classical core characterization, resorting to duality, does not hold in the current setup.