The Social Cost Problem, Rights and the (Non)Empty Core

The “Coase theorem” is made of the efficiency and the neutrality theses. Using cooperative game theory, we show that these two theses are not compatible: there exist only two types of rights assignments that guarantee a nonempty core. Thus, the efficiency thesis holds – there exist (two types of) rights assignments under which the core of the game is nonempty – but the neutrality thesis does not hold – for all other rights assignments the core is empty. This complements the results found in the literature on Coase and the core. Our paper also adds two more results. Indeed, we add two principles that are not discussed in the literature about the Coase theorem: a democratic principle for rights assignments and a fairness principle for the monetary payoffs distributed to the agents, that we translate into two natural properties for a solution. We show, and this is our second main result, that the nonempty core requirement is not compatible with our democratic and fairness properties. Thus, under democratic and fairness criteria, the efficiency thesis does not hold