The Coase theorem holds only if two theses are verified. The efficiency thesis says that,
in the absence of transaction costs and if property rights are well defined, individuals will
always bargain to reach an optimal allocation of resources. The invariance (or neutrality)
thesis says that the outcome of bargaining is independent of the distribution of rights. In
this article we use a cooperative game model to show whether or not these two theses hold.
We study a social cost problem between one polluter interacts and many potential victims.
To analyze the solutions, we introduce three properties. First, Core stability indicates that
the payoff vector of the solution belongs to the core of the associated cooperative game.
Second No veto power for a victim says that no victim has the power to veto an agreement
signed by the rest of the society. Third, Full compensation ensures that the victims are
compensated for the damage caused by pollution. We then demonstrate two theorems.
First, Core stability is satisfied if and only if the rights are assigned either to the polluter
or to the entire set of victims. This means that the efficiency thesis can be satisfied but
at the expense of the invariance thesis. Second, we show that no solution satisfied at the
same time Core stability, No veto power for a victim and Full compensation. Hence, it is
not possible to reach a core-stable agreement which fully compensates all the victims in a
legal structure where no victim has a veto power.