The Coase theorem states that social efficiency can be obtained through bargaining and that the gains to each party involved will be identical regardless of who has the rights.
The net gains to each party depend on the initial allocation of property rights.

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The Coase theorem states that as long as property rights are clearly defined and transaction costs are negligible, parties will bargain to an efficient outcome regardless of the initial allocation of rights. However, it does not claim that the gains to each party will be identical; the distribution of gains depends on the initial allocation of rights.

The Coase Theorem States That Social Efficiency Can Be Obtained