When there are three parties, it is well known that the Coase Theorem may not hold even when there are no transaction costs, due to the emptiness of the core of the corresponding cooperative game [Aivazian and Callen (1981)]. We show that the standard Coasean bargaining game involving three parties is strategically equivalent to an asymmetric three player majority game. Hence, when there are three parties, the Coase Theorem fails if and only if the core of the corresponding three player majority game is empty. We use this equivalence result to derive all instances in which the Coase Theorem will and will not hold with three parties, and show that the Coase Theorem will actually hold most (over 80 per cent) of the time. We also demonstrate, in contrast to Aivazian and Callen (2003), that it is always possible to find a set of transaction costs which, when introduced into a frictionless bargaining situation, will cause an empty core to become non-empty. In other words, with suitably designed transaction costs, it is possible for the Coase Theorem to hold in cases where, in the absence of those transaction costs, it would fail to hold. When there are three parties, rather than hindering agreements, transaction costs can encourage Coasean bargaining.
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机译：当有三方时，众所周知，科斯定理即使在没有交易成本的情况下也可能不成立，这是由于相应的合作博弈的核心是空的[Aivazian and Callen（1981）]。我们证明，涉及三方的标准Coasean讨价还价游戏在策略上等同于不对称的三人多数游戏。因此，当存在三方时，当且仅当相应的三人多数游戏的核心为空时，科斯定理才会失败。我们使用这个等价结果来推导科斯定理将在三个方中均将成立且将不成立的所有情况，并表明科斯定理实际上将持有大部分（超过80％）的时间。与Aivazian和Callen（2003）相比，我们还证明，总是有可能找到一组交易成本，当将这些交易成本引入无摩擦的讨价还价情况时，它将导致一个空核变为非空。换句话说，在设计适当的交易成本的情况下，科斯定理有可能在没有这些交易成本的情况下无法成立的情况下成立。如果有三方，则交易成本可以鼓励科ase讨价还价，而不是阻碍协议。
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