"We analyse the two-dimensional Nash bargaining solution (NBS) deploying a standard labour market negotiations model (McDonald and Solow, 1981). We show that the two-dimensional bargaining problem can be decomposed into two one-dimensional problems such that the two solutions together replicate the solution of the two-dimensional problem, if the NBS is applied. The axiom of Independence of Irrelevant Alternatives turns out to be crucial for decomposability. Our result has significant implications for actual negotiations, as it allows for the decomposition of a multi-dimensional bargaining problem into simpler problems—and thus helps to facilitate real-world negotiations."

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