Theoretical Economics, Volume 11, Number 3 (September 2016)

Theoretical Economics 11 (2016), 937–969

Negotiation across multiple issues

Gabrielle Gayer, Dotan Persitz


In the present work, agreement on allocation of payments from multiple issues requires unanimous consent of all parties involved. The agents are assumed to know the aggregate payoffs but do not know their decomposition by issues. This framework applies to many real-world problems, such as the formation of joint ventures. We present a novel solution concept to the problem, termed the multi-core, wherein an agent consents to participate in the grand coalition if she can envision a decomposition of the proposed allocation for which each coalition to which she belongs derives greater benefit on each issue by cooperating with the grand coalition rather than operating alone. An allocation is in the multi-core if all agents consent to participate in the grand coalition. We provide a theorem characterizing the non-emptiness of the multi-core and show that the multi-core generalizes the core. We prove that the approach of the multi-core has the potential to increase cooperation among parties beyond that of solving issues independently. In addition, we establish that the multi-core wherein agents take into account the specifics of the original issues is a refinement of the core of the sum of individual issues in which such information is ignored.

Keywords: Cooperative games, issue linkage, multi-issue bargaining, multi-core

JEL classification: C71, C78, D74

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