MULTI-MARGINAL OPTIMAL TRANSPORT AND MULTI-AGENT MATCHING PROBLEMS: UNIQUENESS AND STRUCTURE OF SOLUTIONS

作者：Pass Brendan^*

来源：Discrete and Continuous Dynamical Systems, 2014, 34(4): 1623-1639.

DOI：10.3934/dcds.2014.34.1623

• Multi-marginal Monge Kantorovich problems
• optimal transport
• matching
• Monge solutions
• uniqueness
• equilibrium
• purity

We prove uniqueness and Monge solution results for multi-marginal optimal transportation problems with a certain class of surplus functions; this class arises naturally in multi-agent matching problems in economics. This result generalizes a seminal result of Gangbo and Swiech [17]. Of particular interest, we show that this also yields a partial generalization of the Gangbo-Swiech result to manifolds; alternatively, we can think of this as a partial extension of McCann's theorem for quadratic costs on manifolds to the multi-marginal setting [23].
We also show that the class of surplus functions considered here neither contains, nor is contained in, the class of surpluses studied in [27], another generalization of Gangbo and Swiech's result.

• 出版日期2014-4