Economic applications of the theory of graphs.
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Later, the Markov connection is exploited with some new graph theoretic proofs in the end. A gorgeous paper. An interesting connection to how some graph theoretic stuff may be generalized, the requirement of weak acyclicity of best replies in the above can be seen as an analogous requirement to the property of supermodularity seen here ; in effect, both serve to prevent cycles. A nice example of this is Acemoglu, Ozdaglar, Tahbaz-Salehi Network Games This is, I suspect, what you most expected when asking the question.
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There is a branch of game theory that explicitly deals with games that have some sort of graphical structure. Kun, Powers and Reyzin is an example that discusses the relation between pure-strategy Nash equilibria in network games of anti-coordination and graph coloring problems. I'm not sure exactly which flavor of research you're asking for, so this might not be what you wanted.
The mechanism design for kidney exchange literature uses and proves a number of graph-theoretical results. See e. Maximum weight cycle packing in directed graphs, with application to kidney exchange programs By Biro et. By Itai Ashlagi et.
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