Hodge Theoretic Reward Allocation for Generalized Cooperative Games on Graphs
Hodge Theoretic Reward Allocation for Generalized Cooperative Games on Graphs
This paper generalizes L.S. Shapley's celebrated value allocation theory on coalition games by discovering and applying a fundamental connection between stochastic path integration driven by canonical time-reversible Markov chains and Hodge-theoretic discrete Poisson's equations on general weighted graphs.More precisely, we begin by defining cooperative games on general graphs and generalize …