Probability Distributions on Partially Ordered Sets and Network Interdiction Games

This article poses the following problem: Does there exist a probability distribution over subsets of finite partially ordered set (poset), such that constraints involving marginal probabilities poset’s elements and maximal chains is satisfied? We present combinatorial algorithm to positively resolve this question. The can be implemented in polynomial time special case where chain are affine functions their elements. existence problem relevant for equilibrium characterization generic strategic interdiction game on capacitated flow network. involves routing entity sends its through network while facing path transportation costs an interdictor who simultaneously interdicts one or more edges edge costs. Using our result posets strict complementary slackness linear programming, we show Nash equilibria fully described using primal dual solutions minimum-cost circulation problem. Our analysis provides new critical components game. It also leads polynomial-time approach computation.