Probability Distributions on Partially Ordered Sets and Network Interdiction Games
Name
1811.08516.pdf
Description
Submitted version
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603.2 KB
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Adobe PDF
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4546762ceed96b6379dd83aedd468480
Author(s)
Dahan, Mathieu
Amin, Saurabh
Jaillet, Patrick
Date Issued
2022
Journal
Mathematics of Operations Research
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Dahan, Mathieu, Amin, Saurabh and Jaillet, Patrick. 2022. "Probability Distributions on Partially Ordered Sets and Network Interdiction Games." Mathematics of Operations Research, 47 (1).
Version
Original manuscript
Abstract
This article poses the following problem: Does there exist a probability distribution over subsets of a finite partially ordered set (poset), such that a set of constraints involving marginal probabilities of the poset’s elements and maximal chains is satisfied? We present a combinatorial algorithm to positively resolve this question. The algorithm can be implemented in polynomial time in the special case where maximal chain probabilities are affine functions of their elements. This existence problem is relevant for the equilibrium characterization of a generic strategic interdiction game on a capacitated flow network. The game involves a routing entity that sends its flow through the network while facing path transportation costs and an interdictor who simultaneously interdicts one or more edges while facing edge interdiction costs. Using our existence result on posets and strict complementary slackness in linear programming, we show that the Nash equilibria of this game can be fully described using primal and dual solutions of a minimum-cost circulation problem. Our analysis provides a new characterization of the critical components in the interdiction game. It also leads to a polynomial-time approach for equilibrium computation.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Operations Research Center
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1287/MOOR.2021.1140
