Probability Distributions on Partially Ordered Sets and Network Security Games

11/20/2018
by   Mathieu Dahan, et al.
0

We consider 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? In this article, we present a combinatorial algorithm to positively resolve this question. We show that this result plays a crucial role in the equilibrium analysis of a generic security 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. The first (resp. second) player seeks to maximize the value of effective (resp. interdicted) flow net the total transportation (resp. interdiction) cost. Using our existence result on posets and strict complementary slackness in linear programming, we show that the equilibrium properties of this game can be described using primal and dual solutions of a minimum cost circulation problem. Our analysis provides a new characterization of the critical network components.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/18/2021

Efficient Carpooling and Toll Pricing for Autonomous Transportation

In this paper, we address the existence and computation of competitive e...
research
11/09/2022

Decomposition of Probability Marginals for Security Games in Abstract Networks

Given a set system (E, 𝒫), let π∈ [0,1]^𝒫 be a vector of requirement val...
research
11/28/2018

A Game of Martingales

We consider a two player dynamic game played over T ≤∞ periods. In each ...
research
04/27/2023

Conditional dominance in games with unawareness

Heifetz, Meier, and Schipper (2013) introduced dynamic game with unaware...
research
08/11/2022

Incentivizing Hidden Types in Secretary Problem

We study a game between N job applicants who incur a cost c (relative to...
research
03/11/2020

Lifted samplers for partially ordered discrete state-spaces

A technique called lifting is employed in practice for avoiding that the...

Please sign up or login with your details

Forgot password? Click here to reset