Random Simulations of Braess's Paradox
abstract: This paper uses network theory to simulate Nash equilibria for selfish travel within a traffic network. Specifically, it examines the phenomenon of Braess's Paradox, the counterintuitive occurrence in which adding capacity to a traffic network increases the social costs paid by travelers in a new Nash equilibrium. It also employs the measure of the price of anarchy, a ratio between the social cost of the Nash equilibrium flow through a network and the socially optimal cost of travel. These concepts are the basis of the theory behind undesirable selfish routing to identify problematic links and roads in existing metropolitan traffic networks (Youn et al., 2008), suggesting applicative potential behind the theoretical questions this paper attempts to answer. New topologies of networks which generate Braess's Paradox are found. In addition, the relationship between the number of nodes in a network and the number of occurrences of Braess's Paradox, and the relationship between the number of nodes in a network and a network's price of anarchy distribution are studied.
Chotras, Peter Louis (Author)
Armbruster, Dieter (Thesis Director)
Lanchier, Nicolas (Committee Member)
Barrett, The Honors College
School of Mathematical and Statistical Sciences
Economics Program in CLAS
Game Theory
Random Simulation
Nash Equilibrium
Traffic
Braess's Paradox
eng
58 pages
Academic Year 2014-2015
Text
http://hdl.handle.net/2286/R.I.28877
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2015-05