Università degli Studi dell'Aquila
Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica
Via Vetoio, Località Coppito, 67010 L'AQUILA
COURSE PROGRAM
Non-cooperative Networks
A.Y. 2021/22 Prof. Guido Proietti
PART I: Equilibria in
networks
September 29,
2021: Introduction to non-cooperative networks. Basics of
game theory. Equilibria. Dominant strategy equilibrium: the prisoners’ dilemma.
September 30,
2021: Nash equilibrium (NE): the battle of sexes. Games
without equilibria: Head or Tail game. The Nash’s Theorem. Computational
aspects of Nash equilibria: mixed and pure strategies. Existence of NE in pure
and mixed strategies.
October 6, 2021: The selfish routing problem. The price of anarchy (PoA).
Pigou’s example and Braess’ paradox. Existence of a
Nash flow. PoA for the selfish routing: linear and
non-linear latencies.
October 7,
2021: Global connection games. Existence of a NE: the
potential method. Lower and upper bounds for the PoA.
The price of stability (PoS). Lower and upper bounds for the PoS.
Slides: Global connection games
October 13,
2021: Network creation games. Hardness of finding a best
response. Optimal graphs: cliques and stars.
October 14,
2021 (Dott. Gianpiero Monaco): Network creation games are not potential
games. Stable graphs: cliques and stars. Upper bound to the PoS.
Upper bound to the PoA.
Slides: Network creation games
PART II: Algorithmic
mechanism design (AMD)
Lecture notes: Algorithmic Mechanism Design (print from page 2 to
page 14)
October 20, 2021: The implementation problem. Second-price
auction. Mechanism design. Computational aspects of mechanisms. Strategy-proof
mechanisms. Utilitarian problems. VCG mechanisms.
October 21, 2021: VCG mechanisms. Clarke payments.
Algorithmic Mechanism Design for graph optimization problems.
Slides: Algorithmic mechanism design
October 27, 2021: VCG-mechanism for the private-edge
Shortest-Path problem. Trivial O(mn)
time implementation. Efficient O(m + n log n) time
implementation based on the Malik, Mittal, and Gupta algorithm.
Slides: VCG-mechanism for the private-edge SP problem
October 28, 2021: VCG-mechanism for the private-edge
Minimum Spanning Tree problem. Trivial O(mn α(m,n)) time
implementation. Efficient O(m α(m,n)) time implementation based on the transmuter.
Slides: VCG-mechanism for the private-edge MST problem
November 3, 2021 (Dott. Stefano Leucci): Non-utilitarian, one-parameter problems. One-parameter mechanisms.
Truthfulness of one-parameter mechanisms.
Slides: One-parameter mechanisms.
November 4, 2021:
One-parameter mechanism for the private-edge Shortest-Path Tree problem.
Trivial O(mn+n2 log n) time implementation.
Efficient O(m + n log n) time implementation based on
the transmuter. Summary
and question time.
Slides: VCG-mechanism for the private-edge SPT problem.
Mid-term exam: November
16-18 (exact date, time and room to be decided), 2021, in attendance and on a
remote basis for DAD authorized students only on the private channel of the Team ”Non-Cooperative Networks - A.A. 2021-2022”