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. 2020/21 Prof. Guido Proietti
PART I: Equilibria in
networks
October 7,
2020: Introduction to non-cooperative networks. Basics of
game theory. Equilibria. Dominant strategy equilibrium: the prisoners’ dilemma.
Slides: Introductory elements
October 8,
2020: 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 14, 2020: 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 15,
2020 (Dott. Monaco): 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 21,
2020 (Dott. Monaco): Network
creation games. Hardness of finding a best response.
October 22,
2020 (Dott. Monaco): Network
creation 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 28, 2020: The implementation problem. Second-price
auction. Mechanism design. Computational aspects of mechanisms. Strategy-proof
mechanisms. Utilitarian problems. VCG mechanisms.
October 29, 2020: VCG mechanisms. Clarke payments.
Algorithmic Mechanism Design for graph optimization problems.
Slides: Algorithmic mechanism design
November 4, 2020:
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
November 5, 2020:
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 11, 2020 (Dott.
Leucci): Non-utilitarian, one-parameter problems. One-parameter mechanisms.
Truthfulness of one-parameter mechanisms.
Slides: One-parameter mechanisms.
November 12, 2020:
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.
November 19, 2020, at 11.50,
Teams channel 3alrsbo:
Mid-term exam.