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Non-Cooperative Behavior in Wireless Networks

Non-Cooperative Behavior in Wireless Networks. Márk Félegyházi (EPFL) PhD. public defense. July 9, 2007. Summary of my research. Part I: Introduction to game theory. Ch 1: A tutorial on game theory Ch. 2: Multi-radio channel allocation in wireless networks

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Non-Cooperative Behavior in Wireless Networks

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  1. Non-Cooperative Behavior in Wireless Networks Márk Félegyházi (EPFL) PhD. public defense July 9, 2007

  2. Summary of my research Part I: Introduction to game theory • Ch 1: A tutorial on game theory • Ch. 2: Multi-radio channel allocation in wireless networks • Ch. 3: Packet forwarding in static ad-hoc networks • Ch. 4: Packet forwarding in dynamic ad-hoc networks • Ch. 5: Packet forwarding in multi-domain sensor networks • Ch. 6: Cellular operators in a shared spectrum • Ch. 7: Border games in cellular networks Part II: Non-cooperative users Part III: Non-cooperative network operators Márk Félegyházi (EPFL)

  3. Multi-Radio Channel Allocation Problem number of radios by sender i on channel x • C orthogonal channels • N communicating pairs of devices • k radios at each device → Nash equilibrium: No player has an incentive to unilaterally deviate. Proposition: If S* is a NE in GMRCA, then dy,x≤ 1, for any channel x and y. • blabla, • blabla, blabla Márk Félegyházi (EPFL)

  4. How to Share a Pie with Selfish Researchers Who Know Game Theory Márk Félegyházi (EPFL) PhD. public defense July 9, 2007

  5. Problem Dining Game Theoreticians Márk Félegyházi (EPFL)

  6. Motivation BEFORE • pies were controlled by a trusted central authority • “Mark, I would strongly encourage you share the pie with Panos” • it was difficult to get enough plates  • no central control how to cut the pies • it is easy to get more plates to get a bigger share  NOW What is the effect of selfish behavior in pie sharing? Márk Félegyházi (EPFL)

  7. System model SYSTEM: • C pies • N selfish and rational (= hungry) researchers • k plates for each researcher ASSUMPTIONS: • the central authority does not help to share the pies • pies have the same size and quality (strawberry) • each researcher can reach any pie (by allocating a plate there) • pies are fairly shared • one slice on one plate Márk Félegyházi (EPFL)

  8. Example • C = 6 pies • N = 4 hungry researchers • k = 4 plates for each researcher number of plates by researcher i at pie x total number of plates by researcheri total number of plates demanding pie x Márk Félegyházi (EPFL)

  9. The pie-cut functions • pies have all the same size and quality • πt(kx)– total size of the shares of any pie x • π(kx) – size of a share per plate 3 3 Márk Félegyházi (EPFL)

  10. Dining Game Theoreticians (DGT) game selfish (=hungry) researchers non-cooperative game GDGT players→ researchers strategy → plate allocation payoff → total amount of cookie payoff: Márk Félegyházi (EPFL)

  11. Stability: Nash equilibrium Best response: Best strategy of a researcher given the strategies of others. Nash equilibrium: No researcher changes if the others keep their plates. Márk Félegyházi (EPFL)

  12. The Question Where shall I put my plates? Márk Félegyházi (EPFL)

  13. Cut the pies in (almost) the same number of pieces pick two pies x and y, where kx ≥ ky demand: dx,y = kx – ky Recognition: In a stable state (NE), dy,x≤ 1 for any two pies x and y. Márk Félegyházi (EPFL)

  14. Distribute your plates • pick two pies x and y, where kx ≥ ky • demand: dx,y = kx – ky Truth 1: The researchers won’t change the position of their plates (NE), if: • dx,y≤ 1and • ki,x≤ 1. Nash Equilibrium: Put 1 plate per pie Márk Félegyházi (EPFL)

  15. Put more plates to some pies • pick two pies x and y, where kx ≥ ky • demand: dx,y = kx – ky • more and less demanded pies C+ and C– Truth 2:The researchers won’t change the position of their plates (NE), if: • dx,y≤ 1, • for any researcher i who haski,x≥ 2, x in C, • for any researcher i who haski,x≥ 2 and x inC+, ki,y≥ ki,x– 1, for all y inC– Nash Equilibrium: Put more plates to some pies Márk Félegyházi (EPFL)

  16. Convergence to stable states Algorithm with imperfect info: • researchers don’t know the demand for pies they are not demanding themselves • move plates from demanded pies to other randomly chosen pies • desynchronize the changes • convergence is not ensured Márk Félegyházi (EPFL)

  17. Summary • hungry researchers having several plates • Dining Game Theoreticians game • results for a stable pie sharing (NE): • researchers should use all their plates • similar demand for each pie • two types of stable states • NE are efficient both in theory and practice • fairness issues • equilibria for coalitions • algorithms to achieve efficient NE: • centralized algorithm with perfect information • distributed algorithm with imperfect information Márk Félegyházi (EPFL)

  18. Back to wireless networking • C orthogonal channels – C pies • N communicating pairs of devices – N researchers • k radios at each device – k plates Márk Félegyházi (EPFL)

  19. Some contributions • Stability and convergence of multi-radio channel allocation in wireless networks • Cooperation conditions for packet forwarding in ad hoc networks • Spectrum sharing strategies of wireless network (cellular) operators Márk Félegyházi (EPFL)

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