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A saturated strategy robustly ensures stability of the cooperative equilibrium for Prisoner's dilemma

Giordano, Giulia LU ; Bauso, Dario and Blanchini, Franco (2016) 55th IEEE Conference on Decision and Control 2016 In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 p.4427-4432
Abstract

We study diffusion of cooperation in a two-population game in continuous time. At each instant, the game involves two random individuals, one from each population. The game has the structure of a Prisoner's dilemma where each player can choose either to cooperate (c) or to defect (d), and is reframed within the field of approachability in two-player repeated game with vector payoffs. We turn the game into a dynamical system, which is positive, and propose a saturated strategy that ensures local asymptotic stability of the equilibrium (c, c) for any possible choice of the payoff matrix. We show that there exists a rectangle, in the space of payoffs, which is positively invariant for the system. We also prove that there exists a region in... (More)

We study diffusion of cooperation in a two-population game in continuous time. At each instant, the game involves two random individuals, one from each population. The game has the structure of a Prisoner's dilemma where each player can choose either to cooperate (c) or to defect (d), and is reframed within the field of approachability in two-player repeated game with vector payoffs. We turn the game into a dynamical system, which is positive, and propose a saturated strategy that ensures local asymptotic stability of the equilibrium (c, c) for any possible choice of the payoff matrix. We show that there exists a rectangle, in the space of payoffs, which is positively invariant for the system. We also prove that there exists a region in the space of payoffs for which the equilibrium solution (d, d) is an attractor, while all of the trajectories originating outside that region, but still in the positive quadrant, are ultimately bounded in the rectangle and, under suitable assumptions, converge to the solution (c, c).

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
2016 IEEE 55th Conference on Decision and Control, CDC 2016
pages
6 pages
publisher
Institute of Electrical and Electronics Engineers Inc.
conference name
55th IEEE Conference on Decision and Control 2016
external identifiers
  • scopus:85010822238
ISBN
9781509018376
DOI
10.1109/CDC.2016.7798941
language
English
LU publication?
yes
id
e9b361f6-045d-435e-b1af-edaa5c69e2b0
date added to LUP
2017-01-10 11:39:35
date last changed
2017-03-28 10:03:51
@inproceedings{e9b361f6-045d-435e-b1af-edaa5c69e2b0,
  abstract     = {<p>We study diffusion of cooperation in a two-population game in continuous time. At each instant, the game involves two random individuals, one from each population. The game has the structure of a Prisoner's dilemma where each player can choose either to cooperate (c) or to defect (d), and is reframed within the field of approachability in two-player repeated game with vector payoffs. We turn the game into a dynamical system, which is positive, and propose a saturated strategy that ensures local asymptotic stability of the equilibrium (c, c) for any possible choice of the payoff matrix. We show that there exists a rectangle, in the space of payoffs, which is positively invariant for the system. We also prove that there exists a region in the space of payoffs for which the equilibrium solution (d, d) is an attractor, while all of the trajectories originating outside that region, but still in the positive quadrant, are ultimately bounded in the rectangle and, under suitable assumptions, converge to the solution (c, c).</p>},
  author       = {Giordano, Giulia and Bauso, Dario and Blanchini, Franco},
  booktitle    = {2016 IEEE 55th Conference on Decision and Control, CDC 2016},
  isbn         = {9781509018376},
  language     = {eng},
  month        = {12},
  pages        = {4427--4432},
  publisher    = {Institute of Electrical and Electronics Engineers Inc.},
  title        = {A saturated strategy robustly ensures stability of the cooperative equilibrium for Prisoner's dilemma},
  url          = {http://dx.doi.org/10.1109/CDC.2016.7798941},
  year         = {2016},
}