A saturated strategy robustly ensures stability of the cooperative equilibrium for Prisoner's dilemma
(2016) 55th IEEE Conference on Decision and Control 2016 In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 p.44274432 Abstract
We study diffusion of cooperation in a twopopulation 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 twoplayer 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 twopopulation 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 twoplayer 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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 author
 Giordano, Giulia ^{LU} ; Bauso, Dario and Blanchini, Franco
 organization
 publishing date
 20161227
 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
 e9b361f6045d435eb1afedaa5c69e2b0
 date added to LUP
 20170110 11:39:35
 date last changed
 20170328 10:03:51
@inproceedings{e9b361f6045d435eb1afedaa5c69e2b0, abstract = {<p>We study diffusion of cooperation in a twopopulation 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 twoplayer 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 = {44274432}, 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}, }