A saturated strategy robustly ensures stability of the cooperative equilibrium for Prisoner's dilemma
(2016) 55th IEEE Conference on Decision and Control 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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- author
- Giordano, Giulia LU ; Bauso, Dario and Blanchini, Franco
- organization
- publishing date
- 2016-12-27
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- 2016 IEEE 55th Conference on Decision and Control, CDC 2016
- article number
- 7798941
- pages
- 6 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- 55th IEEE Conference on Decision and Control 2016
- conference location
- Las Vegas, NV, United States
- conference dates
- 2016-09-12 - 2016-09-14
- 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
- 2022-02-14 08:08:29
@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 = {{IEEE - 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}},
doi = {{10.1109/CDC.2016.7798941}},
year = {{2016}},
}