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

Giulia Giordano, Dario Bauso, Franco Blanchini

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

1 Citation (Scopus)

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 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).

Original languageEnglish
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherIEEE
Pages4427-4432
ISBN (Electronic)9781509018376
DOIs
Publication statusPublished - 2016
Externally publishedYes
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: 12 Dec 201614 Dec 2016

Conference

Conference55th IEEE Conference on Decision and Control, CDC 2016
Abbreviated titleCDC 2016
CountryUnited States
CityLas Vegas
Period12/12/1614/12/16

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  • Cite this

    Giordano, G., Bauso, D., & Blanchini, F. (2016). A saturated strategy robustly ensures stability of the cooperative equilibrium for Prisoner's dilemma. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 4427-4432). [7798941] IEEE. https://doi.org/10.1109/CDC.2016.7798941