### 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 language | English |
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Title of host publication | 2016 IEEE 55th Conference on Decision and Control, CDC 2016 |

Publisher | IEEE |

Pages | 4427-4432 |

ISBN (Electronic) | 9781509018376 |

DOIs | |

Publication status | Published - 2016 |

Externally published | Yes |

Event | 55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: 12 Dec 2016 → 14 Dec 2016 |

### Conference

Conference | 55th IEEE Conference on Decision and Control, CDC 2016 |
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Abbreviated title | CDC 2016 |

Country | United States |

City | Las Vegas |

Period | 12/12/16 → 14/12/16 |

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## Cite this

*2016 IEEE 55th Conference on Decision and Control, CDC 2016*(pp. 4427-4432). [7798941] IEEE. https://doi.org/10.1109/CDC.2016.7798941