### Abstract

Lingua originale | English |
---|---|

Pagine | 4427-4432 |

Numero di pagine | 6 |

Stato di pubblicazione | Published - 2017 |

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### All Science Journal Classification (ASJC) codes

- Artificial Intelligence
- Decision Sciences (miscellaneous)
- Control and Optimization

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*A Saturated Strategy Robustly Ensures Stability of the Cooperative Equilibrium for Prisoner’s Dilemma*. 4427-4432.

**A Saturated Strategy Robustly Ensures Stability of the Cooperative Equilibrium for Prisoner’s Dilemma.** / Bauso, Dario; Bauso, Dario; Giordano, Giulia; Blanchini, Franco.

Risultato della ricerca: Other

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TY - CONF

T1 - A Saturated Strategy Robustly Ensures Stability of the Cooperative Equilibrium for Prisoner’s Dilemma

AU - Bauso, Dario

AU - Bauso, Dario

AU - Giordano, Giulia

AU - Blanchini, Franco

PY - 2017

Y1 - 2017

N2 - 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).

AB - 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).

UR - http://hdl.handle.net/10447/253237

M3 - Other

SP - 4427

EP - 4432

ER -