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

Dario Bauso, Dario Bauso, Giulia Giordano, Franco Blanchini

Risultato della ricerca: Other

1 Citazione (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).
Lingua originaleEnglish
Pagine4427-4432
Numero di pagine6
Stato di pubblicazionePublished - 2017

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Prisoners' Dilemma
Asymptotic stability
Dynamical systems
Trajectories
Game
Defects
Rectangle
Local Asymptotic Stability
Repeated Games
Quadrant
Equilibrium Solution
Instant
Continuous Time
Attractor
Choose
Dynamical system
Trajectory
Converge
Invariant
Strategy

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. / Bauso, Dario; Bauso, Dario; Giordano, Giulia; Blanchini, Franco.

2017. 4427-4432.

Risultato della ricerca: Other

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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).

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