A robust saturated strategy for n-player prisoner's dilemma

Giulia Giordano, Dario Bauso, Franco Blanchini

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
34 Downloads (Pure)


We study diffusion of cooperation in an n-population game in continuous time. At each instant, the game involves n random individuals, one from each population. The game has the structure of a prisoner's dilemma, where each player can choose a continuous decision variable associated with the probability of cooperating or defecting. We turn the game into a positive dynamical system. Then, we propose a novel strategy that is the saturation of a polynomial function. The strategy requires to each player exclusively the knowledge of her/his own current average payoff, along with her/his own payoffs in the cooperative and noncooperative equilibria; no information about other players' payoffs is required. The proposed strategy guarantees local stability of the cooperative equilibrium if the degree p of the polynomial is greater than or equal to 2. Conversely, the noncooperative equilibrium becomes unstable, for p large enough, if and only if a certain Metzler matrix depending on the payoffs has a positive Frobenius eigenvalue. We prove that the n-dimensional box of all payoffs between the noncooperative and the cooperative ones is positively invariant. Finally we show that, for p large, the domain of attraction of the cooperative equilibrium inside this box becomes arbitrarily close to the box itself.

Original languageEnglish
Pages (from-to)3478-3498
JournalSIAM Journal on Control and Optimization
Issue number5
Publication statusPublished - 2018


  • Dynamic games
  • Equilibria
  • Invariant sets
  • Prisoner's dilemma
  • Stability


Dive into the research topics of 'A robust saturated strategy for n-player prisoner's dilemma'. Together they form a unique fingerprint.

Cite this