---
res:
  bibo_abstract:
  - Cooperative behavior, where one individual incurs a cost to help another, is a
    wide spread phenomenon. Here we study direct reciprocity in the context of the
    alternating Prisoner's Dilemma. We consider all strategies that can be implemented
    by one and two-state automata. We calculate the payoff matrix of all pairwise
    encounters in the presence of noise. We explore deterministic selection dynamics
    with and without mutation. Using different error rates and payoff values, we observe
    convergence to a small number of distinct equilibria. Two of them are uncooperative
    strict Nash equilibria representing always-defect (ALLD) and Grim. The third equilibrium
    is mixed and represents a cooperative alliance of several strategies, dominated
    by a strategy which we call Forgiver. Forgiver cooperates whenever the opponent
    has cooperated; it defects once when the opponent has defected, but subsequently
    Forgiver attempts to re-establish cooperation even if the opponent has defected
    again. Forgiver is not an evolutionarily stable strategy, but the alliance, which
    it rules, is asymptotically stable. For a wide range of parameter values the most
    commonly observed outcome is convergence to the mixed equilibrium, dominated by
    Forgiver. Our results show that although forgiving might incur a short-term loss
    it can lead to a long-term gain. Forgiveness facilitates stable cooperation in
    the presence of exploitation and noise.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Benjamin
      foaf_name: Zagorsky, Benjamin
      foaf_surname: Zagorsky
  - foaf_Person:
      foaf_givenName: Johannes
      foaf_name: Reiter, Johannes
      foaf_surname: Reiter
      foaf_workInfoHomepage: http://www.librecat.org/personId=4A918E98-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-0170-7353
  - foaf_Person:
      foaf_givenName: Krishnendu
      foaf_name: Chatterjee, Krishnendu
      foaf_surname: Chatterjee
      foaf_workInfoHomepage: http://www.librecat.org/personId=2E5DCA20-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-4561-241X
  - foaf_Person:
      foaf_givenName: Martin
      foaf_name: Nowak, Martin
      foaf_surname: Nowak
  bibo_doi: 10.1371/journal.pone.0080814.s001
  dct_date: 2013^xs_gYear
  dct_publisher: Public Library of Science@
  dct_title: Forgiver triumphs in alternating prisoner's dilemma @
...