  In an iterated non-cooperative game, if all the players act to maximize their
individual accumulated payoff, the system as a whole usually converges to a
Nash equilibrium that poorly benefits any player. Here we show that such an
undesirable destiny is avoidable in an iterated Rock-Paper-Scissors (RPS) game
involving two players X and Y. Player X has the option of proactively adopting
a cooperation-trap strategy, which enforces complete cooperation from the
rational player Y and leads to a highly beneficial as well as maximally fair
situation to both players. That maximal degree of cooperation is achievable in
such a competitive system with cyclic dominance of actions may stimulate
creative thinking on how to resolve conflicts and enhance cooperation in human
societies.
