Optimal memoryless CT strategy.

<p>The optimal values of both players' expected payoff per round and are shown in the upper panel (in units of NE payoff ) for each fixed value of , while the optimal values of the CT strategy's choice probabilities , and are shown in the lower panel. When the NE mixed strategy is better for player X than the CT strategy.</p

Optimal CT strategy of finite memory length.

<p>The optimal values of both players' expected payoff per round and are shown in the upper panel (in units of NE payoff ) for each fixed value of , while the minimal memory length of the CT strategy is shown in the lower panel.</p

The Rock-Paper-Scissors game.

<p>(A) The payoff matrix. Each matrix element is the payoff of the row player X's action in competition with the column player Y's action. (B) The cyclic (non-transitive) dominance relationship among the three candidate actions: Rock () beats Scissors (), beats Paper (), and in turn beats .</p

Optimal CT strategy of unit memory length.

<p>The optimal values of both players' expected payoff per round and are shown in the upper panel (in units of NE payoff ) for each fixed value of , while the optimal values of the CT strategy's choice probabilities , and are shown in the lower panel. When the NE mixed strategy is better for player X than the CT strategy.</p