Figure 1.
(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
.
Figure 2.
Optimal memoryless CT strategy.
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.
Figure 3.
Optimal CT strategy of unit memory length.
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.
Figure 4.
Optimal CT strategy of finite memory length.
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.