  How attention scarcity effects the outcomes of a game? We present our
findings on a version of the Iterated Prisoners Dilemma (IPD) game in which
players can accept or refuse to play with their partner. We study the memory
size effect on determining the right partner to interact with. We investigate
the conditions under which the cooperators are more likely to be advantageous
than the defectors. This work demonstrates that, in order to beat defection,
players do not need a full memorization of each action of all opponents. There
exists a critical attention capacity threshold to beat defectors. This
threshold depends not only on the ratio of the defectors in the population but
also on the attention allocation strategy of the players.
