The efficiency of adapting aspiration levels

Win–stay, lose–shift strategies in repeated games are based on an aspiration level. A move is repeated if and only if the outcome, in the previous round, was satisficing in the sense that the pay–off was at least as high as the aspiration level. We investigate the conditions under which adaptive mechanisms acting on the aspiration level (selection, for instance, or learning) can lead to an efficient outcome; in other words, when can satisficing become optimizing? Analytical results for 2 times 2–games are presented. They suggest that in a large variety of social interactions, self–centred rules (based uniquely on one's own pay–off) cannot suffice.