The logic of contrition

A highly successful strategy for the Repeated Prisoner's Dilemma is Contrite Tit For Tat, which bases its decisions on the ''standings'' of the two players. This strategy is as good as Tit For Tat at invading populations of defectors, and much better at overcoming errors in implementation against players who are also using it. However, it is vulnerable to errors in perception. In this paper, we discuss the merits of Contrite Tit For Tat and compare it with other strategies, like Pavlov and the newly-introduced Remorse. We embed these strategies into an eight-dimensional space of stochastic strategies which we investigate by analytical means and numerical simulations. Finally, we show that if one replaces the conventions concerning the ''standing'' by other, even simpler conventions, one obtains an evolutionarily stable strategy (called Prudent Pavlov) which is immune against both mis-perception and mis-implementation. (C) 1997 Academic Press Limited.