‘Raise the stakes’ evolves into a defector

Abstract

To understand how cooperation can evolve by reciprocal altruism when individuals can make variable investments, Roberts and Sherratt have introduced a new strategy, 'raise the stakes' (RTS), for a continuous version of the iterated 'prisoner's dilemma'. An individual investing I bears a cost I, while the recipient gets a benefit kI. For k>1, this generalizes the standard prisoner's dilemma. Over R alternating encounters, RTS is defined as follows: on the first move, invest a, subsequently raise your investment by 2b (or b) if your partner's previous investment bettered (or equalled) your last move, otherwise match your partner's last move. This strategy is denoted by =(a,b). Roberts and Sherratt reported that the strategy =(1,1) performs well in computer simulations against various alternative strategies but did not consider how a population of RTS strategies with different a and b values evolves. We find that selection within RTS populations always acts to lower the values of a and b, hence RTS cooperation is not a robust phenomenon.