Evolution of rumours that discriminate lying defectors

Discrimination of defectors is the key to the evolution of cooperation. In this paper, we examine the effect of rumours on the evolution of cooperation. 'Rumour' is defined as spreading or starting a reputation (concerned with cooperativeness of players), which is passed from one player to another. If players receive a rumour that a given player is a defector, they can avoid being defected by that player. However, to establish and maintain their cooperative relationship, players must also be able to distinguish incorrect rumours from correct ones because the rumour might be untrue. The speed of spreading an incorrect rumour is expected to affect its likelihood of detection and the consequences of detection. In computer simulations (individual-based simulation model), a pair (chosen randomly) plays the Prisoner's Dilemma game once. Each strategy consists of three rules: (1) a rule for the Prisoner's Dilemma game; (2) a rule for spreading a rumour; and (3) a rule for starting rumours. We consider 39 strategies in total. Then we classify strategies into several groups. The ADVISOR group of strategies, whose members are cooperative and start rumours about defectors, is not invaded by the LIAR group, whose members are defectors who tell lies, saying 'I'm cooperative'. ADVISOR (as a group) is not invaded by LIAR even though given pairs (one from each group) seldom meet more than once. If a correct rumour is seldom received, however, and if an incorrect rumour spreads quickly, members of ADVISOR (i.e. members that use strategies from the ADVISOR group) are confused by the incorrect rumour. As a result, ADVISOR is invaded by LIAR. As another group of strategies, we consider CONDITIONAL_ADVISOR, of which each representative member only spreads rumours received from other players who have cooperated with him. Unlike ADVISOR, CONDITIONAL_ADVISOR is able to refuse being invaded by LIAR. On the other hand, if the same conditions hold, but the cooperative strategy is instead based on the individual's own past experience, that group is invaded by LIAR. This implies that a rumour evolves if cooperators can, using that rumour, detect and punish cheaters - especially a lying defector.