Data from: The evolution of cooperation by negotiation in a noisy world

Cooperative interactions among individuals are ubiquitous despite the
possibility of exploitation by selfish free-riders. One mechanism that may
promote cooperation is “negotiation”: individuals altering their behaviour
in response to the behaviour of others. Negotiating individuals decide
their actions through a recursive process of reciprocal observation,
thereby reducing the possibility of free-riding. Evolutionary games with
response rules have shown that infinitely many forms of the rule can be
evolutionarily stable simultaneously, unless there is variation in
individual quality. This potentially restricts the conditions under which
negotiation could maintain cooperation. Organisms interact with one
another in a noisy world in which cooperative effort and the assessment of
effort may be subject to error. Here, we show that such noise can make the
number of evolutionarily stable rules finite, even without quality
variation, and so noise could help maintain cooperative behaviour. We show
that the curvature of the benefit function is the key factor determining
whether individuals invest more or less as their partner's investment
increases; investing less when the benefit to investment has diminishing
returns. If the benefits of low investment are very small then behavioural
flexibility tends to promote cooperation, because negotiation enables
co-operators to reach large benefits. Under some conditions this leads to
a repeating cycle in which cooperative behaviour rises and falls over
time, which may explain between-population differences in cooperative
behaviour. In other conditions negotiation leads to extremely high levels
of cooperative behaviour, suggesting that behavioural flexibility could
facilitate the evolution of eusociality in the absence of high
relatedness.