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In this work, we explore the ecacy of two different ways of using reputation.
Reputation allows agents to be informed about other members of their group
before interacting with them, hence this information can be used in two ways,
either to retaliate against free-riders or to refrain from interacting with them. The
former modality, called “Defect”, consists in Gossipers not contributing to the
PGG when playing in a group containing too many cheaters. The latter modality,
“Refuse” allows agents to refuse the interaction by skipping a turn, taking their
contribution away from the pools, and paying the price of not receiving any
dividend, if the number of known defectors in their current group assignment
would make them active. Refusal cannot be performed twice in a row. In both
modalities, Gossipers transmit information about cheaters, informing their peers
of the identity of non-cooperators and using the information they receive from
them.
4 Experiments and Results
We run three different sets of simulations, each one lasting for 100 time steps.
Each experiment was repeated 20 times for each combination of the selected
parameters. The cost of contributing to the Public Good was set to 1, and the
sum of all the contributions was multiplied by a benefit factor set to 3. The
public good, i.e., the resulting quantity, was divided among all the group mem-
bers, without considering whether they contributed or not. Simulations started
with equal proportions of each strategy. Variables of interest are summarized in
Table 1.
Tabl e 1. Parameters of the simulation
PARAMETERS
COST (cost of punishing) 0.2 1
PUNISHMENT (cost of being punished) 2 5
GROUP SIZE
5 10 25 50
INFORMATION TRANSMITTED
0 1 10
In our first experiment we tested the effect of punishment as a partner con-
trol mechanism on cooperation rates measured as the total number of agents
playing C divided by the total number of active agents per time step. Nice and
Mean Punishers became active when they detected more than 20% of defec-
tions in their group. Punishing costed the punisher x and the punished agent
y , with y
x . We identified 4 different combinations of Punishment and Cost:
LpLc (low punishment, low cost), HpLc (high punishment, low cost), LpHc (low
punishment, High cost) and HpHc (high punishment and high cost). The co-
operation rates are affected by group size, and they change according to the
different combinations of punishment and cost (Figure 1). When punishment is
low and the cost is high, cooperation rates are the lowest for every group size.
 
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