Background: This model simulates what happens under different
payoff scenarios for the four possible combinations of cooperating and defecting.
You may interpret the payoffs as units of resource that will be gained as
a result of a single interaction. These resource units are translated into
offspring at the end of each generation, and the proportion of cooperators
and defectors in the next generation is simply the proportions of offspring
produced by the two types (i.e. there is no adult survival). Although theoretically
the payoffs can be anything, this model considers the case when mutual cooperation
favors mutual defection (i.e. cooperation is good when it works). It is
assumed that there is a 50/50 mix of cooperators and defectors at the start.
Instructions: Type values for each of the four payoffs. The payoff
is for the player on the left when it meets the player on the top. The payoff
for two cooperators must be greater than that for two defectors. All payoffs
must be positive and no two payoffs may be the same. Hit RUN when
you are ready. If you have not constrained your parameters to the defined
conditions, you will be informed "Error Redo."
Interpretation: The table in the lower left provides data for
the theoretically calculated equilibrium
proportions of cooperators and defectors in the left column, and the results
of a simulation in the right column (averaged over the last three generations
(98, 99 and 100)). When a "*" is placed by the output, this means
that the equilibrium is unstable and either type may win. In this case the
calculated output is a best guess at which type this will be. The graph
on the right shows the proportion of cooperators and defectors over time
starting from a 50/50 mix. Note how this graph jumps around randomly. This
indicates that you might want to look at multiple runs for a given set of
payoffs. Good questions to focus on are "Under what conditions do cooperators
win?" and "How do the parameters affect the equilibrium densities?"
