Various signaling probs with mediocre screening

[davidrpugh]

Case where IPD condition is not satisfied

In the plots below, I use the following payoff matrix:

payoffs = {'PiaA': 9.0, 'PiAA': 5.0, 'Piaa': 3.0, 'PiAa': 2.0}

Note the for this payoff matrix the iterated prisoner's dilemma (IPD) condition (i.e., 2 * PiAA > PiaA + PiAa is not satisfied.

Case where IPD condition is satisfied

In the plots below, I use the following payoff matrix:

payoffs = {'PiaA': 7.0, 'PiAA': 5.0, 'Piaa': 3.0, 'PiAa': 2.0}

Note the for this payoff matrix the iterated prisoner's dilemma (IPD) condition (i.e., 2 * PiAA > PiaA + PiAa is satisfied. The only difference between these payoffs and the ones used in the previous example is that the payoff to exploiting altruism has been reduced. As posited by @markeschaffer, imposing the IPD condition seems to eliminate the stable/balanced polymorphism (i.e., interior equilibria).

Personally, I don't think there is sufficient difference between the two sets of plots. Perhaps we should significantly increase the payoff to exploiting altruism in the top set of plots.

@markeschaffer , @PaulSeabright your thoughts?

[markeschaffer]

General question that applies to all of these: are there results where the initial condition is on the horizontal axis and the single parameter of interest is on the vertical axis? Variation in the initial condition(s) gives us a direct grip on the local stability issue.

[davidrpugh]

@markeschaffer

No, both the horizontal and vertical axes are parameters of interest. Variation in the initial condition is captured by the different plots. Note that the title of each subplot indicates the initial condition used in the simulations for that subplot.

Is this clear?

[markeschaffer]

Yes, clear. What I was asking is if you can also pls generate plots as I described. (Pls!)

[davidrpugh]

These graphics are no longer relevant.