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Various screening probs with imperfect signaling #21

Closed davidrpugh closed 9 years ago

davidrpugh commented 9 years ago

Females are relatively ineffective at signaling

In this first case of imperfect signaling, both types of females are relatively ineffective at signaling...

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.

Sweep of signaling probabilities

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).

Sweep of signaling probabilities

Females are relatively effective at signaling

In this second case, both types of females are relatively effective at signaling...

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.

Sweep of signaling probabilities

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).

Sweep of signaling probabilities

@markeschaffer , @PaulSeabright your thoughts?