Second order signaling and Runaway Signals

julien Lie-Panis & jean-louis Dessalles

This is the companion Website for the article:
Runaway signals: Exaggerated displays of commitment may result from second-order signaling


The program used for these simulations is based on the Evolife platform developed at Telecom-Paris (Institut Polytechnique de Paris).
  • Download the program as it is used for the present illustrations from this location.
    Follow instructions from Evolife’s documentation to install the program.
    The main program can then be found in the directory Evolife/Apps/Patriot/Patriot.py.
    Go to the directory Evolife/Apps/Patriot and run the program by typing starter.
  • Evolife’s documentation is available ➜ there.

Effect of outrage on commitment signals

OneLevel.gif

      Evolution with default parameters. When uniform signal is reached, outrage is theoretically expected to be pointless, as there is no-one to be outraged at. We indeed observe a drop of outrage probality. However, some individuals do not signal from time to time due to learning exploration. This helps maintain a certain level of outrage.
red dots are outraged individuals - brown dots are their targets

Here are the main default parameters used in the simulations
parameter value meaning
ContemptImpact     -30     harming effect of outrage (\(h\))
CostDecrease     5     signal cost inequality between low- and high-quality individuals
FollowerImpact     10     advantage for attracting an affiliate (\(s\))
FollowingImpact     0     advantage coefficient for becoming affiated affiated with a high-quality individual
JumpProbability     5     probability of trying any value during learning
LearningSpeed     20     maximal additive exploration during learning
MaxFollowers     5     maximal number of incoming affiliations
MaxFriends     2     maximal number of individuals to affiliate with
NbAgents     200     size of the population
NumberOfGroups     5     number of groups
PolicingCost     -5     cost of outrage (\(c_2\))
SignallingCost     -100     signaling cost coefficient \(c_1\) (cost = \(c_1 \times \text{max signal amplitude}\))
Visibility     10     probability that one’s signal will be visible during an interaction

    

Runaway signaling due to outrage

This slow five-stage run shows how the population steadily climbs regularly spaced signal levels through time. It has been obtained by setting the benefit of being followed (\(s\)) to a small value. In typical runs (i.e. with normal values for \(s\)), intermediary stages are hardly marked, as top-quality (most motivated) individuals have an incentive to climb up the signal ladder as soon as an uniform signal has been reached or nearly reached.

fiveStages_.png

 Obtained with default parameters (see above) except:
ContemptImpact    -150
CostDecrease    7
FollowerImpact    2
JumpProbability    3
LearningSpeed    10
NumberOfGroups    10
PolicingCost    -1
SignallingCost    -120

stages1_NoOutrage_field.gif


 Here we can see on the right ➜ how the population climbs up regularly spaced signal levels. At each transition, top-quality individuals (on the right of the horizontal axis) tend to be the first to climb, whereas lowest-quality individuals (on the left of the horizontal axis) tend to be the last. Red dots are outraged individuals; brown dots are their targets.
As a comparison, we can see on the left ← that in the absence of outrage, no runaway occurs. We are left with a basic separating equilibrium in which only the top-most motivated individuals send the signal.

stages1_field.gif
Parameters used in this simulation
= default parameters (see above) except: 		ContemptImpact    -100 (right) or 0 (left)
LearningSpeed    10 		NumberOfGroups    10
SignallingCost    -300