EvoLudoLab: Continuous Snowdrift Game - Repellor

From EvoLudo

Along the bottom of the applet there are several buttons to control the execution and the speed of the simulations - for details see the EvoLudo GUI documentation. Of particular importance are the parameters button and the data data views pop-up list along the top. The former opens a panel that allows to set and change various parameters concerning the game as well as the population structure, while the latter displays the simulation data in different ways.

Color code: Maximum Minimum Mean
Strategy code: Defect Cooperate
Payoff code: Low High

Note: The shades of grey of the payoff scale are augmented by blueish and reddish shades indicating payoffs for mutual cooperation and defection, respectively.

Continuous Snowdrift game: Repellor

In this scenario, selection and mutation drives the population away from the singular strategy \(x^* = 0.6\), i.e. \(x^*\) is a repellor. The final state of the population now depends on the initial configuration of the population. If the initial strategy was \(x_0 < x^*\) then the investments decrease over time and defectors reign. However, if \(x_0 > x^*\) holds the population evolves towards a cooperative state with maximal investments. Also note that if \(x_0\) lies close to \(x^*\) then few mutants may diffuse to the other side of \(x^*\) and then again two branches evolve. But in contrast to evolutionary branching, this process is not generic as it requires a particular preparation of the initial configuration.

The parameters are set to \(b_2 = -0.5, b_1 = 3.4, c_2 = -1.5, c_1 = 4\) with players imitating better strategies proportional to the payoff difference and an initial traits/investment of \(0.5 \pm 0.05\) in a population of 5'000 individuals. Mutations occur with a probability of 1% and the standard deviation of the Gaussian distributed mutations is \(0.01\). Note that in this case it may or may not happen that a high investing branch evolves, depending on whether early mutants managed to have investment levels higher than \(x^* = 0.6\).

Data views

Strategies - Structure

Snapshot of the spatial arrangement of strategies.

Strategies - Mean

Time evolution of the strategy frequencies.

Strategies - Histogram

Snapshot of strategy distribution in population

Strategies - Distribution

Time evolution of the strategy distribution

Fitness - Structure

Snapshot of the spatial distribution of payoffs.

Fitness - Mean

Time evolution of average population payoff bounded by the minimum and maximum individual payoff.

Fitness - Histogram

Snapshot of payoff distribution in population.

Structure - Degree

Degree distribution in structured populations.

Console log

Message log from engine.

Game parameters

The list below describes only the few parameters related to the continuous snowdrift game. Follow the link for a complete list and descriptions of all other parameters e.g. referring to update mechanisms of players and the population.

Benefit/Cost Functions
A variety of different combinations of cost and benefit functions can be selected.
Benefit \(b_0,\ b_1\)
Two parameters for the benefit function. Note that not all functions require both.
Cost \(c_0,\ c_1\)
Two parameters for the cost function. Note that not all functions require both.
Mean invest
Mean trait value of initial population.
Sdev invest
Standard deviation of initial population. If set to negative values, the population will be initialized with uniform distributed traits.