# EvoLudoLab: Continuous Snowdrift Game - Repellor

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 |
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Strategy code: | Defect | Cooperate |
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Payoff code: | Low | High |
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*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 | |

Snapshot of the spatial arrangement of strategies. | |

Time evolution of the strategy frequencies. | |

Snapshot of strategy distribution in population | |

Time evolution of the strategy distribution | |

Snapshot of the spatial distribution of payoffs. | |

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

Snapshot of payoff distribution in population. | |

Degree distribution in structured populations. | |

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.