EvoLudoLab: 2x2 Game - Coexistence: Difference between revisions
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{{EvoLudoLab:2x2| | {{EvoLudoLab:2x2| | ||
options="--run --delay 200 --view Strategies_-_Mean --reportfreq 0.5 --popsize 10000 --popupdate | options="--game 2x2 --run --delay 200 --view Strategies_-_Mean --reportfreq 0.5 --popsize 10000 --popupdate async --playerupdate imitate --geometry M --intertype a --numinter 1 --references a --init 1,999 --inittype frequencies --mutation 0.0 --basefit 1.0 --selection 1.0 --reward 1.0 --punishment 0.0 --temptation 1.62 --sucker 0.38"| | ||
title=Type A and type B co-exist| | title=Type A and type B co-exist| | ||
doc=Almost independently of the initial configuration, the population quickly converges to a mixed state where type <math>A</math> and <math>B</math> players co-exist. | doc=Almost independently of the initial configuration, the population quickly converges to a mixed state where type <math>A</math> and <math>B</math> players co-exist. | ||
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In the context of cooperation, this scenario is captured by the Snowdrift Game, the Hawk-Dove Game or the Chicken Game: the best strategic option depends on the co-player - if he/she defects, it is better to cooperate but if he/she cooperates then defection pays off. Consequently, in a well-mixed population the rare type is always favored and hence cooperators and defectors co-exist in a stable equilibrium. Such interactions indicate another, slightly relaxed form of a social dilemma. | In the context of cooperation, this scenario is captured by the Snowdrift Game, the Hawk-Dove Game or the Chicken Game: the best strategic option depends on the co-player - if he/she defects, it is better to cooperate but if he/she cooperates then defection pays off. Consequently, in a well-mixed population the rare type is always favored and hence cooperators and defectors co-exist in a stable equilibrium. Such interactions indicate another, slightly relaxed form of a social dilemma. | ||
The above parameters are set to <math>R = 1, P = 0, T = 1.62</math> and <math>S = -0.38</math> with players imitating better strategies proportional to the payoff difference and an initial fraction of cooperators of 99% in a population of size 10'000.}} | The above parameters are set to <math>R = 1, P = 0, T = 1.62</math> and <math>S = -0.38</math> with players imitating better strategies proportional to the payoff difference and an initial fraction of cooperators of 99.9% in a population of size 10'000.}} | ||
[[Category: Christoph Hauert]] | [[Category: Christoph Hauert]] |
Latest revision as of 15:51, 13 October 2023
Color code: | Cooperators | Defectors |
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New cooperator | New defector |
Payoffs: | Low High
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Note: The gradient of the payoff scale is augmented by pale shades of the strategy colours to mark payoffs that are achieved in homogeneous populations of the corresponding type.
Type A and type B co-exist
Almost independently of the initial configuration, the population quickly converges to a mixed state where type [math]\displaystyle{ A }[/math] and [math]\displaystyle{ B }[/math] players co-exist.
In the context of cooperation, this scenario is captured by the Snowdrift Game, the Hawk-Dove Game or the Chicken Game: the best strategic option depends on the co-player - if he/she defects, it is better to cooperate but if he/she cooperates then defection pays off. Consequently, in a well-mixed population the rare type is always favored and hence cooperators and defectors co-exist in a stable equilibrium. Such interactions indicate another, slightly relaxed form of a social dilemma.
The above parameters are set to [math]\displaystyle{ R = 1, P = 0, T = 1.62 }[/math] and [math]\displaystyle{ S = -0.38 }[/math] with players imitating better strategies proportional to the payoff difference and an initial fraction of cooperators of 99.9% in a population of size 10'000.
Data views
Snapshot of the spatial arrangement of strategies. | |
Time evolution of the strategy frequencies. | |
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. | |
Statistics of fixation probabilities. | |
Statistics of fixation and absorption times. | |
Message log from engine. |
Game parameters
The list below describes only the few parameters related to the Prisoner's Dilemma, Snowdrift and Hawk-Dove games. Follow the link for a complete list and detailed descriptions of the user interface and further parameters such as spatial arrangements or update rules on the player and population level.
- --paymatrix <a00,a01;a10,a11>
- 2x2 payoff matrix. Type \(A\) has index 0 and type \(B\) index 1.
- --reward <a11>
- the reward for mutual cooperation. The payoff of type \(A\) against its own type (see --paymatrix).
- --temptation <a10>
- the temptation to defect. The payoff of type \(B\) against type \(A\) (see --paymatrix).
- --sucker <a01>
- the sucker's payoff of an exploited cooperator. The payoff of type \(A\) against type \(B\) (see --paymatrix).
- --punishment <a00>
- the punishment for mutual defection. The payoff of type \(B\) against its own type (see --paymatrix).
- --init <a,b>
- initial frequencies of type \(A\) and \(B\), respectively. Frequencies that do not add up to 100% are scaled accordingly.
- --inittype <type>
- type of initial configuration:
- frequency
- random distribution with given frequency
- uniform
- uniform random distribution
- monomorphic
- monomorphic initialization
- mutant
- single mutant in homogeneous population of another type. Mutant and resident types are determined by the types with the lowest and highest frequency, respectively (see option --init).
- stripes
- stripes of traits
- kaleidoscopes
- (optional) configurations that produce evolutionary kaleidoscopes for deterministic updates (players and population). Not available for all types of games.