EvoLudoLab: Spatial 2x2 Game - Coexistence
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.
Co-existence of type A and type B players
In well-mixed populations type \(A\) and \(B\) players co-exist in a stable equilibrium almost irrespective of the initial configuration. Interestingly, however, spatial structure often shifts the equilibrium in favor of \(B\) players.
The Snowdrift Game, Hawk-Dove game and Chicken Game fall into this category. In contrast to the Prisoner's Dilemma, spatial structure is not necessarily beneficial for cooperation and often actually inhibits or eliminates cooperation altogether. For the chosen parameters it results in roughly 25% cooperators as opposed to 40% in the well-mixed case.
The above parameters are set to \(R = 1, P = 0, T = 1.6\) and \(S = 0.4\) with Moore neighborhood and players imitating better strategies proportional to the payoff difference. The inital fraction of cooperators is 90%.
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.