# EvoLudoLab: Spatial 2x2 Game - Coexistence

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 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: Cooperators Defectors New cooperator New defector
 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.

## 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

Strategies - Structure

Snapshot of the spatial arrangement of strategies.

Strategies - Mean

Time evolution of the strategy frequencies.

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 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.

Reward
reward for mutual cooperation.
Temptation
temptation to defect, i.e. payoff the defector gets when matched with a cooperator. Without loss of generality two out of the four traditional payoff values $$R, S, T$$ and $$P$$ can be fixed and set conveniently to $$R = 1$$ and $$P = 0$$. This means mutual cooperation pays $$1$$ and mutual defection zero. For example for the prisoner's dilemma $$T > R > P > S$$ must hold, i.e. $$T > 1$$ and $$S < 0$$.
Sucker
sucker's payoff which denotes the payoff the cooperator gets when matched with a defector.
Punishment
punishment for mutual defection.
Init Coop, init defect
initial fractions of cooperators and defectors. If they do not add up to 100%, the values will be scaled accordingly. Setting the fraction of cooperators to 100% and of defectors to zero, then the lattice is initialized with a symmetrical configuration suitable for observing evolutionary kaleidoscopes.