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Background: This is a spatial version of the Prisoner's Dilemma. It is similar to the first model in that payoffs may vary, and pairs of individuals only interact a single time. However, in this model instead of individuals being able to interact with anybody in the entire environment, they can only interact with those individuals that are in a local "neighborhood." This can result in a different outcome than with the same parameters in the first model.
Instructions: Provide parameters for the four possible meetings between cooperators and defectors, as in the first model. All parameters must be positive or zero, but there are no other restrictions. When the range is left at the default of 1, everyone interacts with only those individuals that are within one cell's distance. This may be increased to 2 or 3 cells in each direction (range 2 and 3). The default edge condition of "wrap" means that cells on the edges are effectively each other's neighbors (i.e. a cell on the very left edge has as its neighbor a cell on the right edge). You can try starting with the default random starting conditions, by clicking on the random button, or you can load one of the pictures from the image to load menu and then click load image. You may also modify one of the pictures by simply clicking on the different squares in the grid. They will cycle through the four available colors for each time you click. Each time you change the parameters you must re-initialize the grid by clicking again on load image (to use one of the prepared starting conditions) or random (to start from random conditions). You should also make sure you stop before scrolling down, and before changing parameters.
Buttons: Start- Begins the simulation, Step- Advances the simulation one time step, Stop- Stops the simulation. Random- Reinitializes the grid with random colors (alternative to Load Image), Load image- Loads the image selected above (alternative to Random), Image to Load- Selects one of the prepared images to be used as a starting condition instead of Random (hit Load Image to actually load the picture), Save- Saves the current image for later use, Restore- Restores previously saved images (use like Load image, except it only loads a previous picture that you saved).
Interpretation: Due to the relatively small grid size, there is a lot of random fluctuation in this model. When you are starting from a random grid you may want to re-randomize and run it again. The only output here is the view of the grid itself. On the grid, blue represents cooperators, red represents defectors, yellow represents defectors that were just cooperators, and green represents cooperators that were just defectors. Are outcomes necessarily the same (or different) than the same parameters in model one? Are there clusters of like types on the grid or is everything evenly distributed? To simplify things, try fixing three of the parameters and just varying one.
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