2FieldSpatGame

This repository containts generalization of the code used in our research

spatial-evolutionary-game

In this game $2L^2$ individual "players" placed in a two two-dimensional spatial array.

Every individual can play one of two tactics: cooperate($\mathcal{C}$) or defect($\mathcal{D}$). At the beginning of the "game", each player has the probability of being assigned $\mathcal{C}$ with probability $p_c$ and tactics $\mathcal{D}$ otherwise.

In each round individuals "play the game" with 8 its neighbors and the average cooperator from this and another field. Tables of payoffs shown below

Table 1: Payoffs for games with neighbors.

payoffs	$\mathcal{D}$	$\mathcal{C}$
$\mathcal{D}$	0	0
$\mathcal{C}$	$b_j$	1

Table 2: Payoffs for games with average cooperator

payoffs	$\mathcal{D}$	$\mathcal{C}$
$\mathcal{D}$	0	0
$\mathcal{C}$	$b_j f_{ci}$	$f_{ci}$

Where $f_ci$ - fraction of cooperators on the field $i$ and $b_i$ payoff on the field $i$ After playing all games the site occupied either by its original owner or by one of the neighbors who scores the highest total payoff in that round.

In general the total payoff $P(x)$ of the agent $\sigma$ with strategy $s(x)$ placed on field $j$ can be calculated as

$$P(x) = \sum_{y\in n.n.}s^T(x)\hat{H}^js(y) + \sum_{i=1}^2\lambda_{ji}s^T(x)\hat{H}^{ji}_{mf}s(y)$$

Where $s(x) = (1,0)^T$ if $x$ - defector and $s(x) = (0,1)^T$ if $x$ - cooperator

Matrix $\hat{H}^j$ have a simmilar form to the Table 1

Matrix $\hat{H}^{ji}$ has a form

$b_j f_{ci}$	0
0	$f_{ci}$

Setup

To compile Cython file

pip install -r requirements.txt
make

If you need to test To test

make pytest

How to use it?

One can find example of the usage in notebook example.ipynb.

Two most important thing in compiled file is class

TwoFieldSpatialGame

and function

color_field_change(old_field, new_field)

which accept two 2-D array and returns 3-D array where RED - 0$\to$0 YELLOW - 1$\to$0 GREEN - 0$\to$1 BLUE - 1$\to$1