nash/README

This is a small software that simulates the behaviour of a set of individuals
placed (for sake of simplicity) over a matrix where each individual can choose
between two strategies:

- Being cooperative with the other individuals
- Being in competition with the other individuals

From a certain starting point, in which each individuals has its own strategy
independantly from the one chosen by the others, the algorithm goes on, and a
certain individual x changes its strategy if there is a neighbour having a
different strategy and a higher "gain" value (i.e. that strategy takes more
benefit). The algorithm is repeated as long as an equilibrium point is reached
(Nash's equilibrium) in which no individual will change its strategy anymore as
no change is convenient anymore. This balance point won't be always reached
anyway, and the algorithm recognizes a scenario that has no Nash's equilibrium
point when a loop occurs (i.e. when it takes in exam a configuration that was
already met).

Usage of the program: compile simply issuing `make', then start it with
./nash <environment_file> <coop_coop_gain> <coop_comp_gain> <comp_coop_gain> <comp_comp_gain>

where

- environment_file is a file containing the starting configuration of the
environment (an example is included in the file `environment'). In this file the
collaborating individuals are marked by a dot `.', and the ones in competition
are marked by a `X'. Starting from here you can easily create your environment
file;

- coop_coop_gain: Score gained when the individual x cooperates and its neighbour
cooperates as well;

- coop_comp_gain: Score gained when the individual x cooperates and its neighbour
is in competition;

- comp_coop_gain: Score gained when the individual x is in competition and its
neighbour cooperates;

- comp_comp_gain: Score gained when both the individual x and its neighbour are
in competition.

An example is the problem of the two prisoners:

- When A doesn't confess and B doesn't confess too, they both get 8 years of
prison (coop_coop_gain = -8);

- When A doesn't confess and B confesses, A gets 20 years of prison and B is
free (coop_comp_gain = -20);

- When A confesses and B doesn't, A is free and B gets 20 years of prison
(comp_coop_gain = 0);

- When both A and B confess, they both get 14 years of prison (comp_comp_gain =
-14).

For running a simulation of the two prisoners' problem over the example
environment just type

./nash environment -8 -20 0 -14

Have fun.