The code in this repository is meant to find Nash equilibria for the following model:

We assume that $n$ players produce safety, $s$, and performance, $p$, as $s_i=A_i{K}_{s,i}^{{\alpha }_i}{p}_i^{-{\theta }_i},p_i=B_i{K}_{p,i}^{{\beta }_i}.$ for $i=1,\dots ,n$. The $K$ are inputs chosen by the players, and all other variables are fixed parameters.

In a Nash equilibrium, each player $i$ chooses $K_{s,i}$ and $K_{p,i}$ to maximize the payoff ${\pi }_i:=\left(\prod _{j=1}^n\frac{s_j}{1+s_j}\right){\rho }_i(p)-(1-\prod _{j=1}^n\frac{s_j}{1+s_j})d_i-r_i(K_{i,s}+K_{i,p}),$ subject to the other players' choices of $K_s$ and $K_p$. Here ${\rho }_i(p)$ is a contest success function (the expected payoff for player $i$ given a safe outcome and a vector of performances $p$), and $d_i$ is the damage incurred by player $i$ in the event of an unsafe outcome.

The easiest way to use this code is via the API in scenarios.py: just run python3 scenarios.py from this directory to run some example scenarios, or import the Scenario class and run your own scenarios.