Is there a tool for finding Nash equilibria in parametric games? There are a few tools, either online or offline, that could solve (find equilibrium) in a game explicitly given as a real-valued matrix.

Such tools are Game Theory Explorer and Gambit.

However, as far as I know, these can not be used for finding equilibrium in a game with parameters.

For example, consider a two player game symmetric game, parametrized by some $x\in[0,1]$, which is given by the following payoff matrix for the row player (and $A^t(x)$ for the column player):
$$A(x)=
 \left( \begin{array}{ccc}
\frac{x}{2} &amp; x \\
1-x &amp; \frac{1-x}{2} \\
\end{array} \right) $$

Each equilibrium in this game can be represented as $&lt;p_a,p_b&gt;\in[0,1]^2$ where $p_a$ is the probability of the first player playing the first strategy and $p_b$ is the probability the second player plays the first strategy.

Analytically we can find all the equilibriums for this game

$$EQ(x)=
\begin{cases}
\{&lt;1,1&gt;\}&amp;\mbox{if } x&gt;\frac{2}{3}\\
\{&lt;3x-1,3x-1&gt;,&lt;1,0&gt;,&lt;0,1&gt;\}&amp;\mbox{if } \frac{1}{3}\leq x\leq\frac{2}{3}\\
\{&lt;0,0&gt;\}&amp; \mbox{else}
\end{cases}
$$

I'm looking for a solver which is able to understand inputs like $A(x)$ and produce $EQ(x)$.


  Is there a tool which solves parametric games?
Is there a tool which solves parametric games?


Not that I am aware of (I am a co-author of GTE and help with Gambit).

The best suggestion I have if you don't find such a tool (and I doubt one exists) is to do a parameter sweep and solve a bunch of individual instantiations and see what the resulting sets of equilibria say about $EQ()$. Gambit is very tightly integrated with python, so you can easily define your game as a python function with the parameters as arguments and solve a set of instances via a parameter sweep.