I am asked to draw two different sets, S1 and S2 using a program to determine if the sets are equal. But for starters, I don't know how am I supposed to "draw" a set with a program and I have never heard a thing like that. Do you know any good resources to understand more about the topic?
The problem I am talking about:
Given a bimatrix $(A, B)$ we can define two sets: $S_{1},$ the set of all outcomes that can be reached when the players coordinate their strategies and $S_{2}$, the set of outcomes that can be reached when the players cannot coordinate their strategies. (It is the set $S_{1}$ we use in Nash's bargain solution.) If we take the bimatrix
$$ \left(\begin{array}{ll} (2,1) & (1,0) \\ (0,1) & (1,2) \end{array}\right) $$
Then $S_{1}=\{\alpha(2,1)+\beta(1,0)+\gamma(0,1)+\delta(1,2)\}$ where $0 \leq \alpha, \beta, \gamma, \delta \leq 1$, $\alpha+\beta+\gamma+\delta=1$.
The set $S_{2}$ is
$$ \left\{\left(\bar{x}\left(\begin{array}{ll} 2 & 1 \\ 0 & 1 \end{array}\right) \bar{y}^{T}, \bar{x}\left(\begin{array}{ll} 1 & 0 \\ 1 & 2 \end{array}\right) \bar{y}^{T}\right)\right\} $$
where $\bar{x}, \bar{y}$ are probability vectors. Draw both sets (you can use any program or tool). Are the sets equal?
Both sets are subsets of $\ \mathbb{R}^2\ $. I would take the instruction to "draw" these sets as asking you to construct diagrams to represent them, just as you do when you draw the graph of a function. If I were to ask you to draw the set $$ S_3=\left\{x_1(0,0)+x_2(0,1)+x_3(1,0)\,\bigg|\,0\le x_i, \sum_{i=1}^3x_i=1\right\}\ , $$ for instance, I would expect you to produce a diagram something like the one below, not necessarily done with a graphing app like GeoGebra, which I used. A similar hand-drawn diagram should be perfectly acceptable.