Fermi incentive with: $N=80$, $\beta=1$, and $\mu = \frac{3}{2} \frac{1}{N}$
Note that some plots differ from those in the paper because the boundaries have been hidden for better color differentiation or because of different parameters e.g. $\beta = 1/10$ in the graphical abstract compared to (7).
Phase portraits made with Bill Sandholm's Dynamo.
\[(0): \left(\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(1): \left(\begin{matrix} 0 & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(2): \left(\begin{matrix} 0 & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(3): \left(\begin{matrix} 0 & 0 & 1 \\ 0 & 0 & 1 \\ 1 & -1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(4): \left(\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 1 & -1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(5): \left(\begin{matrix} 0 & 1 & 2 \\ 1 & 0 & 1 \\ 2 & -1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(6): \left(\begin{matrix} 0 & 1 & -1 \\ 1 & 0 & -2 \\ -1 & 2 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(7): \left(\begin{matrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(8): \left(\begin{matrix} 0 & -1 & 3 \\ -1 & 0 & 3 \\ 1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(9): \left(\begin{matrix} 0 & 1 & 1 \\ -1 & 0 & 3 \\ 1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(10): \left(\begin{matrix} 0 & 1 & 3 \\ -1 & 0 & 5 \\ 1 & 3 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(11): \left(\begin{matrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ -1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(12): \left(\begin{matrix} 0 & 6 & -4 \\ -3 & 0 & 5 \\ -1 & 3 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(13): \left(\begin{matrix} 0 & 1 & -1 \\ 1 & 0 & -3 \\ -1 & 3 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(14): \left(\begin{matrix} 0 & 3 & -1 \\ 3 & 0 & -1 \\ 1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(15): \left(\begin{matrix} 0 & 3 & -1 \\ 1 & 0 & 1 \\ 3 & -1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(16): \left(\begin{matrix} 0 & -1 & 1 \\ 1 & 0 & -1 \\ -1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(17): \left(\begin{matrix} 0 & 2 & -1 \\ -1 & 0 & 2 \\ 2 & -1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(18): \left(\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(19): \left(\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 0 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(20): \left(\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(21): \left(\begin{matrix} 0 & 0 & -2 \\ 0 & 0 & -1 \\ -1 & -1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(22): \left(\begin{matrix} 0 & 0 & -1 \\ 0 & 0 & 1 \\ -1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(23): \left(\begin{matrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & -1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(24): \left(\begin{matrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(25): \left(\begin{matrix} 0 & 0 & -2 \\ 0 & 0 & -1 \\ -1 & 0 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(26): \left(\begin{matrix} 0 & 0 & -1 \\ 0 & 0 & 1 \\ -1 & 0 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(27): \left(\begin{matrix} 0 & 0 & -1 \\ 0 & 0 & -2 \\ -1 & 0 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(28): \left(\begin{matrix} 0 & 0 & -1 \\ 0 & 0 & -2 \\ -1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(29): \left(\begin{matrix} 0 & 0 & -1 \\ 0 & 0 & -1 \\ 0 & 0 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(30): \left(\begin{matrix} 0 & 0 & -2 \\ 0 & 0 & -1 \\ 0 & 0 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(31): \left(\begin{matrix} 0 & 0 & -1 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(32): \left(\begin{matrix} 0 & 0 & -1 \\ 0 & 0 & 0 \\ 0 & -1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(33): \left(\begin{matrix} 0 & 0 & -1 \\ 0 & 0 & 0 \\ 1 & -1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(34): \left(\begin{matrix} 0 & -1 & 3 \\ -1 & 0 & 1 \\ 3 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(35): \left(\begin{matrix} 0 & 3 & 1 \\ 3 & 0 & 1 \\ 1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(36): \left(\begin{matrix} 0 & 1 & -1 \\ -3 & 0 & 1 \\ -1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(37): \left(\begin{matrix} 0 & 1 & 1 \\ -1 & 0 & 1 \\ 1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(38): \left(\begin{matrix} 0 & 1 & 1 \\ -1 & 0 & 3 \\ 1 & 3 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(39): \left(\begin{matrix} 0 & -1 & -1 \\ 1 & 0 & 1 \\ -1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(40): \left(\begin{matrix} 0 & 1 & -1 \\ 1 & 0 & -1 \\ 1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(41): \left(\begin{matrix} 0 & 1 & -1 \\ 1 & 0 & 1 \\ 1 & -1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(42): \left(\begin{matrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ -1 & -1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(43): \left(\begin{matrix} 0 & 1 & 1 \\ -1 & 0 & 1 \\ -1 & -1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(44): \left(\begin{matrix} 0 & 1 & 1 \\ 0 & 0 & 2 \\ 0 & 3 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(45): \left(\begin{matrix} 0 & -2 & 1 \\ 0 & 0 & -2 \\ 0 & -1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(46): \left(\begin{matrix} 0 & -1 & 1 \\ 0 & 0 & -1 \\ 0 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(47): \left(\begin{matrix} 0 & 2 & 0 \\ 2 & 0 & 0 \\ 1 & 1 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy
\[(48): \left(\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ -1 & 2 & 0 \end{matrix} \right)\]
Left: Stationary Distribution | Right: Phase portrait for Replicator Dynamic
Left: Euclidean | Right: Relative Entropy