Normal-form game catalogue
All reusable normal-form games are stored together in _variables.yml. A lecture inserts a selected matrix with a Quarto variable shortcode, for example games.prisoners_dilemma.matrix. The catalogue below renders those same definitions.
Instigation game
\[ \begin{array}{c|cc} & s & \neg s \\ \hline a & d, -t & -v, m \\ \neg a & 0, r & 0, 0 \end{array} \]
Prisoner’s dilemma
\[ \begin{array}{c|cc} & C & D \\ \hline C & -1, -1 & -4, 0 \\ D & 0, -4 & -3, -3 \end{array} \]
Matching pennies
\[ \begin{array}{c|cc} & H & T \\ \hline H & 1, -1 & -1, 1 \\ T & -1, 1 & 1, -1 \end{array} \]
Bach or Stravinski
\[ \begin{array}{c|cc} & B & S \\ \hline B & 2, 1 & 0, 0 \\ S & 0, 0 & 1, 2 \end{array} \]
Coordination game
\[ \begin{array}{c|cc} & a & b \\ \hline a & 2, 2 & 0, 0 \\ b & 0, 0 & 1, 1 \end{array} \]
Iterated-dominance example
\[ \begin{array}{c|ccc} & c & d & e \\ \hline a & 1, 0 & 1, 2 & 0, 1 \\ b & 0, 3 & 0, 1 & 2, 0 \end{array} \]
Strategic form of the dynamic game
\[ \begin{array}{c|cccc} & ce & cf & de & df \\ \hline ag & 0, 4 & 0, 4 & 2, 1 & 2, 1 \\ ah & 0, 4 & 0, 4 & 2, 1 & 2, 1 \\ bg & 1, 2 & 3, 8 & 1, 2 & 3, 8 \\ bh & 1, 2 & 8, 0 & 1, 2 & 8, 0 \end{array} \]
Expected utility and partial support
\[ \begin{array}{c|ccc} & x & y & z \\ \hline a & 1, 7 & 1, 5 & 3, 4 \\ b & 2, 3 & 0, 4 & 0, 6 \end{array} \]
Indifference is not sufficient
\[ \begin{array}{c|cc} & l & r \\ \hline a & 1, 0 & 0, 1 \\ b & 0, 1 & 1, 0 \\ c & 0.6, 0 & 0.6, 0 \end{array} \]
Penalty kicks
Rows are the kicker’s choices and columns are the goalkeeper’s choices. Entries give scoring probabilities; the goalkeeper’s utility is their negative.
\[ \begin{array}{c|cc} & u & n \\ \hline u & 0.58 & 0.95 \\ n & 0.93 & 0.70 \end{array} \]
Professor’s dilemma
\[ \begin{array}{c|cc} & \text{Listen} & \text{Sleep} \\ \hline \text{Prepare} & 10^6, 10^6 & -10, 0 \\ \text{Slack off} & 0, -10 & 0, 0 \end{array} \]
Good Samaritan: two bystanders
Action \(a\) means providing aid and \(\bar a\) means not providing aid.
\[ \begin{array}{c|cc} & a & \bar a \\ \hline a & 9, 9 & 9, 10 \\ \bar a & 10, 9 & 0, 0 \end{array} \]