| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2002 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Groups |
| Difficulty | Easy -1.8 This is a standard textbook exercise in game theory requiring only routine application of algorithms: finding row minima/column maxima for play-safe strategies, checking if max(row mins) = min(column maxs) for stability, and identifying saddle points. No problem-solving insight or novel reasoning required—purely mechanical procedures from Decision Mathematics. |
| Spec | 7.08a Pay-off matrix: zero-sum games7.08b Dominance: reduce pay-off matrix7.08c Pure strategies: play-safe strategies and stable solutions7.08d Nash equilibrium: identification and interpretation |
| \(B\) | |||||
| I | II | III | IV | ||
| \multirow{3}{*}{\(A\)} | I | - 4 | - 5 | - 2 | 4 |
| II | - 1 | 1 | - 1 | 2 | |
| III | 0 | 5 | - 2 | - 4 | |
| IV | - 1 | 3 | - 1 | 1 | |
2. A two-person zero-sum game is represented by the following pay-off matrix for player $A$.
\begin{center}
\begin{tabular}{ c c | c c c c }
& & \multicolumn{4}{c}{$B$} \\
& & I & II & III & IV \\
\hline
\multirow{3}{*}{$A$} & I & - 4 & - 5 & - 2 & 4 \\
& II & - 1 & 1 & - 1 & 2 \\
& III & 0 & 5 & - 2 & - 4 \\
& IV & - 1 & 3 & - 1 & 1 \\
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Determine the play-safe strategy for each player.
\item Verify that there is a stable solution and determine the saddle points.
\item State the value of the game to $B$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 2002 Q2 [8]}}