| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2003 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Zero-sum game LP formulation |
| Difficulty | Challenging +1.2 This is a standard textbook exercise in D2 requiring recall of zero-sum game theory and LP formulation procedures. Part (a) is trivial (negating entries), and part (b) follows a mechanical template taught in the specification. While it requires multiple steps and careful notation, it demands no problem-solving insight or novel application—students simply apply a memorized algorithm to convert the game matrix into LP constraints. |
| Spec | 7.08a Pay-off matrix: zero-sum games7.08b Dominance: reduce pay-off matrix7.08f Mixed strategies via LP: reformulate as linear programming problem |
| \cline { 2 - 4 } \multicolumn{1}{c|}{} | \(B\) plays I | \(B\) plays II | \(B\) plays III |
| \(A\) plays I | - 3 | 2 | 5 |
| \(A\) plays II | 4 | - 1 | - 4 |
\begin{enumerate}
\item A two person zero-sum game is represented by the following pay-off matrix for player $A$.
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & $B$ plays I & $B$ plays II & $B$ plays III \\
\hline
$A$ plays I & - 3 & 2 & 5 \\
\hline
$A$ plays II & 4 & - 1 & - 4 \\
\hline
\end{tabular}
\end{center}
(a) Write down the pay off matrix for player $B$.\\
(b) Formulate the game as a linear programming problem for player $B$, writing the constraints as equalities and stating your variables clearly.\\
\hfill \mbox{\textit{Edexcel D2 2003 Q1 [6]}}