| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Game theory LP formulation |
| Difficulty | Standard +0.3 This is a standard textbook exercise in game theory requiring knowledge of converting a zero-sum game to an LP problem. While it involves multiple steps (handling negative entries, defining variables, stating objective and constraints), each step follows a mechanical procedure taught directly in D2. The question requires careful application of a known algorithm rather than problem-solving insight, making it slightly easier than average for A-level standard. |
| Spec | 7.08a Pay-off matrix: zero-sum games7.08e Mixed strategies: optimal strategy using equations or graphical method |
| B | ||||
| I | II | III | ||
| \multirow{3}{*}{A} | I | 6 | \(-4\) | \(-1\) |
| II | \(-2\) | 5 | 3 | |
| III | 5 | 1 | \(-3\) | |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | F | FI |
| Answer | Marks |
|---|---|
| G | GI |
| Answer | Marks |
|---|---|
| H | HI |
Question 2:
2 | F | FI
FJ
FK
G | GI
GJ
GK
H | HI
HJ
HKThe payoff matrix for player A in a two-person zero-sum game with value V is shown below.
\begin{tabular}{c|ccc}
& \multicolumn{3}{c}{B} \\
& I & II & III \\
\hline
\multirow{3}{*}{A} & I & 6 & $-4$ & $-1$ \\
& II & $-2$ & 5 & 3 \\
& III & 5 & 1 & $-3$ \\
\end{tabular}
Formulate this information as a linear programming problem, the solution to which will give the optimal strategy for player B.
\begin{enumerate}[label=(\alph*)]
\item Rewrite the matrix as necessary and state the new value of the game, v, in terms of V. [2 marks]
\item Define your decision variables. [2 marks]
\item Write down the objective function in terms of your decision variables. [2 marks]
\item Write down the constraints. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 Q2 [8]}}