| Exam Board | OCR |
|---|---|
| Module | FD1 AS (Further Decision 1 AS) |
| Year | 2017 |
| Session | December |
| Marks | 7 |
| Topic | Dynamic Programming |
| Type | Zero-sum game stable solution |
| Difficulty | Standard +0.3 This is a standard game theory question requiring construction of a 4×4 pay-off matrix using given rules, then applying routine techniques (play-safe strategies, dominance, stability check). While it involves multiple parts and careful calculation, these are all textbook procedures for FD1 with no novel problem-solving required, making it slightly easier than average A-level difficulty. |
| 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 |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | 2.5 | 3.2 |
Question 5:
5 | 2.5 | 3.2 | 0 | 25 In each round of a card game two players each have four cards. Every card has a coloured number.
\begin{itemize}
\item Player A's cards are red 1 , blue 2 , red 3 and blue 4.
\item Player B's cards are red 1 , red 2 , blue 3 and blue 4 .
\end{itemize}
Each player chooses one of their cards. The players then show their choices simultaneously and deduce how many points they have won or lost as follows:
\begin{itemize}
\item If the numbers are the same both players score 0 .
\item If the numbers are different but are the same colour, the player with the lower value card scores the product of the numbers on the cards.
\item If the numbers are different and are different colours, the player with the higher value card scores the sum of the numbers on the cards.
\item The game is zero-sum.\\
(i) Complete the pay-off matrix for this game, with player A on rows.\\
(ii) Determine the play-safe strategy for each player.\\
(iii) Use dominance to show that player A should not choose red 3 . You do not need to identify other rows or columns that are dominated.\\
(iv) Determine, with a reason, whether the game is stable or unstable.
\end{itemize}
\hfill \mbox{\textit{OCR FD1 AS 2017 Q5 [7]}}