Pay-off matrices and play-safe strategiesAQA A-Level Further Maths: Mind map

Exam questions on Pay-off matrices and play-safe strategies

1. Two companies, Rowan Ltd and Colbert Ltd, each choose one of three advertising strategies at the same time. The pay-off matrix for Rowan, in percentage points of market share gained by Rowan (a negative entry is a loss for Rowan and a gain for Colbert), is $\begin{pmatrix} 3 & -1 & 2 \\ 1 & 0 & 4 \\ -2 & 5 & 1 \end{pmatrix}$. Rows are Rowan's strategies and columns are Colbert's.
   Show that this game does not have a stable solution.2 marks
2. A supermarket chain, Firm F, and its rival choose pricing strategies at the same time. The pay-off matrix for Firm F, in percentage points of market share gained by Firm F, is $\begin{pmatrix} 4 & 2 & 5 \\ 3 & 1 & 6 \\ 1 & 0 & 2 \end{pmatrix}$. Rows are Firm F's strategies and columns are the rival's. The game is zero-sum.
   Interpret the value of the game in the context of the problem.2 marks
3. Xavier and Yara play a game. At the same time, Xavier chooses 1, 2 or 3 and Yara chooses 2 or 3. If the sum of the two numbers is even, Yara pays Xavier the product of the two numbers, in pounds. If the sum is odd, Xavier pays Yara the sum of the two numbers, in pounds.
   Construct the pay-off matrix for Xavier, with a row for each of Xavier's choices and a column for each of Yara's choices.3 marks