Two garden centres, Green Grass and Bushy Shrubs, sell a similar range of plant pots, plants and plant food. Both are considering whether to discount or maintain their prices as spring approaches. Their payoffs under different combinations of decisions are given below:
If Green Grass discounts and Bushy Shrubs does not, Green Grass receives a profit of £3500 per week and Bushy Shrubs receives a profit of £1000 per week.
If Green Grass does not discount and Bushy Shrubs discounts, Green Grass receives a profit of £1000 per week and Bushy Shrubs receives a profit of £2700 per week.
If both Green Grass and Bushy Shrubs discount, they will both receive profits of £1500 per week.
If both Green Grass and Bushy Shrubs maintain their prices, they will both receive profits of £2000 per week.
Draw a payoff matrix to show this as a one-shot simultaneous game in which each seller has to make a one-off decision without knowing what the other will do. (5 marks)
Assuming both firms are rational and fully informed about the payoffs of the game, describe any dominant strategies they might have and justify your answer in full. (5 marks)
What, if any, are the Nash equilibria strategies and outcomes of this game? Explain your answer in full. (5 marks)
Suppose both sellers were considering whether or not to discount prices on a daily basis, repeatedly, for the foreseeable future. How would this change the game and the possible outcomes? (5 marks)
Now suppose that Green Grass has the ability to unilaterally discount its prices before Bushy Shrubs can make its decision. Draw a diagram of the sequential game and use backward induction reasoning to explain the rational solution to this game. Is there any change in the outcome compared to the one-shot simultaneous game in Questions 2 and 3? (5 marks)
