MKA Supermarket decides whether to enter the supermarket business in Asempaye town, where Piero supermarket is already

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Question:

MKA Supermarket decides whether to enter the supermarket business in Asempaye town, where Piero supermarket is already located. Piero supermarket observes this decision. If MKA enters, then the two firms simultaneously decide whether to advertise. Otherwise, Piero alone decides whether to advertise. With two firms in the market, the firms earn a revenue of 300,000 cedis each if they both advertise and 500,000 cedis each if they both do not advertise. If only one firm advertises, then it earns 600,000 cedis and the other earns 100,000 cedis.

When Piero supermarket is solely in the industry, it earns 400,000 cedis if it advertises and 350,000 cedis if it does not advertise. MKA supermarket earns nothing if it does not enter the supermarket business in Asempaye. When only one firm advertises, the demand for adverts is low and the cost of an advert is 10,000 cedis. However, if both firms are advertising, they will be competing for advertising space, and it costs each of them 20,000 cedis.

i. represent this game as an extensive form game

ii. how many information set(s) does each player have? Explain.

iii. find all the proper subgames.

iv. compute the subgame perfect Nash equilibria for this game

v. assume that MKA has already entered the market and the two supermarkets are to make their advertising decisions. Also assume that each supermarket observes the other’s advertising decision. Present the resulting game in normal form.

vi. Assume that MKA is already in the market and firms are to choose between advertising or not. Also assume that each supermarket does not observe the other’s advertising decision. Present this as a normal form game.

vii. Assume that firms are playing the normal form game in (vi) infinitely. Using the grim trigger strategy explain the choices that the firms face?