Question

(1) Consider the following game: Firm2 0 1 Firmi 0 0,0 0,27 1 27,0 -c, -C 2 27,0 -C, -C 2 0,2 -CT-C -2c, -2c (a) Find all pure strategy NE of this game (b) Find the mixed strategy NE of this game. (i) In the mixed strategy NE, does a firm's exit in date 0 becomes more likely as c increases? Provide economic intuition behind your finding, (ii) In the mixed strategy NE, does a firm's exit in date 0 becomes more likely as a increases? Provide economic intuition behind your finding.

Answer 1

solution: ( Giren game is firma firm, o I 0,0 0,27 0,21 ato -c, -C CTC 2,0 T-C- Ć -29-20 2 (a) All pure Strategy ne of this game, are: The strategies chosen by each players are known af pure strategy of the game. In this game the Nash equilibrium is where both firm will see their Profit in terms of cort afsociated with that production . In this game film, choose I date and from choose 2 date (ie) (211/0), because choosing this strategy profits the firm & is not the fim can make more

24 making any cost at this point while fim Imaking double profit (271) the firm 2 is not making profit nor facing cost. of this game: strategy Ne (6) The mixed a) The mixed strategy of the firm is meoferred by using a by a matrix Ciey considering the form i Strategy of of I with firma strategy considering ofl in the table we will calculate the mixed strategy by the same method Cie) calculating & by a matrix and in the last we will see the nosh equilibrium of the whole game. • let p be the probability that fim, playso, and (1-P) probability that time plays o. Then firm 18 payoff = Colpt (2TT) (1-p) => [p=42 TT

on the basis of this value we can calculate the best response of the firm. The firm a will want to increase the profit whenever pallett and will decrease when p<1/T. ♡ date o becomes more The firm's that exit in likely of increases or not: =) In the mixed Strategy NE the film will likely to exit if the cost of the fim will increase because when the cost of production in creases then the profit the film is receiving will decrease of a result there are more chances to loose the market share and the fim will exit G) The firm's that exit in date o becomes more likely of it increaff or not,

- In the mixed Strategy NE at date o fim exit will not occur with the increase in the T as the firm profit for another producer increases then there are more chances to enter in the market not to exit the market to profit from the market grab the maximum - 0