ECO 355 Game Theory I need a right answer of this problem Co

ECO 355 Game Theory I need a right answer of this problem.

Consider the Hotelling model of the competition between two firms discussed in class. Select all that apply. a. In the Nash Equilibrium in pure strategies firms will localize together anywhere along the line. b. If Firm 1 and Firm 2 localize at the same point along the line, they will each sell to 50% of the consumers c. If Firm 1 is located at position 112 (ie, center of the line) and firm 2 is located somewhere else, then both firms have incentives to deviate and change their position along the line. d. lf both firms are localized in position 1/2 (i.e., center of the line), neither firm has incentives to deviate and move to a different position.

Solution

The answer is B, C and D .

In hoteling model of the competition between two fims,

If both firms are localized in position  1/2 (i.e., center of the line), neither firm has incentives to deviate and move to a different position. while at the same time If Firm 1 is located at position 1/2 (i.e., center of the line) and firm 2 is located somewhere else, then both firms have incentives to deviate and change their position along the line.

and If Firm localize at the same point along the line, they will each sell to 50% of the consumers. thats what we called the Nash equilbruim . if both firms localize at the same along the line then they grab the maximum costumer along thier own direction and hence they can grab the 50% of market share .

and in the nash equilbruim in pure strategies firms will cannot localize together anywhere along the line because if they move along the line then there is no nash equilbruim remain .