4.) Suppose there are two firms, firm A and firm B, competing in prices. Each fi

Question

4.) Suppose there are two firms, firm A and firm B, competing in prices. Each firm can choose to either price high or price low. If both firms price high, then both firms split the market and receive $100 profit each. If one firm price high and the other prices low, then the low price firm receives $150 and the high price firm receives nothing. Lastly, if both firms price low then the split the market and receive $50 profit each.

a.) Set up a normal form (simultaneous) move game for Firm A and Firm B, making sure to explain what their strategy spaces and payoffs are. (4 points)

b.) What are the dominant strategies for each player in this game? (3 points)

c.) Solve for the Nash Equilibrium/ Equilibria of the game. Make sure you show your work. (3 points)

d.) Suppose this game was repeated for:

i.) A finite period

ii.) An infinite period

In each scenario, explain if the Nash Equilibrium/Equilibria changes. If so, explain why and what conditions are required for this to be true. (4 points)

Explanation / Answer

The pay-off matrix of the game between firm A and firm B IS AS FOLLOWS:

                                                         Firm B                                                            

VALUE OF THE GAME IS 100$

SADDLE POINT=100

THE GAME IS STRICTLY DETERMINABLE...

Firm A price high B1 price low B2 row minimax price high A1 100 150 100 pricelow A2 0 50 0 COLUMN MAXIMIN 100 150                          

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