Firm A & Firm B operate as a duopoly and are competing in terms of price alone.

Question

Firm A & Firm B operate as a duopoly and are competing in terms of price alone. They each have the ability to price their product high or low. If they both price high they will share the market, each earning 20 million in profits per quarter. If they both price low they will also split the market, each earning only 15 million in profits. In the event one firm prices high while the other prices low, the higher price firm will lose market share and earn 10 million while the lower priced firm will gain market share earning 30 million. Use this information to construct a payoff matrix. Determine if there is a dominant strategy Determine if there is a Nash equilibrium. Is this a sequential or simultaneous game?

Explanation / Answer

A) PAYOFF MATRIX

15,15

B) HERE BOTH EARNING 15 MILLION OF PROFIT AND CHARGING LOWER PRICE IS DOMINANT STRATEGY. BECAUSE IF ANY ONE OF THEM GO FOR HIGHER PRICE AND OTHER CHOOSES LOWER PRICE THAN THEIR PRICE WILL FALL TO 10 MILLION. AS THEY DON' TKNOW EACH OTHER DECISION. THEY WILL TRY TO PLAY SAFE AND CHOOSE TO PRICE LOW.

C) ABOVE STRATEGY IS NASH EQUILIBRIUM ALSO, AS NOBODY OF THEM WILL CHOOSE TO DEVIATE AND CHARGE HIGHER PRICE AS THIS WOULD LEAD TO LOSS OF PROFIT OF 5 MILLION IF OTHER CHOOSES LOWER PRICE . AS DECISION NEEDS TO BE TAKEN SIMULATENOUSLY BY BOTH THE FIRMS WITHOUT KNOWING OTHER'S DECISION, THEY WILL CHOOSE TO CHARGE LOWER PRICE. THIS IS NASH EQUILIBRIUM.

D) THIS IS SIMULTANEOUS GAME, THEY HAVE TO TAKE DECISION SIMULTANEOUSLY

FIRM A HIGH PRICE LOW PRICE FIRM B HIGH PRICE 20,20 30,10 LOW PRICE 10,30

15,15

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