Consider a model of two rms (Firm 1 and Firm 2) competing against each other and

Question

Consider a model of two rms (Firm 1 and Firm 2) competing against each other and setting prices simultaneously. Suppose they have a choice of setting either P = $5 or P = $8. If both of them set the lower price they split the total prots of $44 equally(i.e. each of them gets $22). If they both set the higher price, they split the total prots of $82 equally (i.e. each of them gets $41). However, if one of them charges the lower price while the other rm charges the higher price, the lower price rm earns a prot of $60, while the other rm earns a prot of $14. The payo matrix is given below. Does Firm 1 and have a dominant strategy each? What is the Nash Equilibrium in this game? Explain briey. Strategies for Firm2     $5                               $8

(22 , 22)

(60 , 14)

(14 , 60)

(41 , 41)

$5 Strategies

(22 , 22)

(60 , 14)

(14 , 60)

(41 , 41)

Explanation / Answer

whatever choice firm 2 chosses, firm 1 will be better off by choosing lower price because if firm 2 chooses lower price, firm 1 return is higher if he chooses lower price ( 22>14) and if firm 2 chooses higher price, firm 1 return is higher if he chooses lower price (60>14) , so dominant strategy for firm 1 is setting lower price

similarly dominanant strategy for firm 2 is setting lower price

so both will end up setting lower price. so nash equilibrium is both choosing lower price and they split the total prots of $44 equally(i.e. each of them gets $22)

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