Suppose Best Buy is the only electronics store in a particular market but RadioS

Question

Suppose Best Buy is the only electronics store in a particular market but RadioShack is thinking about entering the market. Best Buy chooses how much to produce first and then RadioShack chooses whether to enter the industry. The strategies and corresponding profits for Best Buy (BB) and RadioShack (RS) are depicted in the decision tree to the right. What will the firms do? Best Buy will choose the small quantity and RadioShack will not enter. Best Buy will choose the large quantity and RadioShack will enter. Best Buy will choose the large quantity and RadioShack will not enter. Best Buy will choose the small quantity and RadioShack will enter.

Explanation / Answer

This is simply an application of Method of Backward Induction in Game Theory.

BB is the first mover and based on BB's Decision RS makes decisions.

Look at the payoffs of RS first. We will go backward.

We look at RS Decision Making;

See if BB Chooses Small Quantity, RS has two decisions to make - Either to Enter or to Standout. What he will do it will depend on his payoffs from the game.

If BB chooses Small QUantity and then RS choose to enter - payoff to RS is $49 (We are not concerned for BB's payoff right now).

If BB chooses Small Quantity and then RS chooses to Stand out - payoff to RS is $0 .

So, if BB chooses to produce small quantity which one is the profitable option - Obviously to Enter. So if BB chooses small quantity RS chooses to Enter the market.

Same way we look at if BB produces large quantity what happens to RS.

BB--Large Quantity -- RS Enter--Payoff to RS = -$8

and BB--Large Quantity--RS Standout --Payoff to RS = $0

Which is better for RS? Undoubtly Payoff of $0 so RS will standout

Now we have decision tree as BB--Large Quantity ----- RS ---Enter ----Payoff of both (49,49)

BB -- Large Quantity---RS----Stanout-----Payoff($69,0)

Now BB has one decision to make to choose amontg the two...Now see BB have greater payoff in making Larger Quantity. He have nothing to worry about RS's Payoff. So he will choose Large Quantity.

Option C is correct answer.

So Best Buy will choose the Large quantity and Radio Shack will choose to stand out.

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