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Optimal Search Strategy June 12, 2007

Posted by jyu in Qualifying.
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Choice                    A                          B

Probability      0.1      0.9           0.3       0.7

Payoff             $100    $0            $6        $4

Cost                        $5                         $2

The expected payoffs of the two alternatives, without search, are

A: -5+100*0.1+0*0.9 = 5

B: -2+6*0.3+4*0.7=2.6

Supposed we search B first and the A second:

If we see payoff $6 first, then the payoff is -5+(100*0.1+6*0.9)=10.4

If we see payoff $4 first, then the payoff is -5+(100*0.1+4*0.9)=8.6

The expected payoff of this sequential search is

-2+{[-5+(100*0.1+6*0.9)]*0.3+[-5+(100*0.1+4*0.9)]*0.7} =7.14

Suppose we search A first and then B second:

If we see payoff $100 first, then the payoff must be $100 since it is the highest it can get

If we see payoff $0 first, then the payoff is -2+(6*0.3+4*0.7)=2.6

The expected payoff of this sequential search is

-5{100*0.1+[-2+(6*0.3+4*0.7)]*09]=7.34

Apparently, consumer should search A first and then B second.  The expected payoff of this sequential search is the highest.

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