Optimal Search Strategy June 12, 2007
Posted by jyu in Qualifying.trackback
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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