Question

For example, the auctioneer has estimated that the likelihood that the second bidder will bid $2,000,000 is 90%. a) Use a decision tree to determine the optimal decision strategy for which bid to accept. b) Draw a risk profile for the optimal decision.

Answer 1

Answer:

See explanation to get answer.

Step-by-step explanation:

Solution

As per the data and information given in the question, there are three Bidders, one each on Monday, Tuesday and Wednesday.

Bidder 1 may bid on Monday either for $2,000,000 or $3,000,000 with probabilities 0.5 each

Therefore expected pay-off for Bidder 1 is $2,500,000 (2,000,000*.52 + 3,000,000*.5)

Bidder 2 may bid on Tuesday either for $2,000,000 with probability 0.9 or $4,000,000 with probability 0.1

Therefore expected pay-off for Bidder 2 is $2,200,000 (2,000,000*.9 + 4,000,000*.1)

Bidder 3 may bid on Wednesday either for $1,000,000 with probability 0.7 or for $4,000,000 with probability 0.3

Therefore expected pay-off for Bidder 3 is $1,900,000 (1,000,000*.7 + 4,000,000*.3)

Based on the comparison of the above mentioned calculations for the expected pay-off for the bidders, it is recommended that the optimal decision strategy among the bidders is to go for Bidder 1 with highest expected pay-off of $2,500,000 and accept the bid of Bidder 1.

Risk profile for the optimal solution is $2,000,000 with probability 0.5 and $3,000,000 with probability 0.5

Bid may be for $4,000,000 with probability of 0.1 by Bidder 2 or with probability 0.3 by Bidder 3