The AW procedure has each party assign points independently, but how can one know that the announced point assignments reflect each party's true valuations? There are certain situations, such as a divorce proceeding, in which each person will have more than an inkling of the preferences of the other person. Indeed, the intimate knowledge that a divorcing couple will have of each other's cares and concerns will frequently enable each to make rather accurate estimates of the points that the other spouse is likely to assign to the items in a divorce.

Thus we are led to ask whether the parties under AW can capitalize on their knowledge of each other's preferences. It turns out that if this knowledge is possessed by only one side -- a relatively unlikely scenario -- then the knowledgeable side can, in fact, exploit its informational advantage. However, if knowledge is roughly symmetric, then attempts by both sides to be strategic can lead to disaster, even without each spouse's being spiteful.

To illustrate this, let's start with a simple example. Suppose there are two paintings, a Matisse and a Picasso, and Carol thinks that the Matisse is worth three times as much as the Picasso, whereas Bob thinks the Picasso is worth three times as much as the Matisse. Thus, if Carol and Bob are sincere, then there point assignments will be as follows:

 Matisse Picasso Total Carol's true valuations 75 25 100 Bob's true valuations 25 75 100

Because of the symmetry in the preceding example, Carol will receive the Matisse and Bob will receive the Picasso, and there will be no need for an equability adjustment: both parties will receive 75 points.

Now suppose that Carol knows Bob's preferences, and that Bob does not know Carol's preferences. In the absence of any additional information, Bob will announce his true valuation (75 points for the Picasso and 25 points for the Matisse). Can Carol benefit from her knowledge?

The answer is yes. Carol should pretend that she likes the Matisse only slightly more than Bob likes the Matisse. This way, Carol will get all of the Matisse as she did before, but it will appear that she is getting only a little more than one-fourth of her total value, whereas Bob is getting three-fourths of his value (since he put 75 points on the Picasso). Consequently, a big equability adjustment will be required to transfer much of the value of the Picasso from Bob to Carol.

To be more precise, let's work from the numbers in this example to see the extent to which Carol can manipulate AW to her advantage. Knowing that Bob will place 25 points on the Matisse, Carol should place 26 points on this item and her remaining 74 points on the Picasso. Hence, the announced point totals, assuming Bob is sincere and Carol is not, will be as follows:

 Matisse Picasso Total Carol's announced valuations 26 74 100 Bob's true valuations 25 75 100

Initially Carol will get the Matisse, receiving 26 of her announced points, and Bob will get the Picasso, receiving 75 of his announced (and sincere) points. But now, since it appears that Bob is getting almost three times as many points as Carol does (75 to 26), there must be a large transfer from Bob to Carol.

The exact amount will be determined by solving the following equation for p.

26 + 74p = 75 - 75p

Solving for p, we find

149p = 49

p = 49/149 0.33

This gives Bob, in particular,

75 - 75(0.33) 75 - 25 = 50

of his points. In fact, it will appear that Carol, also, is getting the same low number of points

26 + 74(0.33) 26 + 24 = 50

However, let's consider Carol's true valuations. She is getting 75 points from winning all of the Matisse; in addition, she is getting 33% of the Picasso that she values at 25 points, which might mean that Bob would have to pay Carol one-third of the assessed value of the Picasso to keep it entirely for himself. Altogether, then, Carol is getting

75 + 25(0.33) 75 + 8.33 = 83.33

of her points. Of course, Bob could exploit Carol in the same manner if it were he, rather than Carol, who had one-sided information and capitalized on his knowledge of her preferences.

# How to Optimally Deceive Bob

This section will let you test your ability to deceive Bob. Suppose Bob and Carol are arguing over two items (A and B). Let Carol's valuation of these items be 70 points for A and 30 points for B, and Bob's valuation of these items be 50 points for A and 50 points for B.

Now suppose that Carol knows that Bob's valuation is 50-50, and Bob does not know Carol's valuation. What should Carol announce in order to maximize her total point allocation (valuations are restricted to integers)?

Enter the values that you think Carol should announce in order to deceive Bob. Hit the "What is the total point allocation?" button to see the outcome of your allocation. Scroll down to see the answer.

 Carol should announce for item A Carol should announce for item B Carol's total points (based on announced valuation): Carol's total points (based on true valuation): Bob's total points: