BazermanMoore

54 Chapter 3: Bounded Awareness
wanted to minimize the contestant’s chances of winning. So, after the contestant picked
a door, ‘‘Mean Monty’’ could either declare the game over or open one door and offer a
switch. If Monty wanted to minimize the contestant’s chances of winning the grand
prize, the contestant should never have accepted an offer from Monty to switch. In fact,
since Monty wanted the contestant to lose, the fact that Monty made the offer indicated
that the contestant had already picked the winning door. 2
Thus, you should always switch doors in the ‘‘Monty always opens’’ condition
(Problem 2), but never switch in the ‘‘Mean Monty’’ condition (Problem 5). But if people’s
awareness of the rules of the game and of Monty’s decision processes is bounded,
they are likely to fail to differentiate the two problems. Did you distinguish between the
two versions of the multiparty ultimatum game and the two versions of the Monty Hall
game?
Acquiring a Company
In Problem 3, the ‘‘Acquiring a Company’’ problem, one firm (the acquirer) is considering
making an offer to buy out another firm (the target). However, the acquirer is
uncertain about the ultimate value of the target firm. It knows only that its value under
current management is between $0 and $100, with all values equally likely. Since the
firm is expected to be worth 50 percent more under the acquirer’s management than
under the current ownership, it appears to make sense for a transaction to take place.
While the acquirer does not know the actual value of the firm, the target knows its
current worth exactly. What price should the acquirer offer for the target?
The problem is analytically quite simple, yet intuitively perplexing. Consider the
logical process that a rational response would generate in deciding whether to make an
offer of $60 per share:
If I offer $60 per share, the offer will be accepted 60 percent of the time—whenever the
firm is worth between $0 and $60 to the target. Since all values between $0 and $60
are equally likely, the firm will, on average, be worth $30 per share to the target and $45 to
the acquirer, resulting in a loss of $15 per share ($45 to $60). Consequently, a $60-
per-share offer is unwise.
It is easy to see that similar reasoning applies to any positive offer. On average, the
acquirer obtains a company worth 25 percent less than the price it pays when its offer is
accepted. If the acquirer offers $X and the target accepts, the current value of the company
is worth anywhere between $0 and $X. As the problem is formulated, any value in
that range is equally likely, and the expected value of the offer is therefore equal to $X/
2. Since the company is worth 50 percent more to the acquirer, the acquirer’s expected
value is 1.5($X/2) ¼ .75($X), only 75 percent of its offer price. Thus, for any value of $X,
the best the acquirer can do is not make an offer ($0 per share). The paradox of the
situation is that even though in all circumstances the firm is worth more to the acquirer
than to the target, any offer above $0 generates a negative expected return to the
2 In a dynamic game-theoretic equilibrium, the contestant would not know that she won, but should still keep
her original choice.