BazermanMoore

Bounded Awareness in Strategic Settings 53
your own decisions, note that players who offered anything less than 10-10-10-10-10-10
in Problem 1 were bound to get $0 themselves (because the probability of getting even
15-9-9-9-9-9 was amazingly small). In addition, players who offered anything more than
$1–2 to the other players in Problem 4 were doing so because they wanted to be ‘‘fair’’
or because they made a bad decision; the expected payoff by Player As falls dramatically
as they increase their offers to B–F.
To players who do not attend to the nuances of the rules of the game and the likely
heterogeneity of the other actors, Problems 1 and 4 would look very similar. Bounded
awareness keeps negotiators from failing to differentiate the problems. But those who
note the important difference between these two versions of the multiparty ultimatum
game are likely to do much better. Negotiators often overgeneralize from one situation
to another, even when the generalization is inappropriate. They often assume that what
worked in one context will work in another. But the rational negotiator is attuned to the
important differences that exist, particularly regarding the rules of the game and the
likely decisions of other parties.
The Monty Hall Game
For those too young to have seen him, or for those with limited exposure to American
television, Monty Hall was a television game-show host who would regularly ask contestants
to pick one of three doors, knowing that one of the doors led to the grand prize
and that the other two doors were ‘‘zonks’’ leading to small prizes or gag gifts. Once a
contestant picked a door, Monty would often open one of the other two doors to reveal
a zonk, then offer the contestant the chance to trade their chosen door for the remaining
unchosen and unopened door. A common but false analysis is that with only two
doors remaining following the opening of one door by the host, the odds are 50–50.
Most contestants on the actual show preferred to stick with the door they’d originally
chosen.
Many years after the show, Let’s Make a Deal, went out of production, statisticians,
economists, and journalists (Nalebuff, 1987; Selvin, 1975; vos Savant, 1990a, 1990b,
1991) argued that contestants erred by not switching to the remaining unchosen door.
Their logic, assuming that Monty always opened an unchosen door (known as the
‘‘Monty always opens’’ condition) and then offered a switch, is simple: when they first
chose their door, the contestants had a one-in-three chance of winning the prize. When
Monty opened one door to reveal a zonk, which he could always do, this probability did
not change. Thus, there was still a one-in-three chance that the contestant had the winner
to start with and a two-in-three chance that the big prize was behind one of the
other two doors. When Monty revealed the zonk, he provided useful information. Now
the contestant knew which of the two doors to open to collect the two-in-three chance
of winning. The contestant should therefore always have switched doors, to increase the
odds of winning from one in three to two in three.
Assuming that Monty always opened an unchosen door that did not contain the
grand prize is, of course, a critical element in this analysis. Yet on Let’s Make a Deal,
Monty Hall did not always open one of the three doors to reveal a zonk. Problem 5
posits a ‘‘Mean Monty’’: one who knew where the grand prize was located and who