Schelling's Game Theory: How to Make Decisions

By Robert V. Dodge | Go to book overview

CHAPTER 19
Individual Decisions and Group Outcomes
The following edited question was posed by Schelling to introduce analyzing situations of individual decisions and group outcomes:Consider a social event attended by fifty boys and fifty girls, held in a building that has two large adjoining rooms, either room large enough to hold them all and with easy access between the rooms and good visibility. Several alternative motivations toward companionship, gregariousness, and discrimination, are listed below.For each set of motivations, state whether there is a unique equilibrium that can result, two or more possible equilibriums, or no equilibrium at all. Describe in each case the character of the equilibrium if any. “Equilibrium” is here defined as a situation in which nobody is motivated to change rooms as long as nobody else does.
a. Everybody wants to be in the room with the most people.
b. Everybody wants to be in the room with the fewest people.
c. Boys want to be in the room with the most girls; girls want to be in the room with the fewest boys.
d. Everybody prefers to be in the room that most nearly contains three-fifths of the total number of people.
e. Two-thirds of the boys like to be in the room with the most people; one-third of the boys like to be in the room with fewest people; girls like to be in the room with the fewest boys.
f. All boys prefer to be in a room that contains some girls, but not if the girls are a majority; all girls prefer to be in a room that contains some boys, but not if the boys are a majority.

Looking at this question shows how individual motives sometimes translate with little success when they are combined.

In choice a, “Everybody wants to be in the room with the most people,” we have two equilibriums, one unstable and one stable. If at every stage along the way when people entered the rooms there were equal numbers and half went into each room, there would be fifty in each, which would be equilibrium. However, since everyone wants to be in the room with the most people, everyone can make

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