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A problem

A problem# Economics - 经济

w*g2001-03-01 08:03

1 楼

Assume voters are distributed uniformly onver a line from zero to one. there
are four parties that decided where to locate along the line. Parties locate
simultaneously, attempting to maximize the number of voters received. Each
voter will vote for the party closest to its position. If multiple parties
occupy the same position, the votes received are divided equally among the
parties in that position.
Show that there is a UNIQUE pure-strategy Nash equilibrium, and present
the equilibrium strateg

z*e2001-03-01 08:03

2 楼

The only pure strategy Nash is two of them located at 1/4
point, the other two located at 3/4 point. To show this is
indeed a Nash, you need show none of them has incentive to
deviate.
To show its uniqueness, just show any other location profile
is not a Nash, i.e at least one of them has incentive to
deviate. Be patient to discuss different cases one by one.
It's not hard.

【在 w*****g 的大作中提到】

: Assume voters are distributed uniformly onver a line from zero to one. there
: are four parties that decided where to locate along the line. Parties locate
: simultaneously, attempting to maximize the number of voters received. Each
: voter will vote for the party closest to its position. If multiple parties
: occupy the same position, the votes received are divided equally among the
: parties in that position.
: Show that there is a UNIQUE pure-strategy Nash equilibrium, and present
: the equilibrium strateg