Nash on a Rotary : Two Theorems with Implications for Electoral Politics
The paper provides a complete characterization of Nash equilibria for games in which n candidates choose a strategy in the form of a platform, each from a circle of feasible platforms, with the aim of maximizing the stretch of the circle from where...
| Main Authors: | , |
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| Format: | Working Paper |
| Language: | English en_US |
| Published: |
World Bank, Washington, DC
2016
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| Subjects: | |
| Online Access: | http://documents.worldbank.org/curated/en/2016/06/26449085/nash-rotary-two-theorems-implications-electoral-politics http://hdl.handle.net/10986/24538 |
| Summary: | The paper provides a complete
characterization of Nash equilibria for games in which n
candidates choose a strategy in the form of a platform, each
from a circle of feasible platforms, with the aim of
maximizing the stretch of the circle from where the
candidate’s platform will receive support from the voters.
Using this characterization, it is shown that if the sum of
all players’ payoffs is 1, the Nash equilibrium payoff of
each player in an arbitrary Nash equilibrium must be
restricted to the interval [1/2(n − 1), 2/(n + 1)]. This
implies that in an election with four candidates, a
candidate who is attracting less than one-sixth of the
voters can do better by changing his or her strategy. |
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