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November 12, 2004
Voting Cycles: A Game Theory Problem
I've just been inspired, on reading a draft chapter of Burt Monroe's Electoral Systems in Theory and Practice, to write up a long game theory problem for the next edition of Games and Information. It gets very technical, but I'll post it in case anybody might be interested.
Uno, Duo, and Tres are three people voting on whether the budget devoted to a project should be Increased, kept the Same, or Reduced. Their payoffs from the different outcomes, given below, are not monotonic in budget size. Uno thinks the project could be very profitable if its budget were increased, but will fail otherwise. Duo mildly wants a smaller budget. Tres likes the budget as it is now.
Uno Duo Tres
Increase 100 2 4
Same 3 6 9
Reduce 9 8 1
Each of the three voters writes down his first choice. If a policy gets a majority of the votes, it wins. Otherwise, Same is the chosen policy.
(a) Show that (Same, Same, Same) is a Nash equilibrium. Why does this equilibrium seem unreasonable to us?
... I continue to have severe Movable Type problems. I can't do Extended entries, so for more, go to Problem 4.7 in this page. When I've got time, I'll think about whether to switch weblog software.
Posted by erasmuse at November 12, 2004 03:06 AM
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