Question
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
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 in the table 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 | Dos | 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) Is (Same, Same, Same) a Nash equilibrium?
B) Is (Increase, Same, Same) a Nash equilibrium?
C) Is (Reduce, Reduce, Same) a Nash equilibrium?
D) Speculate about what would happen if the payoffs are in terms of dollar willingness to pay by each player and the players could make binding agreements to buy and sell votes. What, if anything, can you say about which policy would win, and what votes would be bought at what price?
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