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In this game, you will be matched with one other participant. Imagine that you are each candidates competing for office. Your job is to choose a policy platform, which can be any point along the [0, 1] interval. The other player will choose a point simultaneously.
There are seven voters, who have different preferences for the winning platform. Specifically, each voter has a different preferred platform and their payoff is smaller the further the winning platform is from that point. Their idea platforms are as follows:
Voter 1: ideal platform of 0.1
Voter 2: ideal platform of 0.25
Voter 3: ideal platform of 0.35
Voter 4: ideal platform of 0.4
Voter 5: ideal platform of 0.5
Voter 6: ideal platform of 0.75
Voter 7: ideal platform of 0.85
The voters are not participants in the game. The computer will handle voting for them and will vote for whichever platform is closer (and flip a coin in the case of a tie.)
The candidate who wins the most votes wins the election and receives a payoff of 100, while the loser receives a payoff of 0.