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Consider the electoral competition game presented in Lecture 6. In this game there are two candidates who simultaneously choose policies from the real line. There is a distribution of voters with median m and the candidate whose policy is closest to the median wins the election and the winning candidate's policy is implemented. If the two candidates are an equal distance from the median, then the average of the two policies is implemented. For this problem we suppose that both candidates care about both the implemented policy and winning the election. That is, the payo to each candidate has two parts. The first part is the utility from the implemented policy a*. That is, each candidate has utility u(a* ; xi), where xi is the ideal policy of candidate i and utility decreases to the left and right of xi. We suppose that xi < m < xj . The second part is the value of winning office, which we denote wi > 0 for candidate i. Putting these two parts together, we de ne the payoff to candidate i by
Find all Nash equilibria to this game.
In any game, payoffs are numbers that represent the motivations of players. Payoffs might represent profit, quantity, "utility," or different continuous measures (cardinal payoffs)
Treating probability as a logic, Thomas Bayes defined the following: Pr(X|Y)=Pr(Y|X)Pr(X)/Pr(Y) For example, probability that the weather was bad given that our friends playe
WHAT IS DYNAMIC GAME MODEL
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In Bontemps, Louisiana there are only two places to spend time: Merlotte's bar and Fangtasia. Sookie and Eric have made plans to spend Friday night together, but they never decided
A bidding increment is defined by the auctioneer as the least amount above the previous bid that a new bid must be in order to be adequate to the auctioneer. For example, if the in
Two people are engaged in a joint project. If each person i puts in the e ort xi, a nonnegative number equal to at most 1, which costs her c(x i ), the outcome of the project is wo
Suppose that the incumbent monopolist, in the previous question, can decide (before anything else happens) to make an irreversible investment in extra Capacity (C), or Not (N). If
Identification is a problem of model formultion, rather than inf nlnde! estimation or appraisal. We say a model is identified if it is in a unique statistical form, enabling unique
Two people are involved in a dispute. Person 1 does not know whether person 2 is strong or weak; she assigns probability to person 2 being strong. Person 2 is fully informed. Each
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