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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.
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An equilibrium refinement provides how of choosing one or many equilibria from among several in a very game. several games might contain many Nash equilibria, and therefore supply
A sub game excellent Nash equilibrium is an equilibrium such that players' methods represent a Nash equilibrium in each sub game of the initial game. it should be found by backward
A type of auction in which the highest bidder is rewarded the object, but all bidders pay the auctioneer their bids. This differs from traditional first price auctions in which onl
Description The simplest of William Poundstone's social dilemmas during which the every player contains a dominant strategy and also the equilibrium is Pareto optimal. the sole
A proxy bidder represents the interests of a bidder not physically gift at the auction. Typically, the bidder can inform his proxy of the most quantity he's willing to pay, and als
A pure strategy defines a selected move or action that a player can follow in each potential attainable state of affairs in a very game. Such moves might not be random, or drawn fr
A uniform worth auction may be a multiunit auction during which each winning bidder pays identical worth, which can or might not be equal to the participants' bids. Alternatively,
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
A method by that players assume that the methods of their opponents are randomly chosen from some unknown stationary distribution. In every amount, a player selects her best respon
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