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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.
Strategies against Hostage Takers T ypical Situations Terrorists: usually have several hostages, demands are polit- ical, may be fanatics, location may be public or sec
. A bid is an sign by a potential buyer of the price the buyer is ready to pay for the object being auctioned. In a Procurement Auction, the bid is an sign of the price a seller is
Identification may be established either by the examination of the specification of the structural model, or by the examination of the reduced form of the model. Traditionally
In econometric theory two possibie situations of identifiability can arise: Equation under,consideration is identified or not identified: 1) Equation is under-identified-
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
1. This question and the next is based on the following description. Consider the coalitional game (referred to as Game 1) given by: N = {1,2,3,4}; v(N) = 3, v{i} = 0, i = 1,...,4,
Eighteenth century British mathematician who recognized a method for probabilistic mathematical inference. His Bayes Theorem, published posthumously, treats probability as a logic.
Take a news story, old or recent, and analyze it from a game theoretic perspective. Provide a hard copy of the source of your news story and consult relevant game theoretic literat
Consider the Cournot duopoly model in which two rms, 1 and 2, simultaneously choose the quantities they will sell in the market, q 1 and q 2 . The price each receives for each uni
1. (a) True or False: If a 2x2 game has a unique pure strategy Nash Equilibrium, then both players always have dominant strategies. (b) Draw a table representing the Prisoner.s Dil
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