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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 a repeated game it is often unspecified that players move concurrently at predefined time intervals. However, if few players update their policies at different time intervals, t
This version of Twenty-one is a card game played between a player and the dealer (the computer). The aim of the game is to accumulate a higher point total than the dealer but witho
Two people are engaged in a joint project. If each person i puts in the effort xi, the outcome of the project is worth f(x1, x2). Each person’s effort level xi is a number between
Scenario The hawk-dove game is additionally commonly called the sport of chicken. 2 hooligans with one thing to prove drive at one another on a slender road. The primary to swer
1. Two firms, producing an identical good, engage in price competition. The cost functions are c 1 (y 1 ) = 1:17y 1 and c 2 (y 2 ) = 1:19y 2 , correspondingly. The demand functi
Equilibrium payoffs are (4, 5). Player A’s equilibrium strategy is “S then S if n and then N if n again.” Player B’s equilibrium strategy is “n if S and then n if S again and then
The normal kind may be a matrix illustration of a simultaneous game. For 2 players, one is that the "row" player, and also the different, the "column" player. Every rows or column
In a Variable add game, the add of all player's payoffs differs counting on the methods they utilize. this can be the other of a continuing add game during which all outcomes invol
An auction during which just one item is on the market for sale. Procedures embody English, Dutch, and sealed bid auctions. When multiple units are sold in one auction, the auction
A multiunit auction mechanism for assigning heterogeneous (different) objects. The highest bidder in the first round selects one item among those offered for sale. Then, a second r
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