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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.
Two individuals (i ∈ {1, 2}) work independently on a joint project. They each independently decide how much e ort ei they put. E ort choice has to be any real number between 0 and
A strategy sometimes applied to repeated prisoner's dilemmas during which a player begins by cooperating however defects to cheating for a predefined amount of your time as a respo
A game frequently displayed in tv police dramas. 2 partners in crime are separated into separate rooms at the police station and given an identical deal. If one implicates the oppo
a) Show that A counting proof could be fun(?). But any old proof will do. (Note that the coefficients (1,2,1) in the above are just the elements of the second row of Pas
1. Consider a two-player game where player A chooses "Up," or "Down" and player B chooses "Left," "Center," or "Right". Their payoffs are as follows: When player A chooses "Up" and
Discussion in the preceding section suggests that if we want to measure a given hnction belonging to a simultaneous-equations model, the hnction must be fairly stable over the samp
in a rectangular game pay off matrix of player a is as follows B1 B2 A1 5 7 A2 4 0 salve the game write down the pay off matrix of B and then solve the game.
1. Find all NE of the following 2×2 game. Determine which of the NE are trembling-hand perfect. 2. Consider the following two-person game where player 1 has three strategie
A priori knowledge usually enables us to decide that some coefficients must be zero in the particular equation, while they assume non-zero values in other equations of the system.
A Nash equilibrium, named when John Nash, may be a set of methods, one for every player, such that no player has incentive to unilaterally amendment her action. Players are in equi
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