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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.
GAME PLAYING IN CLASS GAME 1 Adding Numbers—Win at 100 This game is described in Exercise 3.7a. In this version, two players take turns choosing a number between 1 and 10 (inclus
a) Define the term Nash equilibrium b) You are given the following pay-off matrix: Strategies for player 1 Strategies for player 2
Write a bouncing ball video game. The game is similar to the one described and depicted in The balls bounce within the screen where the two horizontal walls are fixed. The two v
The following is a payoff matrix for a non-cooperative simultaneous move game between 2 players. The payoffs are in the order (Player 1; Player 2): What is the Nash Equilibri
Combining Simultaneous and Sequential Moves The material in this chapter covers a variety of issues that require some knowledge of the analysis of both sequential- move
Scenario The French thinker, Jean Jacques Rousseau, presented the subsequent state of affairs. 2 hunters will either jointly hunt a stag (an adult deer and rather massive meal)
How did link die
Limitations of game theory in finance
what will be the best strategy for a bidder in an auction comprised of four bidders?
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
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