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Median voter theorem:-
Show that when the policy space is one dimensional and the players' preferences are single-peaked the unique Condorcet winner is the median of the players' favorite positions. (This result is known as the median voter theorem.) A one-dimensional space captures some policy choices, but in other situations a higher dimensional space is needed.
For example, a government has to choose the amounts to spend on health care and defense, and not all citizens' preferences are aligned on these issues. Unfortunately, for most configurations of the players' preferences, a Condorcet winner does not exist in a policy space of two or more dimensions, so that the core is empty. To see why this claim is plausible, suppose the policy space is two-dimensional and there are three players. Place the players' favorite positions at three arbitrary points, like x∗1, x∗2, and x∗3 in Figure 1.
Assume that each player i's distaste for a position x different from her favorite position x∗i is exactly the distance between x and x∗i, so that for any value of r she is indifferent between all policies on the circle with radius r centered at x∗i.
Show that the game has an ESS that assigns positive probability only to the demands 2 and 8 and also has an ESS that assigns positive probability only to the demands 4 and 6.
Finally profiles in which the winner obtains three or more votes more than the loser.) Is there any equilibrium in which no player uses a weakly dominated action?
Calculate each player's best-response function as a function of the opposing player's pure strategy. - Find and report the Nash equilibrium of the game.
Now consider the variant in which each player, on her turn, has the additional option of shooting into the air. Find the subgame perfect equilibria of this game when pA pB. Explain the logic behind A's equilibrium action.
Formulate problem as a two-person, zero-sum game and use the concept of dominated strategies to determine the best strategy for each side.
For the time-frame of this study, once a market has reached a higher category, it won't fall back to a lower category. What is the probability that Logistics will stop providing service to an Intermediate market before becoming a High market?
What is the appropriate definition of a Nash equilibrium for this location game? Find the Nash equilibrium locations of the two drinking establishments.
Construct a 95% confidence interval estimate for the population proportion of social media users who would say it is not okay to friend their boss.
Construct a 90% confidence interval for the population average weight of the candies.
Find all the ESSs, in pure and mixed strategies, of the game. - Pairs of players bargain over the division of a pie of size 10.
Find all the pure-strategy subgame-perfect equilibria with no discounting (δ = 1). Be precise in defining history-contingent strategies for both players.
Discuss a real-world example of a contractual situation with limited verifiability. - How do the parties deal with this contractual imperfection?
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