ECON 3340 Lecture Notes - Single-Photon Emission Computed Tomography, Coase Theorem, Net Present Value

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mauvegerbil995

13 May 2012

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Chapter 3: (a) the pareto criterion cannot satisfy completeness, the axiom that a desirable choice mechanism should provide ranking between any two choices. Pareto criterion says a is preferred to b if everyone prefers a; b is preferred to a if everyone prefers b. Of course, in social choice generally some people prefer a and some b. For instance, if there are 35 voters, if candidates x, y and z run for election, candidate x gets 10 votes, y gets 12 votes and z gets 13 votes. But if z does not run, if z and x have similar platforms (ie. they are both liberal), then suppose x gets 20 votes and y gets 15 votes. Since z splits the votes between x and y, the preference for x over y depends on whether z is running for election. (c) majority rule voting cannot provide transitivity.

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D democrats and r Republicans are voting in the US Presidential election. Each person decides whether to vote or not vote. The voters get a payoff of 2,1,0 if their preferred candidate wins, ties, or loses (respectively). Voters that vote incur a cost of 0 1, find the set of Nash equilibrium. Hints: Is there any NE in which everyone votes? Is there any NE in which there are a tie and not everyone votes? Is there any NE in which one of the candidates wins by one vote? Is there any NE in which one of the candidates wins by 2 or more votes?

a) Suppose that d = r = 1. Write out the normal form game table, tell what game this is, and determine the Nash equilibrium.

b) Now Suppose d = r > 1, find the set of Nash equilibrium. Hints: Is there any NE in which everyone votes? Is there any NE in which there are a tie and not everyone votes? Is there any NE in which one of the candidates wins by one vote? Is there any NE in which one of the candidates wins by 2 or more votes?

whitereindeer348

a) Suppose that d = r = 1. Write out the normal form game table, tell what game this is, and determine the Nash equilibrium.

b) Now Suppose d = r > 1, find the set of Nash equilibria. Hints: Is there any NE in which everyone votes? Is there any NE in which there are a tie and not everyone votes? Is there any NE in which one of the candidates wins by one vote? Is there any NE in which one of the candidates wins by 2 or more votes?

c) Now Suppose d < r, find the set of Nash equilibria.

byzantiumfly561

Assume ESPN introduces a new performance comparison system for NBA players (basketball), i.e. preference relation for ranking players as strictly better, weakly better, or indifferent (equally good). ESPN's new criterion (the preference relation) is defined as a better defender and better 3-point shooter". Please analyze which of the three axioms (completeness, reflexiveness, and transitivity) does ESPN's new preference relation satisfies.

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ECON 3340 Lecture Notes - Single-Photon Emission Computed Tomography, Coase Theorem, Net Present Value

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