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Stat155 Game Theory - Homework 1: Incentive Problems, Nash equilibrium and Auctions
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Suppose there are k identical copies of an item and n > k bidders. Suppose also that each bidder can receive at most one item. What is the analog of the second-price auction? Prove that your auction is DSIC.
COMP6207 Algorithmic Game Theory - Coursework 3: Gale-Shaply Algorithm and Stable Matching Problem
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Suppose the preferences of men and women are given by the following tables, in which 1 is their most preferred partner and 5 is their least preferred partner. Find a stable matching using the Gale-Shapley algorithm with men making proposals.
ETH Zu ̈rich Algorithmic Game Theory - Exercise Set 3: Nash equilibria and Congestion Game
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In this exercise, we adapt the definition of Price of Anarchy for cost-minimization games, to games with positive utilities in the natural way.
Economics 482 Game Theory and Economics - Problem Set 1 : Rock-Paper-Scissors and Dominant Strategy
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The game Rock-Paper-Scissors is popular in several countries around the world (some- times under a different name). It is a game for two players, in which the players take single actions simultaneously. Thus
Economics 482 Game Theory and Economics - Problem Set 3 : Nash equilibrium Pure Strategies
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There is a town with 99 residents. The residents must decide individually and simultaneously whether to spend time lobbying the local government for better trash collection.
Economics 482 Game Theory and Economics - Problem Set 4 : Nash equilibrium
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Consider the following Bertrand game between two firms, firm 1 and firm 2. As in the standard Bertrand game, each firm’s action is a choice of price (that is, some nonnegative real number).
CSCI 1440/2440 Introduction to Game Theory - Homework 1: Nash equilibrium
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In the game rock-paper-scissors, two players simultaneously se- lect one of three possible actions: rock, paper, or scissors. You might recall from your childhood, or The Simpsons, that rock beats scissors, scissors beats paper, and paper beats rock
CSCI 1440/2440 Introduction to Game Theory - Homework 2: Introduction to Auctions
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Alice and Bob devise a plan to steal the jade monkey before the next full moon. They realize that it’s in a glove compartment, and decide to use a 3d-printed key to break in. However, Alice forgets to bring the key, so the pair gets caught and put into jail.
CSCI 1440/2440 Introduction to Game Theory - Homework 3: Myerson’s Lemma - Welfare Maximization
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The key difference between optimization and mechanism design problems is that in mechanism design problems the constants (e.g., vi and wi) are not assumed to be known to the center / optimizer; on the contrary, they must be elicted, after which the optimization problem can then be solved as usual.
CSCI 1440/2440 Introduction to Game Theory - Homework 4: Myerson’s Theorem - Revenue Maximization
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Recall the Bayesian (i.e., interim) formulation of the auction design problem from Homework 4. Since the interim constraints are weaker than the ex-post constraints presented in lecture, you might imagine that the welfare achieved by the welfare-maximizing auction in the interim case exceeds that of the ex-post case
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