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Game Theory - 博弈论

博弈论Game Theory
AMS 335/ECO 355 PROBLEM SET 1: Penalty Kicks, Meeting Up and Price Competition
博弈论Game Theory
Imagine a kicker and a goalie who confront each other in a penalty kick that will determine the outcome of a soccer game. The kicker can kick the ball left or right, while the goalie can choose to jump left or right
ECON 601 - Microeconomics: Theory and Applications - Final Exam - Question 1: Games and game theory
博弈论Game Theory
Suppose table A is the payoff matrix for the row player in a two-person symmetrical game. Indicate restrictions on the relative values of the payoffs in table A that would be sufficient to define the game as a Prisoner’s Dilemma
STAT155 Game Theory - Homework 5: Selfish Routing, the Price of Anarchy, Over-Provisioning and Atomic Selfish Routing
博弈论Game Theory
Prove that if C is the set of nonnegative, nondecreasing, and concave cost functions, then α(C)=43 .
STAT155 Game Theory - Homework 4: Simple Near-Optimal Auctions, Multi-Parameter Mechanism, Spectrum Auctions and Stable Matching
博弈论Game Theory
Consider a combinatorial auction in which bidders can submit multiple bids under different names, unbeknownst to the mechanism.
Stat155 Game Theory - 2022 Fall - Homework 3: Algorithmic Mechanism Design and Revenue Maximizing
博弈论Game Theory
Continuing the previous exercise, restrict now to feasible sets X that contain only 0-1 vectors—that is, each bidder either wins or loses. We can identify each feasible outcome with a “feasible set” of bidders (the winners).
Stat155 Game Theory - Homework 2: Auction, Allocation and Payment Rules
博弈论Game Theory
Suppose a subset S of the bidders in a second-price single-item auction decide to collude, meaning that they submit their bids in a coordinated way to maximize the sum of their utilities.
ETH Zu ̈rich Algorithmic Game Theory - Exercise Set 3: Nash equilibria and Congestion Game
博弈论Game Theory
In this exercise, we adapt the definition of Price of Anarchy for cost-minimization games, to games with positive utilities in the natural way.
INFR11020 Algorithmic Game Theory and Applications - Homework 2: Network Congestion Game, Pareto Optimal and VCG Mechanism
博弈论Game Theory
Recall that a Nash equilibrium in an extensive game is subgame perfect nash equilibrium (SPNE) if it is also a Nash equilibrium in every subgame of the original game
INFR11020 Algorithmic Game Theory and Applications - Homework 1: Nash equilibrium and Farkas Lemma
博弈论Game Theory
One variant of the Farkas Lemma says the following: Farkas Lemma A linear system of inequalities Ax ≤ b has a solution x if and only if there is no vector y satisfying y ≥ 0 and yT A = 0 (i.e., 0 in every coordinate) and such that yT b < 0.
CSCI 1440/2440 Introduction to Game Theory - Homework 8: EPIC Auctions
博弈论Game Theory
This problem concerns Japanese auctions, a variant of the classic English auction that poses demand queries rather than value queries, and that forbids bidders from re-entering after exiting (i.e., skipping even one round of bidding in) the auction.
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