CourseNana | Game Theory

INFR11020 Algorithmic Game Theory and Applications - Homework 1: Nash equilibrium and Farkas Lemma

University of EdinburghINFR11020Algorithmic Game Theory and ApplicationsNash equilibriumFarkas Lemma

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.

INFR11020 Algorithmic Game Theory and Applications - Homework 2: Network Congestion Game, Pareto Optimal and VCG Mechanism

University of EdinburghINFR11020Algorithmic Game Theory and ApplicationsNash equilibriumNetwork Congestion GamePareto Optimal

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

Stat155 Game Theory - Homework 2: Auction, Allocation and Payment Rules

Single-Item AuctionsFirst-Price AuctionsSecond-Price AuctionsSponsored Search AuctionsAllocation and Payment RulesMyerson’s Lemma

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.

STAT155 Game Theory - Homework 4: Simple Near-Optimal Auctions, Multi-Parameter Mechanism, Spectrum Auctions and Stable Matching

UC BerkeleySTAT155Game TheorySimple Near-Optimal AuctionsMulti-Parameter MechanismSpectrum Auctions

Consider a combinatorial auction in which bidders can submit multiple bids under different names, unbeknownst to the mechanism.

STAT155 Game Theory - Homework 5: Selfish Routing, the Price of Anarchy, Over-Provisioning and Atomic Selfish Routing

UC BerkeleySTAT155Game TheorySimple Near-Optimal AuctionsMulti-Parameter MechanismSpectrum Auctions

Prove that if C is the set of nonnegative, nondecreasing, and concave cost functions, then α(C)=43 .

ECON 601 - Microeconomics: Theory and Applications - Final Exam - Question 1: Games and game theory

University of San FranciscoEconomicsECON 601MicroeconomicsTheory and ApplicationsGame 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

AMS 335/ECO 355 PROBLEM SET 1: Penalty Kicks, Meeting Up and Price Competition

Stony Brook UniversityAMS 335ECO 355ECO355AMS335Game 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

COMP3477 Algorithmic Game theory - Summative Assignment: Nash Equilibrium, Strategies and Payoffs

Durham UniversityCOMP3477 Algorithmic Game theoryNash EquilibriumPure Nash EquilibriumStrategies and Payoffs

Exercise 1. A set Nof|N|=nneighbours decide simultaneously and independently from each other, on hand whether to build an extension to their home without getting proper planning permission, and on the other hand which of their neighbours to notify the local authority’s planning department about