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CSCI 1440/2440 Introduction to Game Theory - Homework 5: Posted-Price Mechanisms

经济学EconomicsGame Theory

Bids are collected. A reserve price is chosen by removing an arbitrary bidder j from the auction, and setting the reserve price to be j’s bid. The auctioneer then allocates the good to the bidder with the highest bid iff their bid is at least this reserve, and charges the winner, if any, the greater of the second-highest bid and the reserve price.

CSCI 1440/2440 Introduction to Game Theory - Homework 6: Approximation Mechanisms

经济学EconomicsGame Theory

Recall the game that motivated the Prophet Inequality: Assume n independent random variables π with non-negative, continuous distributions Gi. The distributions Gi are known in advance, but the “prize” πi is not revealed until period i.

CSCI 1440/2440 Introduction to Game Theory - Homework 7: Vickrey-Clarke-Groves Mechanism

经济学EconomicsGame Theory

Consider a single-good auction, and assume bidders’ values are drawn i.i.d. from a regular distribution F. Prove that the expected revenue of the Vickrey auction (second-price without a reserve) with n bidders,

CSCI 1440/2440 Introduction to Game Theory - Homework 8: EPIC Auctions

经济学EconomicsGame 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.

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

经济学EconomicsGame 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.

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

经济学EconomicsGame 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

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

经济学EconomicsGame 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.

Econ 104 Advanced Microeconomic Theory - Assignment 1: Choice Theory

经济学EconomicsGame Theory

The Associated Press constructs a weekly national ranking of the 25 best College Football Teams. This ranking is constructed by a survey completed by a “panel of 63 sports writers and broad- casters from around the country”, where each person submits their own ranking

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

经济学EconomicsGame Theory

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

经济学EconomicsGame Theory

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

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