Algorithmic Game Theory by Nisan N. (Ed), Vazirani V. (Ed), Roughgarden T. (Ed)

By Nisan N. (Ed), Vazirani V. (Ed), Roughgarden T. (Ed)

Within the previous few years video game conception has had a considerable effect on machine technology, particularly on net- and e-commerce-related concerns. greater than forty of the head researchers during this box have written chapters that pass from the rules to the state-of-the-art. simple chapters on algorithmic tools for equilibria, mechanism layout and combinatorial auctions are by way of chapters on incentives and pricing, fee sharing, details markets and cryptography and protection. scholars, researchers and practitioners alike have to examine extra approximately those interesting theoretical advancements and their common functional software.

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Changing the strategy si to some other strategy si ∈ Si the player can change his utility to ui (si , s−i ), assuming that all other players stick to their strategies in s−i . We say that a change from strategy si to si is an improving response for player i if ui (si , s−i ) > ui (s) and best response if si maximizes the players’ utility maxsi ∈Si ui (si , s−i ). Playing a game by repeatedly allowing some player to make an improving or a best response move is perhaps the most natural game play.

1 An Algorithm for a Simple Market In this section, we will give a gist of the models and algorithms studied using a very simple market model. Consider a market consisting of a set A of divisible goods and a set B of buyers. We are specified for each buyer i, the amount mi ∈ Z+ of money she possesses, and for each good j , the amount aj ∈ Z+ of this good. Each buyer i has access to only a subset, say Si ⊆ A of the goods. She is indifferent between goods in Si , but is interested in maximizing the total amount of goods obtained.

2 Vickrey Auction: Designing Games with Dominant Strategy Solutions Perhaps the most common situation in which we need to design a game is an auction. Suppose that we are faced with designing an auction to sell a valuable painting. To model this situation as a game, assume that each player (bidder) i has a value vi for the painting. His value or payoff for not winning it is 0, and his payoff for winning it at a price of p is vi − p. The strategy of each player is simply his bid. What is a good mechanism (or game) for selling this painting?

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