Vickrey–Clarke–Groves auction

In auction theory, a Vickrey–Clarke–Groves (VCG) auction is a type of sealed-bid auction of multiple items. Bidders submit bids that report their valuations for the items, without knowing the bids of the other people in the auction. The auction system assigns the items in a socially optimal manner: it charges each individual the harm they cause to other bidders. It also gives bidders an incentive to bid their true valuations, by ensuring that the optimal strategy for each bidder is to bid their true valuations of the items. It is a generalization of a Vickrey auction for multiple items.

The auction is named after William Vickrey,Edward H. Clarke, and Theodore Groves for their papers that successively generalized the idea.

Formal description

For any set of auctioned items and any set of bidders , let be the social value of the VCG auction for a given bid-combination. For a bidder and item , let the bidder's bid for the item be . The notation means the set of elements of A which are not elements of B.

Sonic the Hedgehog (1991 video game)

Sonic the Hedgehog (Japanese: ソニック・ザ・ヘッジホッグ, Hepburn: Sonikku za Hejjihoggu) is a platform video game developed by Sonic Team and published by Sega for the Sega Genesis console. The game was released in North America, Europe and Australia on June 23, 1991, and in Japan the following month. It stars Sonic the Hedgehog in a quest to defeat Dr. Robotnik, an evil scientist who has imprisoned animals in robots and stolen the magical Chaos Emeralds. Sonic the Hedgehog's gameplay involves collecting rings as a form of health and a simple control scheme, with jumping and attacking controlled by a single button.

The game's development began in 1990, when Sega ordered its AM8 development team to create a game featuring a mascot for the company. After considering a number of suggestions, the developers decided on a blue hedgehog with spikes along his head and spine and renamed themselves "Sonic Team" to match their character. Sonic the Hedgehog, designed for fast gameplay, was influenced by the games of Shigeru Miyamoto. It uses a novel technique that allows Sonic's sprite to roll along curved scenery, which originated in a tech demo created by Yuji Naka.