Concepts inTruthful mechanisms with implicit payment computation
Payment
A payment is the transfer of money from one party (such as a person or company) to another. A payment is usually made in exchange for the provision of goods, services or both, or to fulfill a legal obligation. The simplest and oldest form of payment is barter, the exchange of one good or service for another.
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Mechanism design
Mechanism design (sometimes called reverse game theory) is a field in game theory studying solution concepts for a class of private information games. The distinguishing features of these games are: that a game "designer" chooses the game structure rather than inheriting one that the designer is interested in the game's outcome Such a game is called a "game of mechanism design" and is usually solved by motivating agents to disclose their private information.
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Vickrey¿Clarke¿Groves auction
A Vickrey¿Clarke¿Groves (VCG) auction of multiple goods is a sealed-bid auction wherein bidders report their valuations for the items. The auction system assigns the items in a socially optimal manner, while ensuring each bidder receives at most one item. This system charges each individual the harm they cause to other bidders, and ensures that the optimal strategy for a bidder is to bid the true valuations of the objects. It is a generalization of a Vickrey auction for multiple items.
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Communication complexity
The notion of communication complexity was introduced by Yao in 1979, who investigated the following problem involving two separated parties. Alice receives an n-bit string x and Bob another n-bit string y, and the goal is for one of them (say Bob) to compute a certain function f(x,y) with the least amount of communication between them. Note that here we are not concerned about the number of computational steps, or the size of the computer memory used.
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Dijkstra's algorithm
Dijkstra's algorithm, conceived by Dutch computer scientist Edsger Dijkstra in 1956 and published in 1959, is a graph search algorithm that solves the single-source shortest path problem for a graph with nonnegative edge path costs, producing a shortest path tree. This algorithm is often used in routing and as a subroutine in other graph algorithms. For a given source vertex (node) in the graph, the algorithm finds the path with lowest cost (i.e.
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Randomization
Randomization is the process of making something random; this means: Generating a random permutation of a sequence (such as when shuffling cards). Selecting a random sample of a population. Generating random numbers: see Random number generation. Transforming a data stream (such as when using a scrambler in telecommunications).
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Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and communicating data.
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