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Vickrey–Clarke–Groves Mechanism
In mechanism design, a Vickrey–Edward H. Clarke, Clarke–Groves (VCG) mechanism is a generic truthful mechanism for achieving a socially-optimal solution. It is a generalization of a Vickrey–Clarke–Groves auction. A VCG auction performs a specific task: dividing items among people. A VCG ''mechanism'' is more general: it can be used to select any outcome out of a set of possible outcomes. Notation There is a set X of possible outcomes. There are n agents which have different valuations for each outcome. The valuation of agent i is represented as a function: : v_i : X \longrightarrow R_+ which expresses the value it has for each alternative, in monetary terms. It is assumed that the agents have Quasilinear utility functions; this means that, if the outcome is x and in addition the agent receives a payment p_i (positive or negative), then the total utility of agent i is: : u_i := v_i(x) + p_i Our goal is to select an outcome that maximizes the sum of values, i.e.: : x ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanism Design
Mechanism design is a field in economics and game theory that takes an objectives-first approach to designing economic mechanisms or incentives, toward desired objectives, in strategic settings, where players act rationally. Because it starts at the end of the game, then goes backwards, it is also called reverse game theory. It has broad applications, from economics and politics in such fields as market design, auction theory and social choice theory to networked-systems (internet interdomain routing, sponsored search auctions). Mechanism design studies solution concepts for a class of private-information games. Leonid Hurwicz explains that 'in a design problem, the goal function is the main "given", while the mechanism is the unknown. Therefore, the design problem is the "inverse" of traditional economic theory, which is typically devoted to the analysis of the performance of a given mechanism.' So, two distinguishing features of these games are: * that a game "designer" choos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double Auction
A double auction is a process of buying and selling goods with multiple sellers and multiple buyers. Potential buyers submit their bids and potential sellers submit their ask prices to the market institution, and then the market institution chooses some price ''p'' that clears the market: all the sellers who asked less than ''p'' sell and all buyers who bid more than ''p'' buy at this price ''p''. Buyers and sellers that bid or ask for exactly ''p'' are also included. A common example of a double auction is stock exchange. As well as their direct interest, double auctions are reminiscent of Walrasian auction and have been used as a tool to study the determination of prices in ordinary markets. A double auction is also possible without any exchange of currency in barter trade. A barter double auction is an auction where every participant has a demand and an offer consisting of multiple attributes and no money is involved. For the mathematical modelling of satisfaction level Euclid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incentive Compatibility
A mechanism is called incentive-compatible (IC) if every participant can achieve the best outcome to themselves just by acting according to their true preferences. There are several different degrees of incentive-compatibility: * The stronger degree is dominant-strategy incentive-compatibility (DSIC). It means that truth-telling is a weakly-dominant strategy, i.e. you fare best or at least not worse by being truthful, regardless of what the others do. In a DSIC mechanism, strategic considerations cannot help any agent achieve better outcomes than the truth; hence, such mechanisms are also called strategyproof or truthful. (See Strategyproofness) * A weaker degree is Bayesian-Nash incentive-compatibility (BNIC). It means that there is a Bayesian Nash equilibrium in which all participants reveal their true preferences. I.e, ''if'' all the others act truthfully, ''then'' it is also best or at least not worse for you to be truthful. Every DSIC mechanism is also BNIC, but a BNIC me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithmic Mechanism Design
Algorithmic mechanism design (AMD) lies at the intersection of economic game theory, optimization, and computer science. The prototypical problem in mechanism design is to design a system for multiple self-interested participants, such that the participants' self-interested actions at equilibrium lead to good system performance. Typical objectives studied include revenue maximization and social welfare maximization. Algorithmic mechanism design differs from classical economic mechanism design in several respects. It typically employs the analytic tools of theoretical computer science, such as worst case analysis and approximation ratios, in contrast to classical mechanism design in economics which often makes distributional assumptions about the agents. It also considers computational constraints to be of central importance: mechanisms that cannot be efficiently implemented in polynomial time are not considered to be viable solutions to a mechanism design problem. This often, for exam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximation Algorithm
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one. Approximation algorithms naturally arise in the field of theoretical computer science as a consequence of the widely believed P ≠ NP conjecture. Under this conjecture, a wide class of optimization problems cannot be solved exactly in polynomial time. The field of approximation algorithms, therefore, tries to understand how closely it is possible to approximate optimal solutions to such problems in polynomial time. In an overwhelming majority of the cases, the guarantee of such algorithms is a multiplicative one expressed as an approximation ratio or approximation factor i.e., the optimal solution is always guaranteed to be within a (predetermined) multiplicative factor of the returned solution. However, there are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-hard
In computational complexity theory, NP-hardness ( non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard problem is the subset sum problem. A more precise specification is: a problem ''H'' is NP-hard when every problem ''L'' in NP can be reduced in polynomial time to ''H''; that is, assuming a solution for ''H'' takes 1 unit time, ''H''s solution can be used to solve ''L'' in polynomial time. As a consequence, finding a polynomial time algorithm to solve any NP-hard problem would give polynomial time algorithms for all the problems in NP. As it is suspected that P≠NP, it is unlikely that such an algorithm exists. It is suspected that there are no polynomial-time algorithms for NP-hard problems, but that has not been proven. Moreover, the class P, in which all problems can be solved in polynomial time, is contained in the NP class. Defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Connected Set
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties that are used to distinguish topological spaces. A subset of a topological space X is a if it is a connected space when viewed as a subspace of X. Some related but stronger conditions are path connected, simply connected, and n-connected. Another related notion is ''locally connected'', which neither implies nor follows from connectedness. Formal definition A topological space X is said to be if it is the union of two disjoint non-empty open sets. Otherwise, X is said to be connected. A subset of a topological space is said to be connected if it is connected under its subspace topology. Some authors exclude the empty set (with its unique topology) as a connected space, but this article does not follow that practice. For a topologic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truthful Job Scheduling
Truthful job scheduling is a mechanism design variant of the job shop scheduling problem from operations research. We have a project composed of several "jobs" (tasks). There are several workers. Each worker can do any job, but for each worker it takes a different amount of time to complete each job. Our goal is to allocate jobs to workers such that the total makespan of the project is minimized. In the standard job shop scheduling problem, the timings of all workers are known, so we have a standard optimization problem. In contrast, in the truthful job scheduling problem, the timings of the workers are not known. We ask each worker how much time he needs to do each job, but, the workers might lie to us. Therefore, we have to give the workers an incentive to tell us their true timings by paying them a certain amount of money. The challenge is to design a payment mechanism which is incentive compatible. The truthful job scheduling problem was introduced by Nisan and Ronen in their 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Matching
Maximum cardinality matching is a fundamental problem in graph theory. We are given a graph , and the goal is to find a matching containing as many edges as possible; that is, a maximum cardinality subset of the edges such that each vertex is adjacent to at most one edge of the subset. As each edge will cover exactly two vertices, this problem is equivalent to the task of finding a matching that covers as many vertices as possible. An important special case of the maximum cardinality matching problem is when is a bipartite graph, whose vertices are partitioned between left vertices in and right vertices in , and edges in always connect a left vertex to a right vertex. In this case, the problem can be efficiently solved with simpler algorithms than in the general case. Algorithms for bipartite graphs Flow-based algorithm The simplest way to compute a maximum cardinality matching is to follow the Ford–Fulkerson algorithm. This algorithm solves the more general problem o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimum Spanning Tree
A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. That is, it is a spanning tree whose sum of edge weights is as small as possible. More generally, any edge-weighted undirected graph (not necessarily connected) has a minimum spanning forest, which is a union of the minimum spanning trees for its connected components. There are many use cases for minimum spanning trees. One example is a telecommunications company trying to lay cable in a new neighborhood. If it is constrained to bury the cable only along certain paths (e.g. roads), then there would be a graph containing the points (e.g. houses) connected by those paths. Some of the paths might be more expensive, because they are longer, or require the cable to be buried deeper; these paths would be represented by edges with larger weights ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shortest Path Problem
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length of the segment. Definition The shortest path problem can be defined for graphs whether undirected, directed, or mixed. It is defined here for undirected graphs; for directed graphs the definition of path requires that consecutive vertices be connected by an appropriate directed edge. Two vertices are adjacent when they are both incident to a common edge. A path in an undirected graph is a sequence of vertices P = ( v_1, v_2, \ldots, v_n ) \in V \times V \times \cdots \times V such that v_i is adjacent to v_ for 1 \leq i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Auction
A combinatorial auction is a type of smart market in which participants can place bids on combinations of discrete heterogeneous items, or “packages”, rather than individual items or continuous quantities. These packages can be also called lots and the whole auction a multi-lot auction. Combinatorial auctions are applicable when bidders have non-additive valuations on bundles of items, that is, they value combinations of items more or less than the sum of the valuations of individual elements of the combination. Simple combinatorial auctions have been used for many years in estate auctions, where a common procedure is to accept bids for packages of items. They have been used recently for truckload transportation, bus routes, industrial procurement, and in the allocation of radio spectrum for wireless communications. In recent years, procurement teams have applied reverse combinatorial auctions in the procurement of goods and services. This application is often referred to as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
