|
Strategic Fair Division
Strategic fair division is the branch of fair division in which the participants are assumed to hide their preferences and act strategically in order to maximize their own utility, rather than playing sincerely according to their true preferences. To illustrate the difference between strategic fair division and classic fair division, consider the divide and choose procedure for dividing a cake among two agents. In classic fair division, it is assumed that the cutter cuts the cake into two pieces that are equal in his eyes, and thus he always gets a piece that he values at exactly 1/2 of the total cake value. However, if the cutter knows the chooser's preferences, he can get much more than 1/2 by acting strategically. For example, suppose the cutter values a piece by its size while the chooser values a piece by the amount of chocolate in it. So the cutter can cut the cake into two pieces with almost the same amount of chocolate, such that the smaller piece has slightly more chocol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Division
Fair division is the problem in game theory of dividing a set of resources among several people who have an entitlement to them so that each person receives their due share. That problem arises in various real-world settings such as division of inheritance, partnership dissolutions, divorce settlements, electronic frequency allocation, airport traffic management, and exploitation of Earth observation satellites. It is an active research area in mathematics, economics (especially social choice theory), dispute resolution, etc. The central tenet of fair division is that such a division should be performed by the players themselves, maybe using a mediator but certainly not an arbiter as only the players really know how they value the goods. The archetypal fair division algorithm is divide and choose. It demonstrates that two agents with different tastes can divide a cake such that each of them believes that he got the best piece. The research in fair division can be seen as an exten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divide And Choose
Divide and choose (also Cut and choose or I cut, you choose) is a procedure for fair division of a continuous resource, such as a cake, between two parties. It involves a heterogeneous good or resource ("the cake") and two partners who have different preferences over parts of the cake. The protocol proceeds as follows: one person ("the cutter") cuts the cake into two pieces; the other person ("the chooser") selects one of the pieces; the cutter receives the remaining piece. The procedure has been used since ancient times to divide land, cake and other resources between two parties. Currently, there is an entire field of research, called fair cake-cutting, devoted to various extensions and generalizations of cut-and-choose. History Divide and choose is mentioned in the Bible, in the Book of Genesis (chapter 13). When Abraham and Lot come to the land of Canaan, Abraham suggests that they divide it among them. Then Abraham, coming from the south, divides the land to a "left" (western) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nash Equilibrium
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs. If each player has chosen a strategy an action plan based on what has happened so far in the game and no one can increase one's own expected payoff by changing one's strategy while the other players keep their's unchanged, then the current set of strategy choices constitutes a Nash equilibrium. If two players Alice and Bob choose strategies A and B, (A, B) is a Nash equilibrium if Alice has no other strategy available that does better than A at maximizing her payoff in response to Bob choosing B, and Bob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subgame-perfect Equilibrium
In game theory, a subgame perfect equilibrium (or subgame perfect Nash equilibrium) is a refinement of a Nash equilibrium used in dynamic games. A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game. Informally, this means that at any point in the game, the players' behavior from that point onward should represent a Nash equilibrium of the continuation game (i.e. of the subgame), no matter what happened before. Every finite extensive game with perfect recall has a subgame perfect equilibrium. Perfect recall is a term introduced by Harold W. Kuhn in 1953 and ''"equivalent to the assertion that each player is allowed by the rules of the game to remember everything he knew at previous moves and all of his choices at those moves"''. A common method for determining subgame perfect equilibria in the case of a finite game is backward induction. Here one first considers the last actions of the game and determi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Price Of Anarchy
The Price of Anarchy (PoA) is a concept in economics and game theory that measures how the efficiency of a system degrades due to selfish behavior of its agents. It is a general notion that can be extended to diverse systems and notions of efficiency. For example, consider the system of transportation of a city and many agents trying to go from some initial location to a destination. Let efficiency in this case mean the average time for an agent to reach the destination. In the 'centralized' solution, a central authority can tell each agent which path to take in order to minimize the average travel time. In the 'decentralized' version, each agent chooses its own path. The Price of Anarchy measures the ratio between average travel time in the two cases. Usually the system is modeled as a game and the efficiency is some function of the outcomes (e.g. maximum delay in a network, congestion in a transportation system, social welfare in an auction, etc.). Different concepts of equilibriu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fisher Market
Fisher market is an economic model attributed to Irving Fisher. It has the following ingredients: * A set of m divisible products with pre-specified supplies (usually normalized such that the supply of each good is 1). * A set of n buyers. * For each buyer i=1,\dots,n, there is a pre-specified monetary budget B_i. Each product j has a price p_j; the prices are determined by methods described below. The price of a ''bundle'' of products is the sum of the prices of the products in the bundle. A bundle is represented by a vector x = x_1,\dots,x_m, where x_j is the quantity of product j. So the price of a bundle x is p(x)=\sum_^m p_j\cdot x_j. A bundle is ''affordable'' for a buyer if the price of that bundle is at most the buyer's budget. I.e, a bundle x is affordable for buyer i if p(x)\leq B_i. Each buyer has a preference relation over bundles, which can be represented by a utility function. The utility function of buyer i is denoted by u_i. The ''demand set'' of a buyer is the s ... [...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] |
Truthful Mechanism
In game theory, an asymmetric game where players have private information is said to be strategy-proof or strategyproof (SP) if it is a weakly-dominant strategy for every player to reveal his/her private information, i.e. given no information about what the others do, you fare best or at least not worse by being truthful. SP is also called truthful or dominant-strategy-incentive-compatible (DSIC), to distinguish it from other kinds of incentive compatibility. An SP game is not always immune to collusion, but its robust variants are; with group strategyproofness no group of people can collude to misreport their preferences in a way that makes every member better off, and with strong group strategyproofness no group of people can collude to misreport their preferences in a way that makes at least one member of the group better off without making any of the remaining members worse off. Examples Typical examples of SP mechanisms are majority voting between two alternatives, second- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truthful Cake-cutting
Truthful cake-cutting is the study of algorithms for fair cake-cutting that are also truthful mechanisms, i.e., they incentivize the participants to reveal their true valuations to the various parts of the cake. The classic divide and choose procedure for cake-cutting is not truthful: if the cutter knows the chooser's preferences, he can get much more than 1/2 by acting strategically. For example, suppose the cutter values a piece by its size while the chooser values a piece by the amount of chocolate in it. So the cutter can cut the cake into two pieces with almost the same amount of chocolate, such that the smaller piece has slightly more chocolate. Then, the chooser will take the smaller piece and the cutter will win the larger piece, which may be worth much more than 1/2 (depending on how the chocolate is distributed). Randomized mechanisms There is a trivial randomized truthful mechanism for fair cake-cutting: select a single agent uniformly at random, and give him/her the en ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truthful Resource Allocation
Truthful resource allocation is the problem of allocating resources among agents with different valuations over the resources, such that agents are incentivized to reveal their true valuations over the resources. Model There are ''m'' resources that are assumed to be ''homogeneous'' and ''divisible''. Examples are: * Materials, such as wood or metal; * Virtual resources, such as CPU time or computer memory; * Financial resources, such as shares in firms. There are ''n'' agents. Each agent has a function that attributes a numeric value to each "bundle" (combination of resources). It is often assumed that the agents' value functions are ''linear'', so that if the agent receives a fraction ''rj'' of each resource ''j'', then his/her value is the sum of ''rj'' *''vj'' . Design goals The goal is to design a truthful mechanism, that will induce the agents to reveal their true value functions, and then calculate an allocation that satisfies some fairness and efficiency objectives. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rental Harmony
Rental harmony is a kind of a fair division problem in which indivisible items and a fixed monetary cost have to be divided simultaneously. The housemates problem and room-assignment-rent-division are alternative names to the same problem. In the typical setting, there are n partners who rent together an n-room house for cost fixed by the homeowner. Each housemate may have different preferences — one may prefer a large room, another may prefer a room with a view to the main road, etc. The following two problems should be solved simultaneously: * (a) Assign a room to each partner, * (b) Determine the amount each partner should pay, such that the sum of payments equals the fixed cost. There are several properties that we would like the assignment to satisfy. * Non-negativity (NN): all prices must be 0 or more: no partner should be paid to get a room. * Envy-freeness (EF): Given a pricing scheme (an assignment of rent to rooms), we say that a partner ''prefers'' a given room if he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
