Profit Extraction Mechanism
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Profit Extraction Mechanism
In mechanism design and auction theory, a profit extraction mechanism (also called profit extractor or revenue extractor) is a truthful mechanism whose goal is to win a pre-specified amount of profit, if it is possible. Jason D. Hartline and Anna R. Karlin, "Profit Maximization in Mechanism Design". Chapter 13 in Profit extraction in a digital goods auction Consider a digital goods auction in which a movie producer wants to decide on a price in which to sell copies of his movie. A possible approach is for the producer to decide on a certain revenue, R, that he wants to make. Then, the ''R-profit-extractor'' works in the following way: * Ask each agent how much he is willing to pay for the movie. * For each integer k=1,2,..., let N_k be the number of agents willing to pay at least R/k. Note that N_k is weakly increasing with k. * If there exists k such that N_k\geq k, then find the largest such k (which must be equal to N_k), sell the movie to these k agents, and charge each suc ...
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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 ...
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Auction Theory
Auction theory is an applied branch of economics which deals with how bidders act in auction markets and researches how the features of auction markets Incentivisation, incentivise predictable outcomes. Auction theory is a tool used to inform the design of real-world auctions. Sellers use auction theory to raise higher revenues while allowing buyers to procure at a lower cost. The conference of the price between the buyer and seller is an economic equilibrium. Auction theorists design rules for auctions to address issues which can lead to market failure. The design of these rulesets encourages optimal bidding strategies among a variety of informational settings. The 2020 Nobel Prize for Economics was awarded to Paul R. Milgrom and Robert B. Wilson “for improvements to auction theory and inventions of new Auction#Types, auction formats.” Introduction Auctions facilitate transactions by enforcing a specific set of rules regarding the resource allocations of a group of bidders. T ...
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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- ...
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Digital Goods Auction
In auction theory, a digital goods auction is an auction in which a seller has an unlimited supply of a certain item. A typical example is when a company sells a digital good, such as a movie. The company can create an unlimited number of copies of that movie in a negligible cost. The company's goal is to maximize its profit; to do this, it has to find the optimal price: if the price is too high, only few people will buy the item; if the price is too low, many people will buy but the total revenue will be low. The optimal price of the movie depends on the ''valuations'' of the potential consumers - how much each consumer is willing to pay to buy a movie. If the valuations of all potential consumers are known, then the company faces a simple optimization problem - selecting the price that maximizes the profit. For concreteness, suppose there is a set S of consumers and that they are ordered by their valuation, so that the consumer with the highest valuation (willing to pay the larg ...
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Single-parametric Utility
In mechanism design, an agent is said to have single-parameter utility if his valuation of the possible outcomes can be represented by a single number. For example, in an auction for a single item, the utilities of all agents are single-parametric, since they can be represented by their monetary evaluation of the item. In contrast, in a combinatorial auction for two or more related items, the utilities are usually not single-parametric, since they are usually represented by their evaluations to all possible bundles of items. Notation There is a set X of possible outcomes. There are n agents which have different valuations for each outcome. In general, each agent can assign a different and unrelated value to every outcome in X. In the special case of single-parameter utility, each agent i has a publicly known outcome proper subset W_i \subset X which are the "winning outcomes" for agent i (e.g., in a single-item auction, W_i contains the outcome in which agent i wins the item). ...
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Monotonicity (mechanism Design)
In mechanism design, monotonicity is a property of a social choice function. It is a necessary condition for being able to implement the function using a strategyproof mechanism. Its verbal description is: In other words: 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 assigns to each alternative. The vector of all value-functions is denoted by v. For every agent i, the vector of all value-functions of the ''other'' agents is denoted by v_. So v \equiv (v_i,v_). A social choice function is a function that takes as input the value-vector v and returns an outcome x\in X. It is denoted by \text(v) or \text(v_i,v_). In mechanisms without money A social choice function satisfies the strong monotonicity property (SMON) if for every agent i and every v_i,v_i',v_, if: x = \text(v_i, v_) x' = \text ...
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Random-sampling Mechanism
A random-sampling mechanism (RSM) is a truthful mechanism that uses sampling in order to achieve approximately-optimal gain in prior-free mechanisms and prior-independent mechanisms. Suppose we want to sell some items in an auction and achieve maximum profit. The crucial difficulty is that we do not know how much each buyer is willing to pay for an item. If we know, at least, that the valuations of the buyers are random variables with some known probability distribution, then we can use a Bayesian-optimal mechanism. But often we do not know the distribution. In this case, random-sampling mechanisms provide an alternative solution. RSM in large markets Market-halving scheme When the market is large, the following general scheme can be used: # The buyers are asked to reveal their valuations. # The buyers are split to two sub-markets, M_L ("left") and M_R ("right"), using simple random sampling: each buyer goes to one of the sides by tossing a fair coin. # In each sub-market M_s ...
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Consensus Estimate
Consensus estimate is a technique for designing truthful mechanisms in a prior-free mechanism design setting. The technique was introduced for digital goods auctions and later extended to more general settings. Suppose there is a digital good that we want to sell to a group of buyers with unknown valuations. We want to determine the price that will bring us maximum profit. Suppose we have a function that, given the valuations of the buyers, tells us the maximum profit that we can make. We can use it in the following way: # Ask the buyers to tell their valuations. # Calculate R_ - the maximum profit possible given the valuations. # Calculate a price that guarantees that we get a profit of R_. Step 3 can be attained by a profit extraction mechanism, which is a truthful mechanism. However, in general the mechanism is not truthful, since the buyers can try to influence R_ by bidding strategically. To solve this problem, we can replace the exact R_ with an approximation - R_ - that, with ...
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Single-parameter Utility
In mechanism design, an agent is said to have single-parameter utility if his valuation of the possible outcomes can be represented by a single number. For example, in an auction for a single item, the utilities of all agents are single-parametric, since they can be represented by their monetary evaluation of the item. In contrast, in a combinatorial auction for two or more related items, the utilities are usually not single-parametric, since they are usually represented by their evaluations to all possible bundles of items. Notation There is a set X of possible outcomes. There are n agents which have different valuations for each outcome. In general, each agent can assign a different and unrelated value to every outcome in X. In the special case of single-parameter utility, each agent i has a publicly known outcome proper subset W_i \subset X which are the "winning outcomes" for agent i (e.g., in a single-item auction, W_i contains the outcome in which agent i wins the item). ...
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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 ...
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Cost Sharing
In health care, cost sharing occurs when patients pay for a portion of health care costs not covered by health insurance. The "out-of-pocket" payment varies among healthcare plans and depends on whether or not the patient chooses to use a healthcare provider who is contracted with the healthcare plan's network. Examples of out-of-pocket payments involved in cost sharing include copays, deductibles, and coinsurance. In accounting, cost sharing or matching means that portion of project or program costs not borne by the funding agency. It includes all contributions, including cash and in-kind, that a recipient makes to an award. If the award is federal, only acceptable non-federal costs qualify as cost sharing and must conform to other necessary and reasonable provisions to accomplish the program objectives. Cost sharing effort is included in the calculation of total committed effort. Effort is defined as the portion of time spent on a particular activity expressed as a percentage of th ...
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