A Vickrey auction or sealed-bid second-price auction (SBSPA) is a type of sealed-bid auction. Bidders submit written bids without knowing the bid of the other people in the auction. The highest bidder wins but the price paid is the second-highest bid. This type of auction is strategically similar to an English auction and gives bidders an incentive to bid their true value. The auction was first described academically by Columbia University professor William Vickrey in 1961 though it had been used by stamp collectors since 1893. In 1797 Johann Wolfgang von Goethe sold a manuscript using a sealed-bid, second-price auction.
A Japanese auction is a dynamic auction format. It proceeds in the following way.
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.
The Myerson–Satterthwaite theorem is an important result in mechanism design and the economics of asymmetric information, and named for Roger Myerson and Mark Satterthwaite. Informally, the result says that there is no efficient way for two parties to trade a good when they each have secret and probabilistically varying valuations for it, without the risk of forcing one party to trade at a loss.
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 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 formats.”
Entitlement in fair division describes that proportion of the resources or goods to be divided that a player can expect to receive. In many fair division settings, all agents have equal entitlements, which means that each agent is entitled to 1/n of the resource. But there are practical settings in which agents have different entitlements. Some examples are:
Fair cake-cutting is a kind of fair division problem. The problem involves a heterogeneous resource, such as a cake with different toppings, that is assumed to be divisible – it is possible to cut arbitrarily small pieces of it without destroying their value. The resource has to be divided among several partners who have different preferences over different parts of the cake, i.e., some people prefer the chocolate toppings, some prefer the cherries, some just want as large a piece as possible. The division should be unanimously fair - each person should receive a piece that he or she believes to be a fair share.
A proportional cake-cutting is a kind of fair cake-cutting. It is a division of a heterogeneous resource ("cake") that satisfies the proportionality criterion, namely, that every partner feels that his allocated share is worth at least 1/n of the total.
Utilitarian cake-cutting is a rule for dividing a heterogeneous resource, such as a cake or a land-estate, among several partners with different cardinal utility functions, such that the sum of the utilities of the partners is as large as possible. It is a special case of the utilitarian social choice rule. Utilitarian cake-cutting is often not "fair"; hence, utilitarianism is often in conflict with fair cake-cutting.
Bayesian-optimal pricing is a kind of algorithmic pricing in which a seller determines the sell-prices based on probabilistic assumptions on the valuations of the buyers. It is a simple kind of a Bayesian-optimal mechanism, in which the price is determined in advance without collecting actual buyers' bids.
A sequential auction is an auction in which several items are sold, one after the other, to the same group of potential buyers. In a sequential first-price auction (SAFP), each individual item is sold using a first price auction, while in a sequential second-price auction (SASP), each individual item is sold using a second price auction.
A picking sequence is a protocol for fair item assignment. Suppose m items have to be divided among n agents. One way to allocate the items is to let one agent select a single item, then let another agent select a single item, and so on. A picking-sequence is a sequence of m agent-names, where each name determines what agent is the next to pick an item.
The Price of Anarchy (PoA) is a concept in game theory and mechanism design that measures how the social welfare of a system degrades due to selfish behavior of its agents. It has been studied extensively in various contexts, particularly in auctions.
Various experiments have been made to evaluate various procedures for fair division, the problem of dividing resources among several people. These include case studies, computerized simulations, and lab experiments.
A supply-chain auction is an auction for coordinating trade among various suppliers and consumers in a supply chain. It is a generalization of a double auction. In a double auction, each deal involves two agents - a buyer and a seller, so the "supply-chain" contains only a single link. In a general supply-chain auction, each deal may involve many different agents, for example: a seller, a mediator, a transporter and a buyer.
In various parts of economics, the term free disposal implies that resources can be discarded without any cost. For example, a fair division setting with free disposal is a setting where some resources have to be divided fairly, but some of the resources may be left undivided, discarded or donated.
Envy-free pricing is a kind of fair item allocation. There is a single seller that owns some items, and a set of buyers who are interested in these items. The buyers have different valuations to the items, and they have a quasilinear utility function; this means that the utility an agent gains from a bundle of items equals the agent's value for the bundle minus the total price of items in the bundle. The seller should determine a price for each item, and sell the items to some of the buyers, such that there is no envy. Two kinds of envy are considered:
In computer science, the Robertson–Webb (RW) query model is a model of computation used by algorithms for the problem of fair cake-cutting. In this problem, there is a resource called a "cake", and several agents with different value measures on the cake. The goal is to divide the cake among the agents such that each agent will consider his/her piece as "fair" by his/her personal value measure. Since the agents' valuations can be very complex, they cannot - in general - be given as inputs to a fair division algorithm. The RW model specifies two kinds of queries that a fair division algorithm may ask the agents: Eval and Cut. Informally, an Eval query asks an agent to specify his/her value to a given piece of the cake, and a Cut query asks an agent to specify a piece of cake with a given value.
Fair division among groups is a class of fair division problems, in which the resources are allocated among groups of agents, rather than among individual agents. After the division, all members in each group consume the same share, but they may have different preferences; therefore, different members in the same group might disagree on whether the allocation is fair or not. Some examples of group fair division settings are:
