Some branches of economics and game theory deal with indivisible goods, discrete items that can be traded only as a whole. For example, in combinatorial...

utility functions of divisible goods. These functions are commonly used as examples in consumer theory. The functions are ordinal utility functions,...

bicycle as 200, and the bundle {car, bicycle} as 900 (see Utility functions on indivisible goods for more examples). There are two problems with this approach:...

(higher-order function) Group by (SQL), SQL clause OLAP cube Online analytical processing Pivot table Relational algebra Utility functions on indivisible goods#Aggregates...

unit-demand function is an extreme case of a submodular set function. It is characteristic of items that are pure substitute goods. Utility functions on indivisible...

f(S\cup T)} . Utility functions on indivisible goods Nimrod Megiddo (1988). "ON FINDING ADDITIVE, SUPERADDITIVE AND SUBADDITIVE SET-FUNCTIONS SUBJECT TO...

game theory (as functions modeling user preferences) and electrical networks. Recently, submodular functions have also found utility in several real world...

An additive utility function is characteristic of independent goods. For example, an apple and a hat are considered independent: the utility a person receives...

submodular set function is XOS, and every XOS function is a subadditive set function. See also: Utility functions on indivisible goods. Nisan, Noam (2000)...

Pseudo-Boolean function Topkis's theorem Submodular set function Superadditive Utility functions on indivisible goods Topkis, Donald M., ed. (1998). Supermodularity...

function Utility functions on indivisible goods Feige, Uriel (2009). "On Maximizing Welfare when Utility Functions are Subadditive". SIAM Journal on Computing...

In economics, gross substitutes (GS) is a class of utility functions on indivisible goods. An agent is said to have a GS valuation if, whenever the prices...

equilibrium with that assignment. In the case of indivisible item assignment, when the utility functions of all agents are GS (and thus an equilibrium exists)...

Pareto efficient social choice function must be a linear combination of the utility functions of each individual utility function (with strictly positive weights)...

allocation of indivisible public goods (FAIPG), society has to choose a set of indivisible public goods, where there is are feasibility constraints on what subsets...

Y|y\succeq z\}|} The AU extension is based on the notion of an additive utility function. Many different utility functions are compatible with a given ordering...

used to attain exact fairness of indivisible goods. Corradi and Corradi define an allocation as equitable if the utility of each agent i (defined as the...

(2018). "Fair Allocation of Indivisible Goods: Improvements and Generalizations". Proceedings of the 2018 ACM Conference on Economics and Computation....

additive utilities. They show that a fractional CE (where some goods are divided) can always be rounded to an integral CE (where goods remain indivisible), by...

good as the bundle of any other agent.: 296–297  Since the items are indivisible, an EF assignment may not exist. The simplest case is when there is a...

procedure for fair item allocation. It can be used to allocate several indivisible items among several people, such that the allocation is "almost" envy-free:...

the valuations of the bidders – they may have arbitrary utility functions on indivisible goods. In contrast, if all auctions are done simultaneously, a...

, … , x n ′ } {\displaystyle \{x_{1}',\dots ,x_{n}'\}} where, for utility function u i {\displaystyle u_{i}} for each agent i {\displaystyle i} , u i...

dividing a set of indivisible heterogeneous goods (e.g., rooms in an apartment), and simultaneously a homogeneous divisible bad (the rent on the apartment)...

agents' utility functions. Concavity: the most general assumption (made by Fisher and Arrow&Debreu) is that the agents' utilities are concave functions, i...

possible subset of items. It is usually assumed that the utility functions are monotone set functions, that is, Z 1 ⊇ Z 2 {\displaystyle Z_{1}\supseteq Z_{2}}...

cardinal utility function on bundles of items. This utility function has to be monotone (the utility of a set is at least as large as the utility of its...

agent has an additive utility function (this implies that the items are independent goods). The agents may have different rankings on the items, but there...

pay for public goods according to their marginal benefits. In other words, they pay according to the amount of satisfaction or utility they derive from...

ex-post EF allocation of indivisible objects. Ex-ante EF is a weaker property, relevant for agents with cardinal utilities. It means that no agent prefers...