In algorithmic game theory, a branch of both computer science and economics, a demand oracle is a function that, given a price-vector, returns the demand of an agent. It is used by many algorithms related to pricing and optimization in online market. It is usually contrasted with a value oracle, which is a function that, given a set of items, returns the value assigned to them by an agent.
Demand.
The demand of an agent is the bundle of items that the agent most prefers, given some fixed prices of the items. As an example, consider a market with three objects and one agent, with the following values and prices.
Suppose the agent's utility function is additive (= the value of a bundle is the sum of values of the items in the bundle), and quasilinear (= the utility of a bundle is the value of the bundle minus its price). Then, the demand of the agent, given the prices, is the set {Banana, Cherry}, which gives a utility of (4+6)-(3+1) = 6. Every other set gives the agent a smaller utility. For example, the empty set gives utility 0, while the set of all items gives utility (2+4+6)-(5+3+1)=3.
Oracle.
With additive valuations, the demand function is easy to compute - there is no need for an "oracle". However, in general, agents may have "combinatorial valuations". This means that, for each combination of items, they may have a different value, which is not necessarily a sum of their values for the individual items. Describing such a function on "m" items might require up to 2"m" numbers - a number for each subset. This may be infeasible when "m" is large. Therefore, many algorithms for markets use two kinds of oracles:
Applications.
Some examples of algorithms using demand oracles are:
References.
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