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 of some items increase and the prices of other items remain constant, the agent's demand for the items whose price remain constant weakly increases. The GS condition was introduced by Kelso and Crawford in 1982 and was greatly publicized by Gul and Stacchetti.Since then it has found many applications, mainly in auction theory and competitive equilibrium theory.

Property Value
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• 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 of some items increase and the prices of other items remain constant, the agent's demand for the items whose price remain constant weakly increases. An example is shown on the right. The table shows the valuations (in dollars) of Alice and Bob to the four possible subsets of the set of two items: {apple, bread}. Alice's valuation is GS, but Bob's valuation is not GS. To see this, suppose that initially both apple and bread are priced at \$6. Bob's optimal bundle is apple+bread, since it gives him a net value of \$3. Now, the price of bread increases to \$10. Now, Bob's optimal bundle is the empty bundle, since all other bundles give him negative net value. So Bob's demand to apple has decreased, although only the price of bread has increased. The GS condition was introduced by Kelso and Crawford in 1982 and was greatly publicized by Gul and Stacchetti.Since then it has found many applications, mainly in auction theory and competitive equilibrium theory. (en)
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