9 research outputs found
Ascending auctions and Walrasian equilibrium
We present a family of submodular valuation classes that generalizes gross
substitute. We show that Walrasian equilibrium always exist for one class in
this family, and there is a natural ascending auction which finds it. We prove
some new structural properties on gross-substitute auctions which, in turn,
show that the known ascending auctions for this class (Gul-Stacchetti and
Ausbel) are, in fact, identical. We generalize these two auctions, and provide
a simple proof that they terminate in a Walrasian equilibrium
Double Auctions in Markets for Multiple Kinds of Goods
Motivated by applications such as stock exchanges and spectrum auctions,
there is a growing interest in mechanisms for arranging trade in two-sided
markets. Existing mechanisms are either not truthful, or do not guarantee an
asymptotically-optimal gain-from-trade, or rely on a prior on the traders'
valuations, or operate in limited settings such as a single kind of good. We
extend the random market-halving technique used in earlier works to markets
with multiple kinds of goods, where traders have gross-substitute valuations.
We present MIDA: a Multi Item-kind Double-Auction mechanism. It is prior-free,
truthful, strongly-budget-balanced, and guarantees near-optimal gain from trade
when market sizes of all goods grow to at a similar rate.Comment: Full version of IJCAI-18 paper, with 2 figures. Previous names:
"MIDA: A Multi Item-type Double-Auction Mechanism", "A Random-Sampling
Double-Auction Mechanism". 10 page
Walrasian equilibria in markets with small demands
We study the complexity of finding a Walrasian equilibrium in markets where the agents have k-demand valuations. These valuations are an extension of unit-demand valuations where a bundle's value is the maximum of its k-subsets' values. For unit-demand agents, where the existence of a Walrasian equilibrium is guaranteed, we show that the problem is in quasi-NC. For k = 2, we show that it is NP-hard to decide if a Walrasian equilibrium exists even if the valuations are submodular, while for k = 3 the hardness carries over to budget-additive valuations. In addition, we give a polynomial-time algorithm for markets with 2-demand single-minded valuations, or unit-demand valuations
Do Prices Coordinate Markets?
Walrasian equilibrium prices can be said to coordinate markets: They support
a welfare optimal allocation in which each buyer is buying bundle of goods that
is individually most preferred. However, this clean story has two caveats.
First, the prices alone are not sufficient to coordinate the market, and buyers
may need to select among their most preferred bundles in a coordinated way to
find a feasible allocation. Second, we don't in practice expect to encounter
exact equilibrium prices tailored to the market, but instead only approximate
prices, somehow encoding "distributional" information about the market. How
well do prices work to coordinate markets when tie-breaking is not coordinated,
and they encode only distributional information?
We answer this question. First, we provide a genericity condition such that
for buyers with Matroid Based Valuations, overdemand with respect to
equilibrium prices is at most 1, independent of the supply of goods, even when
tie-breaking is done in an uncoordinated fashion. Second, we provide
learning-theoretic results that show that such prices are robust to changing
the buyers in the market, so long as all buyers are sampled from the same
(unknown) distribution