9 research outputs found
Fixed Price Approximability of the Optimal Gain From Trade
Bilateral trade is a fundamental economic scenario comprising a strategically
acting buyer and seller, each holding valuations for the item, drawn from
publicly known distributions. A mechanism is supposed to facilitate trade
between these agents, if such trade is beneficial. It was recently shown that
the only mechanisms that are simultaneously DSIC, SBB, and ex-post IR, are
fixed price mechanisms, i.e., mechanisms that are parametrised by a price p,
and trade occurs if and only if the valuation of the buyer is at least p and
the valuation of the seller is at most p. The gain from trade is the increase
in welfare that results from applying a mechanism; here we study the gain from
trade achievable by fixed price mechanisms. We explore this question for both
the bilateral trade setting, and a double auction setting where there are
multiple buyers and sellers. We first identify a fixed price mechanism that
achieves a gain from trade of at least 2/r times the optimum, where r is the
probability that the seller's valuation does not exceed the buyer's valuation.
This extends a previous result by McAfee. Subsequently, we improve this
approximation factor in an asymptotic sense, by showing that a more
sophisticated rule for setting the fixed price results in an expected gain from
trade within a factor O(log(1/r)) of the optimal gain from trade. This is
asymptotically the best approximation factor possible. Lastly, we extend our
study of fixed price mechanisms to the double auction setting defined by a set
of multiple i.i.d. unit demand buyers, and i.i.d. unit supply sellers. We
present a fixed price mechanism that achieves a gain from trade that achieves
for all epsilon > 0 a gain from trade of at least (1-epsilon) times the
expected optimal gain from trade with probability 1 - 2/e^{#T epsilon^2 /2},
where #T is the expected number of trades resulting from the double auction
Simple and Near-Optimal Mechanisms For Market Intermediation
A prevalent market structure in the Internet economy consists of buyers and
sellers connected by a platform (such as Amazon or eBay) that acts as an
intermediary and keeps a share of the revenue of each transaction. While the
optimal mechanism that maximizes the intermediary's profit in such a setting
may be quite complicated, the mechanisms observed in reality are generally much
simpler, e.g., applying an affine function to the price of the transaction as
the intermediary's fee. Loertscher and Niedermayer [2007] initiated the study
of such fee-setting mechanisms in two-sided markets, and we continue this
investigation by addressing the question of when an affine fee schedule is
approximately optimal for worst-case seller distribution. On one hand our work
supplies non-trivial sufficient conditions on the buyer side (i.e. linearity of
marginal revenue function, or MHR property of value and value minus cost
distributions) under which an affine fee schedule can obtain a constant
fraction of the intermediary's optimal profit for all seller distributions. On
the other hand we complement our result by showing that proper affine
fee-setting mechanisms (e.g. those used in eBay and Amazon selling plans) are
unable to extract a constant fraction of optimal profit in the worst-case
seller distribution. As subsidiary results we also show there exists a constant
gap between maximum surplus and maximum revenue under the aforementioned
conditions. Most of the mechanisms that we propose are also prior-independent
with respect to the seller, which signifies the practical implications of our
result.Comment: To appear in WINE'14, the 10th conference on Web and Internet
Economic
Multi-unit Bilateral Trade
We characterise the set of dominant strategy incentive compatible (DSIC),
strongly budget balanced (SBB), and ex-post individually rational (IR)
mechanisms for the multi-unit bilateral trade setting. In such a setting there
is a single buyer and a single seller who holds a finite number k of identical
items. The mechanism has to decide how many units of the item are transferred
from the seller to the buyer and how much money is transferred from the buyer
to the seller. We consider two classes of valuation functions for the buyer and
seller: Valuations that are increasing in the number of units in possession,
and the more specific class of valuations that are increasing and submodular.
Furthermore, we present some approximation results about the performance of
certain such mechanisms, in terms of social welfare: For increasing submodular
valuation functions, we show the existence of a deterministic 2-approximation
mechanism and a randomised e/(1-e) approximation mechanism, matching the best
known bounds for the single-item setting
Approximately Efficient Double Auctions with Strong Budget Balance
Mechanism design for one-sided markets is an area of extensive research in economics and, since more than a decade, in computer science as well. Two-sided markets, on the other hand, have not received the same attention despite the numerous applications to web advertisement, stock exchange, and frequency spectrum allocation. This work studies double auctions, in which unit-demand buyers and unit-supply sellers act strategically.
An ideal goal in double auction design is to maximize the social welfare of buyers and sellers with individually rational (IR), incentive compatible (IC) and strongly budget-balanced (SBB) mechanisms. The first two properties are standard. SBB requires that the payments charged to the buyers are entirely handed to the sellers. This property is crucial in all the contexts that do not allow the auctioneer retaining a share of buyers' payments or subsidizing the market.
Unfortunately, this goal is known to be unachievable even for the special case of bilateral trade, where there is only one buyer and one seller. Therefore, in subsequent papers, meaningful trade-offs between these requirements have been investigated.
Our main contribution is the first IR, IC and SBB mechanism that provides an O(1)-approximation to the optimal social welfare. This result holds for any number of buyers and sellers with arbitrary, independent distributions. Moreover, our result continues to hold when there is an additional matroid constraint on the sets of buyers who may get allocated an item. To prove our main result, we devise an extension of sequential posted price mechanisms to two-sided markets. In addition to this, we improve the best-known approximation bounds for the bilateral trade problem
On the theory of truthful and fair pricing for banner advertisements
We consider revenue maximization problem in banner advertisements under two fundamental concepts: Envy-freeness and truthfulness. Envy-freeness captures fairness requirement among buyers while truthfulness gives buyers the incentive to announce truthful private bids. A extension of envy-freeness named competitive equilibrium, which requires both envy-freeness and market clearance conditions, is also investigated. For truthfulness also called incentive compatible, we adapt Bayesian settings, where each buyer's private value is drawn independently from publicly known distributions. Therefore, the truthfulness we adopt is Bayesian incentive compatible mechanisms. Most of our results are positive. We study various settings of revenue maximizing problem e.g. competitive equilibrium and envy-free solution in relaxed demand, sharp demand and consecutive demand case; Bayesian incentive compatible mechanism in relaxed demand, sharp demand, budget constraints and consecutive demand cases. Our approach allows us to argue that these simple mechanisms give optimal or approximate-optimal revenue guarantee in a very robust manner