19,668 research outputs found
Selling to a No-Regret Buyer
We consider the problem of a single seller repeatedly selling a single item
to a single buyer (specifically, the buyer has a value drawn fresh from known
distribution in every round). Prior work assumes that the buyer is fully
rational and will perfectly reason about how their bids today affect the
seller's decisions tomorrow. In this work we initiate a different direction:
the buyer simply runs a no-regret learning algorithm over possible bids. We
provide a fairly complete characterization of optimal auctions for the seller
in this domain. Specifically:
- If the buyer bids according to EXP3 (or any "mean-based" learning
algorithm), then the seller can extract expected revenue arbitrarily close to
the expected welfare. This auction is independent of the buyer's valuation ,
but somewhat unnatural as it is sometimes in the buyer's interest to overbid. -
There exists a learning algorithm such that if the buyer bids
according to then the optimal strategy for the seller is simply
to post the Myerson reserve for every round. - If the buyer bids according
to EXP3 (or any "mean-based" learning algorithm), but the seller is restricted
to "natural" auction formats where overbidding is dominated (e.g. Generalized
First-Price or Generalized Second-Price), then the optimal strategy for the
seller is a pay-your-bid format with decreasing reserves over time. Moreover,
the seller's optimal achievable revenue is characterized by a linear program,
and can be unboundedly better than the best truthful auction yet simultaneously
unboundedly worse than the expected welfare
Optimal Design of Robust Combinatorial Mechanisms for Substitutable Goods
In this paper we consider multidimensional mechanism design problem for
selling discrete substitutable items to a group of buyers. Previous work on
this problem mostly focus on stochastic description of valuations used by the
seller. However, in certain applications, no prior information regarding
buyers' preferences is known. To address this issue, we consider uncertain
valuations and formulate the problem in a robust optimization framework: the
objective is to minimize the maximum regret. For a special case of
revenue-maximizing pricing problem we present a solution method based on
mixed-integer linear programming formulation
Robust Monopoly Pricing
We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version of the problem the seller only knows that demand will be in a neighborhood of a given model distribution. We characterize the optimal pricing policy under two distinct, but related, decision criteria with multiple priors: (i) maximin expected utility and (ii) minimax expected regret. While the classic monopoly policy and the maximin criterion yield a single deterministic price, minimax regret always prescribes a random pricing policy, or equivalently, a multi-item menu policy. The resulting optimal pricing policy under either criterion is robust to the model uncertainty. Finally we derive distinct implications of how a monopolist responds to an increase in ambiguity under each criterion.Monopoly, Optimal pricing, Robustness, Multiple priors, Regret
Robust Monopoly Pricing
We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the optimal pricing policy under two distinct, but related, decision criteria with multiple priors: (i) maximin expected utility and (ii) minimax expected regret. The resulting optimal pricing policy under either criterion yields a robust policy to the model uncertainty. While the classic monopoly policy and the maximin criterion yield a single deterministic price, minimax regret always prescribes a random pricing policy, or equivalently, a multi-item menu policy. Distinct implications of how a monopolist responds to an increase in uncertainty emerge under the two criteria.Monopoly, Optimal pricing, Robustness, Multiple priors, Regret
Optimal Multi-Unit Mechanisms with Private Demands
In the multi-unit pricing problem, multiple units of a single item are for
sale. A buyer's valuation for units of the item is ,
where the per unit valuation and the capacity are private information
of the buyer. We consider this problem in the Bayesian setting, where the pair
is drawn jointly from a given probability distribution. In the
\emph{unlimited supply} setting, the optimal (revenue maximizing) mechanism is
a pricing problem, i.e., it is a menu of lotteries. In this paper we show that
under a natural regularity condition on the probability distributions, which we
call \emph{decreasing marginal revenue}, the optimal pricing is in fact
\emph{deterministic}. It is a price curve, offering units of the item for a
price of , for every integer . Further, we show that the revenue as a
function of the prices is a \emph{concave} function, which implies that
the optimum price curve can be found in polynomial time. This gives a rare
example of a natural multi-parameter setting where we can show such a clean
characterization of the optimal mechanism. We also give a more detailed
characterization of the optimal prices for the case where there are only two
possible demands
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