158 research outputs found
Optimal Auctions vs. Anonymous Pricing: Beyond Linear Utility
The revenue optimal mechanism for selling a single item to agents with
independent but non-identically distributed values is complex for agents with
linear utility (Myerson,1981) and has no closed-form characterization for
agents with non-linear utility (cf. Alaei et al., 2012). Nonetheless, for
linear utility agents satisfying a natural regularity property, Alaei et al.
(2018) showed that simply posting an anonymous price is an e-approximation. We
give a parameterization of the regularity property that extends to agents with
non-linear utility and show that the approximation bound of anonymous pricing
for regular agents approximately extends to agents that satisfy this
approximate regularity property. We apply this approximation framework to prove
that anonymous pricing is a constant approximation to the revenue optimal
single-item auction for agents with public-budget utility, private-budget
utility, and (a special case of) risk-averse utility.Comment: Appeared at EC 201
Screening Signal-Manipulating Agents via Contests
We study the design of screening mechanisms subject to competition and
manipulation. A social planner has limited resources to allocate to multiple
agents using only signals manipulable through unproductive effort. We show that
the welfare-maximizing mechanism takes the form of a contest and characterize
the optimal contest. We apply our results to two settings: either the planner
has one item or a number of items proportional to the number of agents. We show
that in both settings, with sufficiently many agents, a winner-takes-all
contest is never optimal. In particular, the planner always benefits from
randomizing the allocation to some agents
Optimal Scoring for Dynamic Information Acquisition
A principal seeks to learn about a binary state and can do so by enlisting an
agent to acquire information over time using a Poisson information arrival
technology. The agent learns about this state privately, and his effort choices
are unobserved by the principal. The principal can reward the agent with a
prize of fixed value as a function of the agent's sequence of reports and the
realized state. We identify conditions that each individually ensure that the
principal cannot do better than by eliciting a single report from the agent
after all information has been acquired. We also show that such a static
contract is suboptimal under sufficiently strong violations of these
conditions. We contrast our solution to the case where the agent acquires
information "all at once;" notably, the optimal contract in the dynamic
environment may provide strictly positive base rewards to the agent even if his
prediction about the state is incorrect
Efficient Approximations for the Online Dispersion Problem
The dispersion problem has been widely studied in computational geometry and facility location, and is closely related to the packing problem. The goal is to locate n points (e.g., facilities or persons) in a k-dimensional polytope, so that they are far away from each other and from the boundary of the polytope. In many real-world scenarios however, the points arrive and depart at different times, and decisions must be made without knowing future events. Therefore we study, for the first time in the literature, the online dispersion problem in Euclidean space.
There are two natural objectives when time is involved: the all-time worst-case (ATWC) problem tries to maximize the minimum distance that ever appears at any time; and the cumulative distance (CD) problem tries to maximize the integral of the minimum distance throughout the whole time interval. Interestingly, the online problems are highly non-trivial even on a segment. For cumulative distance, this remains the case even when the problem is time-dependent but offline, with all the arriving and departure times given in advance.
For the online ATWC problem on a segment, we construct a deterministic polynomial-time algorithm which is (2ln2+epsilon)-competitive, where epsilon>0 can be arbitrarily small and the algorithm\u27s running time is polynomial in 1/epsilon. We show this algorithm is actually optimal. For the same problem in a square, we provide a 1.591-competitive algorithm and a 1.183 lower-bound. Furthermore, for arbitrary k-dimensional polytopes with k>=2, we provide a 2/(1-epsilon)-competitive algorithm and a 7/6 lower-bound. All our lower-bounds come from the structure of the online problems and hold even when computational complexity is not a concern. Interestingly, for the offline CD problem in arbitrary k-dimensional polytopes, we provide a polynomial-time black-box reduction to the online ATWC problem, and the resulting competitive ratio increases by a factor of at most 2. Our techniques also apply to online dispersion problems with different boundary conditions
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