10 research outputs found
Simplicity-Expressiveness Tradeoffs in Mechanism Design
A fundamental result in mechanism design theory, the so-called revelation
principle, asserts that for many questions concerning the existence of
mechanisms with a given outcome one can restrict attention to truthful direct
revelation-mechanisms. In practice, however, many mechanism use a restricted
message space. This motivates the study of the tradeoffs involved in choosing
simplified mechanisms, which can sometimes bring benefits in precluding bad or
promoting good equilibria, and other times impose costs on welfare and revenue.
We study the simplicity-expressiveness tradeoff in two representative settings,
sponsored search auctions and combinatorial auctions, each being a canonical
example for complete information and incomplete information analysis,
respectively. We observe that the amount of information available to the agents
plays an important role for the tradeoff between simplicity and expressiveness
Auctions with Severely Bounded Communication
We study auctions with severe bounds on the communication allowed: each
bidder may only transmit t bits of information to the auctioneer. We consider
both welfare- and profit-maximizing auctions under this communication
restriction. For both measures, we determine the optimal auction and show that
the loss incurred relative to unconstrained auctions is mild. We prove
non-surprising properties of these kinds of auctions, e.g., that in optimal
mechanisms bidders simply report the interval in which their valuation lies in,
as well as some surprising properties, e.g., that asymmetric auctions are
better than symmetric ones and that multi-round auctions reduce the
communication complexity only by a linear factor
Communication, Distortion, and Randomness in Metric Voting
In distortion-based analysis of social choice rules over metric spaces, one
assumes that all voters and candidates are jointly embedded in a common metric
space. Voters rank candidates by non-decreasing distance. The mechanism,
receiving only this ordinal (comparison) information, should select a candidate
approximately minimizing the sum of distances from all voters. It is known that
while the Copeland rule and related rules guarantee distortion at most 5, many
other standard voting rules, such as Plurality, Veto, or -approval, have
distortion growing unboundedly in the number of candidates.
Plurality, Veto, or -approval with small require less communication
from the voters than all deterministic social choice rules known to achieve
constant distortion. This motivates our study of the tradeoff between the
distortion and the amount of communication in deterministic social choice
rules.
We show that any one-round deterministic voting mechanism in which each voter
communicates only the candidates she ranks in a given set of positions must
have distortion at least ; we give a mechanism achieving an
upper bound of , which matches the lower bound up to a constant. For
more general communication-bounded voting mechanisms, in which each voter
communicates bits of information about her ranking, we show a slightly
weaker lower bound of on the distortion.
For randomized mechanisms, it is known that Random Dictatorship achieves
expected distortion strictly smaller than 3, almost matching a lower bound of
for any randomized mechanism that only receives each voter's
top choice. We close this gap, by giving a simple randomized social choice rule
which only uses each voter's first choice, and achieves expected distortion
.Comment: An abbreviated version appear in Proceedings of AAAI 202
Implementation with a bounded action space
While traditional mechanism design typically assumes isomorphism between the agents’ type- and action spaces, in many situations the agents face strict restrictions on their action space due to, e.g., technical, behavioral or regulatory reasons. We devise a general framework for the study of mechanism design in single-parameter environments with restricted action spaces. Our contribution is threefold. First, we characterize sufficient conditions under which the information-theoretically optimal social-choice rule can be implemented in dominant strategies, and prove that any multilinear social-choice rule is dominant-strategy implementable with no additional cost. Second, we identify necessary conditions for the optimality of actionbounded mechanisms, and fully characterize the optimal mechanisms and strategies in games with two players and two alternatives. Finally, we prove that for any multilinear social-choice rule, the optimal mechanism with k actions incurs an expected loss of O ( 1 k2) compared to the optimal mechanisms with unrestricted action spaces. Our results apply to various economic and computational settings, and we demonstrate their applicability to signaling games, public-good models and routing in networks.
Implementation with a Bounded Action Space
While traditional mechanism design typically assumes isomorphism between the agents' type- and action spaces, in many situations the agents face strict restrictions on their action space due to, e.g., technical, behavioral or regulatory reasons. We devise a general framework for the study of mechanism design in single-parameter environments with restricted action spaces. Our contribution is threefold. First, we characterize sufficient conditions under which the information-theoretically optimal social-choice rule can be implemented in dominant strategies, and prove that any multilinear social-choice rule is dominant-strategy implementable with no additional cost. Second, we identify necessary conditions for the optimality of action-bounded mechanisms, and fully characterize the optimal mechanisms and strategies in games with two players and two alternatives. Finally, we prove that for any multilinear social-choice rule, the optimal mechanism with k actions incurs an expected loss of O(1/k^2) compared to the optimal mechanisms with unrestricted action spaces. Our results apply to various economic and computational settings, and we demonstrate their applicability to signaling games, public-good models and routing in networks.