257 research outputs found
Leadership in Singleton Congestion Games: What is Hard and What is Easy
We study the problem of computing Stackelberg equilibria Stackelberg games
whose underlying structure is in congestion games, focusing on the case where
each player can choose a single resource (a.k.a. singleton congestion games)
and one of them acts as leader. In particular, we address the cases where the
players either have the same action spaces (i.e., the set of resources they can
choose is the same for all of them) or different ones, and where their costs
are either monotonic functions of the resource congestion or not. We show that,
in the case where the players have different action spaces, the cost the leader
incurs in a Stackelberg equilibrium cannot be approximated in polynomial time
up to within any polynomial factor in the size of the game unless P = NP,
independently of the cost functions being monotonic or not. We show that a
similar result also holds when the players have nonmonotonic cost functions,
even if their action spaces are the same. Differently, we prove that the case
with identical action spaces and monotonic cost functions is easy, and propose
polynomial-time algorithm for it. We also improve an algorithm for the
computation of a socially optimal equilibrium in singleton congestion games
with the same action spaces without leadership, and extend it to the
computation of a Stackelberg equilibrium for the case where the leader is
restricted to pure strategies. For the cases in which the problem of finding an
equilibrium is hard, we show how, in the optimistic setting where the followers
break ties in favor of the leader, the problem can be formulated via
mixed-integer linear programming techniques, which computational experiments
show to scale quite well
Regret-Minimizing Contracts: Agency Under Uncertainty
We study the fundamental problem of designing contracts in principal-agent
problems under uncertainty. Previous works mostly addressed Bayesian settings
in which principal's uncertainty is modeled as a probability distribution over
agent's types. In this paper, we study a setting in which the principal has no
distributional information about agent's type. In particular, in our setting,
the principal only knows some uncertainty set defining possible agent's action
costs. Thus, the principal takes a robust (adversarial) approach by trying to
design contracts which minimize the (additive) regret: the maximum difference
between what the principal could have obtained had them known agent's costs and
what they actually get under the selected contract
Online Learning under Budget and ROI Constraints via Weak Adaptivity
We study online learning problems in which a decision maker has to make a
sequence of costly decisions, with the goal of maximizing their expected reward
while adhering to budget and return-on-investment (ROI) constraints. Existing
primal-dual algorithms designed for constrained online learning problems under
adversarial inputs rely on two fundamental assumptions. First, the decision
maker must know beforehand the value of parameters related to the degree of
strict feasibility of the problem (i.e. Slater parameters). Second, a strictly
feasible solution to the offline optimization problem must exist at each round.
Both requirements are unrealistic for practical applications such as bidding in
online ad auctions. In this paper, we show how such assumptions can be
circumvented by endowing standard primal-dual templates with weakly adaptive
regret minimizers. This results in a ``dual-balancing'' framework which ensures
that dual variables stay sufficiently small, even in the absence of knowledge
about Slater's parameter. We prove the first best-of-both-worlds no-regret
guarantees which hold in absence of the two aforementioned assumptions, under
stochastic and adversarial inputs. Finally, we show how to instantiate the
framework to optimally bid in various mechanisms of practical relevance, such
as first- and second-price auctions
Persuading Voters: It's Easy to Whisper, It's Hard to Speak Loud
We focus on the following natural question: is it possible to influence the
outcome of a voting process through the strategic provision of information to
voters who update their beliefs rationally? We investigate whether it is
computationally tractable to design a signaling scheme maximizing the
probability with which the sender's preferred candidate is elected. We focus on
the model recently introduced by Arieli and Babichenko (2019) (i.e., without
inter-agent externalities), and consider, as explanatory examples, -voting
rule and plurality voting. There is a sharp contrast between the case in which
private signals are allowed and the more restrictive setting in which only
public signals are allowed. In the former, we show that an optimal signaling
scheme can be computed efficiently both under a -voting rule and plurality
voting. In establishing these results, we provide two general (i.e., applicable
to settings beyond voting) contributions. Specifically, we extend a well known
result by Dughmi and Xu (2017) to more general settings, and prove that, when
the sender's utility function is anonymous, computing an optimal signaling
scheme is fixed parameter tractable w.r.t. the number of receivers' actions. In
the public signaling case, we show that the sender's optimal expected return
cannot be approximated to within any factor under a -voting rule. This
negative result easily extends to plurality voting and problems where utility
functions are anonymous
Public Bayesian persuasion: being almost optimal and almost persuasive
We study algorithmic Bayesian persuasion problems in which the principal (a.k.a. the sender) has to persuade multiple agents (a.k.a. receivers) by using public communication channels. Specifically, our model follows the multi-receiver model with no inter-agent externalities introduced by Arieli and Babichenko (J Econ Theory 182:185–217, 2019). It is known that the problem of computing a sender-optimal public persuasive signaling scheme is not approximable even in simple settings. Therefore, prior works usually focus on determining restricted classes of the problem for which efficient approximation is possible. Typically, positive results in this space amounts to finding bi-criteria approximation algorithms yielding an almost optimal and almost persuasive solution in polynomial time. In this paper, we take a different perspective and study the persuasion problem in the general setting where the space of the states of nature, the action space of the receivers, and the utility function of the sender can be arbitrary. We fully characterize the computational complexity of computing a bi-criteria approximation of an optimal public signaling scheme in such settings. In particular, we show that, assuming the Exponential Time Hypothesis, solving this problem requires at least a quasi-polynomial number of steps even in instances with simple utility functions and binary action spaces such as an election with the k-voting rule. In doing so, we prove that a relaxed version of the MAXIMUM FEASIBLE SUBSYSTEM OF LINEAR INEQUALITIES problem requires at least quasi-polynomial time to be solved. Finally, we close the gap by providing a quasi-polynomial time bi-criteria approximation algorithm for arbitrary public persuasion problems that, under mild assumptions, yields a QPTAS
Signaling in Bayesian Network Congestion Games: the Subtle Power of Symmetry
Network congestion games are a well-understood model of multi-agent strategic
interactions. Despite their ubiquitous applications, it is not clear whether it
is possible to design information structures to ameliorate the overall
experience of the network users. We focus on Bayesian games with atomic
players, where network vagaries are modeled via a (random) state of nature
which determines the costs incurred by the players. A third-party entity---the
sender---can observe the realized state of the network and exploit this
additional information to send a signal to each player. A natural question is
the following: is it possible for an informed sender to reduce the overall
social cost via the strategic provision of information to players who update
their beliefs rationally? The paper focuses on the problem of computing optimal
ex ante persuasive signaling schemes, showing that symmetry is a crucial
property for its solution. Indeed, we show that an optimal ex ante persuasive
signaling scheme can be computed in polynomial time when players are symmetric
and have affine cost functions. Moreover, the problem becomes NP-hard when
players are asymmetric, even in non-Bayesian settings
Signaling in Posted Price Auctions
We study single-item single-unit Bayesian posted price auctions, where buyers
arrive sequentially and their valuations for the item being sold depend on a
random, unknown state of nature. The seller has complete knowledge of the
actual state and can send signals to the buyers so as to disclose information
about it. For instance, the state of nature may reflect the condition and/or
some particular features of the item, which are known to the seller only. The
problem faced by the seller is about how to partially disclose information
about the state so as to maximize revenue. Unlike classical signaling problems,
in this setting, the seller must also correlate the signals being sent to the
buyers with some price proposals for them. This introduces additional
challenges compared to standard settings. We consider two cases: the one where
the seller can only send signals publicly visible to all buyers, and the case
in which the seller can privately send a different signal to each buyer. As a
first step, we prove that, in both settings, the problem of maximizing the
seller's revenue does not admit an FPTAS unless P=NP, even for basic instances
with a single buyer. As a result, in the rest of the paper, we focus on
designing PTASs. In order to do so, we first introduce a unifying framework
encompassing both public and private signaling, whose core result is a
decomposition lemma that allows focusing on a finite set of possible buyers'
posteriors. This forms the basis on which our PTASs are developed. In
particular, in the public signaling setting, our PTAS employs some ad hoc
techniques based on linear programming, while our PTAS for the private setting
relies on the ellipsoid method to solve an exponentially-sized LP in polynomial
time. In the latter case, we need a custom approximate separation oracle, which
we implement with a dynamic programming approach
No-Regret Learning in Bilateral Trade via Global Budget Balance
Bilateral trade revolves around the challenge of facilitating transactions
between two strategic agents -- a seller and a buyer -- both of whom have a
private valuations for the item. We study the online version of the problem, in
which at each time step a new seller and buyer arrive. The learner's task is to
set a price for each agent, without any knowledge about their valuations. The
sequence of sellers and buyers is chosen by an oblivious adversary. In this
setting, known negative results rule out the possibility of designing
algorithms with sublinear regret when the learner has to guarantee budget
balance for each iteration. In this paper, we introduce the notion of global
budget balance, which requires the agent to be budget balance only over the
entire time horizon. By requiring global budget balance, we provide the first
no-regret algorithms for bilateral trade with adversarial inputs under various
feedback models. First, we show that in the full-feedback model the learner can
guarantee regret against the best fixed prices in
hindsight, which is order-wise optimal. Then, in the case of partial feedback
models, we provide an algorithm guaranteeing a regret
upper bound with one-bit feedback, which we complement with a nearly-matching
lower bound. Finally, we investigate how these results vary when measuring
regret using an alternative benchmark
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