اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSignaling in Quasipolynomial time
203
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Strategic interactions often take place in an environment rife with uncertainty. As a result, the equilibrium of a game is intimately related to the information available to its players. The emph{signaling problem} abstracts the task faced by an informed market maker, who must choose how to reveal information in order to effect a desirable equilibrium. In this paper, we consider two fundamental signaling problems: one for abstract normal form games, and the other for single item auctions. For the former, we consider an abstract class of objective functions which includes the social welfare and weighted combinations of players utilities, and for the latter we restrict our attention to the social welfare objective and to signaling schemes which are constrained in the number of signals used. For both problems, we design approximation algorithms for the signaling problem which run in quasi-polynomial time under various conditions, extending and complementing the results of various recent works on the topic. Underlying each of our results is a meshing scheme which effectively overcomes the curse of dimensionality and discretizes the space of essentially different posterior beliefs -- in the sense of inducing essentially different equilibria. This is combined with an algorithm for optimally assembling a signaling scheme as a convex combination of such beliefs. For the normal form game setting, the meshing scheme leads to a convex partition of the space of posterior beliefs and this assembly procedure is reduced to a linear program, and in the auction setting the assembly procedure is reduced to submodular function maximization.
قيم البحث
اقرأ أيضاً
Zielonkas classic recursive algorithm for solving parity games is perhaps the simplest among the many existing parity game algorithms. However, its complexity is exponential, while currently the state-of-the-art algorithms have quasipolynomial comple
xity. Here, we present a modification of Zielonkas classic algorithm that brings its complexity down to $n^{mathcal{O}left(logleft(1+frac{d}{log n}right)right)}$, for parity games of size $n$ with $d$ priorities, in line with previous quasipolynomial-time solutions.
Modern ad auctions allow advertisers to target more specific segments of the user population. Unfortunately, this is not always in the best interest of the ad platform. In this paper, we examine the following basic question in the context of second-p
rice ad auctions: how should an ad platform optimally reveal information about the ad opportunity to the advertisers in order to maximize revenue? We consider a model in which bidders valuations depend on a random state of the ad opportunity. Different from previous work, we focus on a more practical, and challenging, situation where the space of possible realizations of ad opportunities is extremely large. We thus focus on developing algorithms whose running time is independent of the number of ad opportunity realizations. We examine the auctioneers algorithmic question of designing the optimal signaling scheme. When the auctioneer is restricted to send a public signal to all bidders, we focus on a well-motivated Bayesian valuation setting in which the auctioneer and bidders both have private information, and present two main results: 1. we exhibit a characterization result regarding approximately optimal schemes and prove that any constant-approximate public signaling scheme must use exponentially many signals; 2. we present a simple public signaling scheme that serves as a constant approximation under mild assumptions. We then initiate an exploration on the power of being able to send different signals privately to different bidders. Here we examine a basic setting where the auctioneer knows bidders valuations, and exhibit a polynomial-time private scheme that extracts almost full surplus even in the worst Bayes Nash equilibrium. This illustrates the surprising power of private signaling schemes in extracting revenue.
We pose and study a fundamental algorithmic problem which we term mixture selection, arising as a building block in a number of game-theoretic applications: Given a function $g$ from the $n$-dimensional hypercube to the bounded interval $[-1,1]$, and
an $n times m$ matrix $A$ with bounded entries, maximize $g(Ax)$ over $x$ in the $m$-dimensional simplex. This problem arises naturally when one seeks to design a lottery over items for sale in an auction, or craft the posterior beliefs for agents in a Bayesian game through the provision of information (a.k.a. signaling). We present an approximation algorithm for this problem when $g$ simultaneously satisfies two smoothness properties: Lipschitz continuity with respect to the $L^infty$ norm, and noise stability. The latter notion, which we define and cater to our setting, controls the degree to which low-probability errors in the inputs of $g$ can impact its output. When $g$ is both $O(1)$-Lipschitz continuous and $O(1)$-stable, we obtain an (additive) PTAS for mixture selection. We also show that neither assumption suffices by itself for an additive PTAS, and both assumptions together do not suffice for an additive FPTAS. We apply our algorithm to different game-theoretic applications from mechanism design and optimal signaling. We make progress on a number of open problems suggested in prior work by easily reducing them to mixture selection: we resolve an important special case of the small-menu lottery design problem posed by Dughmi, Han, and Nisan; we resolve the problem of revenue-maximizing signaling in Bayesian second-price auctions posed by Emek et al. and Miltersen and Sheffet; we design a quasipolynomial-time approximation scheme for the optimal signaling problem in normal form games suggested by Dughmi; and we design an approximation algorithm for the optimal signaling problem in the voting model of Alonso and C^{a}mara.
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 net
work 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.
We analyze in this paper finite horizon hierarchical signaling games between (information provider) senders and (decision maker) receivers in a dynamic environment. The underlying information evolves in time while sender and receiver interact repeate
dly. Different from the classical communication (control) models, however, the sender (sensor) and the receiver (controller) have different objectives and there is a hierarchy between the players such that the sender leads the game by announcing his policies beforehand. He needs to anticipate the reaction of the receiver and the impact of the actions on the horizon while controlling the transparency of the disclosed information at each interaction. With quadratic cost functions and multivariate Gaussian processes, evolving according to first order auto-regressive models, we show that memoryless linear sender signaling rules are optimal (in the sense of game-theoretic hierarchical equilibrium) within the general class of measurable policies in the noncooperative communication context. In the noncooperative control context, we also analyze the hierarchical equilibrium for linear signaling rules and provide an algorithm to compute the optimal linear signaling rules numerically with global optimality guarantees.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
