No Arabic abstract
Lagrangian duality underlies both classical and modern mechanism design. In particular, the dual perspective often permits simple and detail-free characterizations of optimal and approximately optimal mechanisms. This paper applies this same methodology to a close cousin of traditional mechanism design, one which shares conceptual and technical elements with its more mature relative: the burgeoning field of persuasion. The dual perspective permits us to analyze optimal persuasion schemes both in settings which have been analyzed in prior work, as well as for natural generalizations which we are the first to explore in depth. Most notably, we permit combining persuasion policies with payments, which serve to augment the persuasion power of the scheme. In both single and multi-receiver settings, as well as under a variety of constraints on payments, we employ duality to obtain structural insights, as well as tractable and simple characterizations of optimal policies.
In 1974 E.W. Dijkstra introduced the seminal concept of self-stabilization that turned out to be one of the main approaches to fault-tolerant computing. We show here how his three solutions can be formalized and reasoned about using the concepts of game theory. We also determine the precise number of steps needed to reach self-stabilization in his first solution.
Data driven segmentation is the powerhouse behind the success of online advertising. Various underlying challenges for successful segmentation have been studied by the academic community, with one notable exception - consumers incentives have been typically ignored. This lacuna is troubling as consumers have much control over the data being collected. Missing or manipulated data could lead to inferior segmentation. The current work proposes a model of prior-free segmentation, inspired by models of facility location, and to the best of our knowledge provides the first segmentation mechanism that addresses incentive compatibility, efficient market segmentation and privacy in the absence of a common prior.
Motivated in part by online marketplaces such as ridesharing and freelancing platforms, we study two-sided matching markets where agents are heterogeneous in their compatibility with different types of jobs: flexible agents can fulfill any job, whereas each specialized agent can only be matched to a specific subset of jobs. When the set of jobs compatible with each agent is known, the full-information first-best throughput (i.e. number of matches) can be achieved by prioritizing dispatch of specialized agents as much as possible. When agents are strategic, however, we show that such aggressive reservation of flexible capacity incentivizes flexible agents to pretend to be specialized. The resulting equilibrium throughput could be even lower than the outcome under a baseline policy, which does not reserve flexible capacity, and simply dispatches jobs to agents at random. To balance matching efficiency with agents strategic considerations, we introduce a novel robust capacity reservation policy (RCR). The RCR policy retains a similar structure to the first best policy, but offers additional and seemingly incompatible edges along which jobs can be dispatched. We show a Braess paradox-like result, that offering these additional edges could sometimes lead to worse equilibrium outcomes. Nevertheless, we prove that under any market conditions, and regardless of agents strategies, the proposed RCR policy always achieves higher throughput than the baseline policy. Our work highlights the importance of considering the interplay between strategic behavior and capacity allocation policies in service systems.
We study a variant of Vickreys classic bottleneck model. In our model there are $n$ agents and each agent strategically chooses when to join a first-come-first-served observable queue. Agents dislike standing in line and they take actions in discrete time steps: we assume that each agent has a cost of $1$ for every time step he waits before joining the queue and a cost of $w>1$ for every time step he waits in the queue. At each time step a single agent can be processed. Before each time step, every agent observes the queue and strategically decides whether or not to join, with the goal of minimizing his expected cost. In this paper we focus on symmetric strategies which are arguably more natural as they require less coordination. This brings up the following twist to the usual price of anarchy question: what is the main source for the inefficiency of symmetric equilibria? is it the players strategic behavior or the lack of coordination? We present results for two different parameter regimes that are qualitatively very different: (i) when $w$ is fixed and $n$ grows, we prove a tight bound of $2$ and show that the entire loss is due to the players selfish behavior (ii) when $n$ is fixed and $w$ grows, we prove a tight bound of $Theta left(sqrt{frac{w}{n}}right)$ and show that it is mainly due to lack of coordination: the same order of magnitude of loss is suffered by any symmetric profile.
We study a Bayesian persuasion setting with binary actions (adopt and reject) for Receiver. We examine the following question - how well can Sender perform, in terms of persuading Receiver to adopt, when ignorant of Receivers utility? We take a robust (adversarial) approach to study this problem; that is, our goal is to design signaling schemes for Sender that perform well for all possible Receivers utilities. We measure performance of signaling schemes via the notion of (additive) regret: the difference between Senders hypothetically optimal utility had she known Receivers utility function and her actual utility induced by the given scheme. On the negative side, we show that if Sender has no knowledge at all about Receivers utility, then Sender has no signaling scheme that performs robustly well. On the positive side, we show that if Sender only knows Receivers ordinal preferences of the states of nature - i.e., Receivers utility upon adoption is monotonic as a function of the state - then Sender can guarantee a surprisingly low regret even when the number of states tends to infinity. In fact, we exactly pin down the minimum regret value that Sender can guarantee in this case, which turns out to be at most 1/e. We further show that such positive results are not possible under the alternative performance measure of a multiplicative approximation ratio by proving that no constant ratio can be guaranteed even for monotonic Receivers utility; this may serve to demonstrate the merits of regret as a robust performance measure that is not too pessimistic. Finally, we analyze an intermediate setting in between the no-knowledge and the ordinal-knowledge settings.