We propose a model of discrete time dynamic congestion games with atomic players and a single source-destination pair. The latencies of edges are composed by free-flow transit times and possible queuing time due to capacity constraints. We give a precise description of the dynamics induced by the individual strategies of players and of the corresponding costs, either when the traffic is controlled by a planner, or when players act selfishly. In parallel networks, optimal and equilibrium behavior eventually coincides, but the selfish behavior of the first players has consequences that cannot be undone and are paid by all future generations. In more general topologies, our main contributions are three-fold.First, we show that equilibria are usually not unique. In particular, we prove that there exists a sequence of networks such that the price of anarchy is equal to n − 1, where n is the number of vertices, and the price of stability is equal to 1.Second, we illustrate a new dynamic version of Braess's paradox: the presence of initial queues in a network may decrease the long-run costs in equilibrium. This paradox may arise even in networks for which no Braess's paradox was previously known.Third, we propose an extension to model seasonalities by assuming that departure flows fluctuate periodically over time. We introduce a measure that captures the queues induced by periodicity of inflows. This measure is the increase in costs compared to uniform departures for optimal and equilibrium flows in parallel networks.

We consider a Bayesian persuasion problem where the persuader and the decision maker communicate through an imperfect channel that has a fixed and limited number of messages and is subject to exogenous noise. We provide an upper bound on the payoffs the persuader can secure by communicating through the channel. We also show that the bound is tight, i.e., if the persuasion problem consists of a large number of independent copies of the same base problem, then the persuader can achieve this bound arbitrarily closely by using strategies that tie all the problems together. We characterize this optimal payoff as a function of the information-theoretic capacity of the communication channel. for stimulating discussions and comments. We thank the editor Alessandro Pavan, an anonymous associate editor and anonymous referees for helpful comments and suggestions. We also thank participants of the 6th workshop on /site/tristantomala2. Tristan Tomala gratefully acknowledges the support the HEC foundation and ANR/Investissements d'Avenir under grant ANR-11-IDEX-0003/Labex Ecodec/ANR-11-LABX-0047. 1 See e.g., Perez and Skreta, 2018. 2 See Boleslavsky and Cotton, 2015 for a model of grading standards through Bayesian persuasion.3 of good or bad quality. When a project is approved, it yields a positive return of +1 to the investors if it is good, and a negative return of −7 if it is bad; rejecting a project yields a payoff of 0. The objective of the firm is to get a maximum number of projects approved.Suppose that the firm commits to an information disclosure mechanism, i.e., distributions of messages conditional on states (as in Kamenica and Gentzkow, 2011) and faces no restriction on the number of messages. To invest, the board of investors must be persuaded that the project is good with probability at least 7/8. Thus, for each project, the firm would optimally draw a good message g or a bad message b with the following probabilities:This way, the belief that the project is good upon receiving the good message is as follows: P(project is good | g) = 7/8, and the project is accepted with probability 4/7 (see Section 4). Now, suppose that the auditing board gives the firm only half the time it would require to talk about all projects. Namely, there is an even number n of projects, but the firm has only n/2 messages available.A simple strategy the firm can adopt would be to select half of the projects, focus on them, and communicate optimally for each of them. With this strategy, half of the projects are accepted with probability 4/7 each, so in expectation, the average number of accepted projects is 2/7. This is not optimal, and a better strategy would be to pair projects by two and to draw one message g, b for each pair in the following way: P(g | both projects are good) = 1, P(g | both projects are bad) = 0, P(g | only one project is good) = 1/6.The total probability of g is 1/3 and upon observing this message, the beliefs about quality are as follows:P(both projects are good | g) = 6/8, P(only project 1 is good | g) = P(only p...

No abstract

We characterize belief-free equilibria in infinitely repeated games with incomplete information with N ≥ 2 players and arbitrary information structures. This characterization involves a new type of individual rational constraint linking the lowest equilibrium payoffs across players. The characterization is tight: we define a set of payoffs that contains all the belief-free equilibrium payoffs; conversely, any point in the interior of this set is a belief-free equilibrium payoff vector when players are sufficiently patient. Further, we provide necessary conditions and sufficient conditions on the information structure for this set to be non-empty, both for the case of known-own payoffs, and for arbitrary payoffs.

Abstract. We characterize the maximum payoff that a team can guarantee against another in a class of repeated games with imperfect monitoring. Our result relies on the optimal trade-off for the team between optimization of stage-payoffs and generation of signals for future correlation.