It is well known that in an M/M/1 queueing model where customers strategically decide whether or not to enter a queue, and if and when to renege, under a first-come-first-served regime, customers' selfish behavior produces an outcome that is socially suboptimal. Optimality could be achieved by adopting a different queuing regime. In particular, optimality is achieved by any regime where a new arriving customer is put in a position that is not the last. The priority slots regime, is also universally optimal. Under this regime, there is a sequence of slots indexed by the positive integers. A new arriving customer who enters the queue occupies the available slot with the smallest index. At any given time the customer occupying the slot with the smallest index is being served. A new customer who finds the first slot vacant preempts the current service. Once served, a customer leaves the system and frees the slot she occupied.

Potential buyers of a product or service, before making their decisions, tend to read reviews written by previous consumers. We consider Bayesian consumers with heterogeneous preferences, who sequentially decide whether to buy an item of unknown quality, based on previous buyers’ reviews. The quality is multi-dimensional and may occasionally vary over time; the reviews are also multi-dimensional. In the simple uni-dimensional and static setting, beliefs about the quality are known to converge to its true value. Our paper extends this result in several ways. First, a multi-dimensional quality is considered, second, rates of convergence are provided, third, a dynamical Markovian model with varying quality is studied. In this dynamical setting the cost of learning is shown to be small.

We study online learning for optimal allocation when the resource to be allocated is time. An agent receives task proposals sequentially according to a Poisson process and can either accept or reject a proposed task. If she accepts the proposal, she is busy for the duration of the task and obtains a reward that depends on the task duration. If she rejects it, she remains on hold until a new task proposal arrives. We study the regret incurred by the agent first when she knows her reward function but does not know the distribution of the task duration, and then when she does not know her reward function, either. Faster rates are finally obtained by adding structural assumptions on the distribution of rides or on the reward function. This natural setting bears similarities with contextual (one-armed) bandits, but with the crucial difference that the normalized reward associated to a context depends on the whole distribution of contexts.

Wardrop equilibria in nonatomic congestion games are in general inefficient as they do not induce an optimal flow that minimizes the total travel time. Network tolls are a prominent and popular way to induce an optimum flow in equilibrium. The classical approach to find such tolls is marginal cost pricing which requires the exact knowledge of the demand on the network. In this paper, we investigate under which conditions demand-independent optimum tolls exist that induce the system optimum flow for any travel demand in the network. We give several characterizations for the existence of such tolls both in terms of the cost structure and the network structure of the game. Specifically we show that demand-independent optimum tolls exist if and only if the edge cost functions are shifted monomials as used by the Bureau of Public Roads. Moreover, non-negative demand-independent optimum tolls exist when the network is a directed acyclic multi-graph. Finally, we show that any network with a single origin-destination pair admits demand-independent optimum tolls that, although not necessarily non-negative, satisfy a budget constraint.