Strategic experimentation in queues

Abstract

We analyze the social and private learning at the symmetric equilibria of a queueing game with strategic experimentation. An infinite sequence of agents arrive at a server that processes them at an unknown rate. The number of agents served at each date is either a geometric random variable in the good state or zero in the bad state. The queue lengthens with each new arrival and shortens if the agents are served or choose to quit the queue. Agents can observe only the evolution of the queue after they arrive; they, therefore, solve a strategic experimentation problem when deciding how long to wait to learn about the probability of service. The agents, in addition, benefit from an informational externality by observing the length of the queue and the actions of other agents. They also incur a negative payoff externality, as those at the front of the queue delay the service of those at the back. We solve for the long-run equilibrium behavior of this queue and show there are typically mass exits from the queue, even if the server is in the good state.Cripps thanks the Cowles Foundation for its hospitality. Thomas gratefully acknowledges support from Deutsche Bank through IAS Princeton. We are grateful to V. Bhaskar, Max Stinchcombe, and Tom Wiseman for their comments. We thank four remarkably constructive referees for their comments and suggestions.Finally, in our equilibria, information can aggregate "in waves": in between informational cascades and ensuing herds, there will be periods of relative inactivity during which learning occurs gradually. Our model shares this feature with Bulow and Klemperer (1994), Toxvaerd (2008), and Murto and Välimäki (2011). The modelTime is discrete, doubly infinite, and indexed by τ ∈ Z. At each date τ, one new agent arrives at the queue. 7 The state of the server of our queue is either good or bad. The server is selected by nature once and for all at the outset of the game: nature selects the good server with probability μ ∈ (0 1). A bad server never produces service capacity, 8 and g τ = 0 for all τ, where g τ ∈ N 0 = {0 1 } denotes the service capacity produced by the server at date τ. Only a good server produces service. In this state g τ is an independent and identically distributed (i.i.d.) geometric 9 random variable with commonly known parameter α ∈ (0 1):Let n τ ∈ N 0 be the number of agents in the queue at the beginning of period τ. The queue discipline is first-come-first-served (FCFS), that is, agents are served in the order of the queue. At each date τ, we distinguish three consecutive stages: service (S), exit (E), and arrival (A). The S, E, and A stages proceed as follows.Service. If n τ > g τ , then the agents at the first g τ positions in line are served at the service stage of date τ and disappear from the queue. Each remaining agent observes this and advances by g τ positions. If n τ ≤ g τ , the entire queue is served and the excess service capacity, g τ − n τ , disappears. (It cannot be stored for use in subsequent periods.)Exit. This is the only stage of date τ...

Contests for Experimentation

“…More broadly, the exponential-bandit framework has recently been used in many papers to study multi-agent strategic experimentation. Keller et al (2005), Keller and Rady (2010), Klein and Rady (2011), and Murto and Välimäki (2011) feature only an informational interdependence across agents; Bonatti and Hörner (2011) and Cripps and Thomas (2014) also have a payoff interdependence, but both take a different form than the contests we study. 7 Finally, questions about how much information a principal should disclose about agents' outcomes have been raised in various contexts.…”

Observational learning in large anonymous games

“…Arieli studies when complete learning occurs. In addition to the points already mentioned, my paper differs from Eyster et al (), Cripps and Thomas (forthcoming), and Arieli () in that an agent's payoff depends on the actions of those before and also after him in the sequence. This adds a strategic consideration to the analysis, as agents may affect future decisions.…”

“…Eyster et al study whether learning occurs as a function of congestion costs. Cripps and Thomas (forthcoming) present a model of (possibly informative) queues. Service to those in the queue is provided only in the good state of the world, but at a stochastic rate.…”

“…Service to those in the queue is provided only in the good state of the world, but at a stochastic rate. Cripps and Thomas study the dynamics of the queue. Arieli () focuses on recurring games: successive generations of agents play the same game.…”

Learning, Experimentation, and Information Design

“…Consider a simple cheap-talk model based on Crawford and Sobel (1982, CS). 15 We assume that the state is uniformly distributed on [0, 1], and that preferences are quadratic. The receiver is unbiased, with preferences −(t − y) 2 , where t is the state of the world (the sender's type) and y ∈ R + is the action by the receiver.…”