Colin Stewart

Testing Multiple Forecasters

We consider a cross-calibration test of predictions by multiple potential experts in a stochastic environment. This test checks whether each expert is calibrated conditional on the predictions made by other experts. We show that this test is good in the sense that a true expert--one informed of the true distribution of the process--is guaranteed to pass the test no matter what the other potential experts do, and false experts will fail the test on all but a small (category one) set of true distributions. Furthermore, even when there is no true expert present, a test similar to cross-calibration cannot be simultaneously manipulated by multiple false experts, but at the cost of failing some true experts. In contrast, tests that allow false experts to make precise predictions can be jointly manipulated.

Dynamic coordination with individual learning

We study coordination in dynamic global games with private learning. Players choose whether and when to invest irreversibly in a project whose success depends on its quality and the timing of investment. Players gradually learn about project quality. We identify conditions on temporal incentives under which, in sufficiently long games, players coordinate on investing whenever doing so is not dominated. Roughly speaking, this outcome occurs whenever playersʼ payoffs are sufficiently tolerant of non-simultaneous coordination. We also identify conditions under which players coordinate on the risk-dominant action. We provide foundations for these results in terms of higher order beliefs.

Rational inattention dynamics: Inertia and delay in decision-making

We solve a general class of dynamic rational-inattention problems in which an agent repeatedly acquires costly information about an evolving state and selects actions. The solution resembles the choice rule in a dynamic logit model, but it is biased towards an optimal default rule that does not depend on the realized state. We apply the general solution to the study of (i) the sunk-cost fallacy; (ii) inertia in actions leading to lagged adjustments to shocks; and (iii) the tradeoff between accuracy and delay in decision-making.

All Aboard at All Doors: Route Selection and Running-Time Savings Estimation for Multiscenario All-Door Bus Boarding

The time that buses spend waiting for passengers to board can be a significant portion of a bus routes overall running time. A key determinant of boarding time is the number of doors through which passengers are permitted to board. Transit agencies that allow boarding through all doors, instead of just through the front door, typically enjoy decreased boarding times and decreased running times. This study focused on the feasibility of an all-door boarding policy for La Société de transport de Montréal (STM), the public transit agency of Montreal, Canada. The potential benefits of such a policy were assessed through three main steps. First, a selection methodology was developed to determine which of STMs bus routes would benefit most from various all-door boarding strategies. Second, a multivariate regression analysis was implemented with STMs archived automatic vehicle location and automatic passenger counter data to estimate the dwell and running-time savings that would result under various implementation scenarios. Third, a sensitivity analysis was developed to demonstrate the savings associated with implementing the policy. The findings showed that all-door boardings could yield substantial savings in running time, with morning peak savings as much as 15.8% on the best routes. In many cases, the running-time savings were enough to remove a bus from a route while still maintaining existing frequencies. The findings from this research may be beneficial for transit planners and operators since the presented methodologies show substantial savings from all-door boarding and can be adopted by other transit agencies.

Influential Opinion Leaders

We present a two-stage coordination game in which early choices of experts with special interests are observed by followers who move in the second stage. We show that the equilibrium outcome is biased toward the experts’ interests even though followers know the distribution of expert interests and can account for it when evaluating observed experts’ actions. Expert influence is fully decentralized in the sense that each individual expert has a negligible impact. The bias in favor of experts results from a social learning effect that is multiplied through a coordination motive. The total effect can be large even if the direct social learning effect is small. We apply our results to the onset of social movements and to the diffusion of products with network externalities.

Communication, Timing, and Common Learning

We study the effect of stochastically delayed communication on common knowledge acquisition (common learning). If messages do not report dispatch times, communication prevents common learning under general conditions even if common knowledge is acquired without communication. If messages report dispatch times, communication can destroy common learning under more restrictive conditions. The failure of common learning in the two cases is based on different infection arguments. Communication can destroy common learning even if it ends in finite time, or if agents communicate all of their information. We also identify conditions under which common learning is preserved in the presence of communication.

Nonmanipulable Bayesian testing

This paper considers the problem of testing an expert who makes probabilistic forecasts about the outcomes of a stochastic process. I show that, as long as uninformed experts do not learn the correct forecasts too quickly, a likelihood test can distinguish informed from uninformed experts with high prior probability. The test rejects informed experts on some data-generating processes; however, the set of such processes is topologically small. These results contrast sharply with many negative results in the literature.

Learning by Similarity in Coordination Problems

We study a learning process in which subjects extrapolate from their experience of similar past strategic situations to the current decision problem. When applied to coordination games, this learning process leads to contagion of behavior from problems with extreme payoffs and unique equilibria to very dissimilar problems. In the long-run, contagion results in unique behavior even though there are multiple equilibria when the games are analyzed in isolation. Characterization of the long-run state is based on a formal parallel to rational equilibria of games with subjective priors. The results of contagion due to learning share the qualitative features of those from contagion due to incomplete information, but quantitatively they differ.

Price distortions under coarse reasoning with frequent trade

We study the effect of frequent trading opportunities and categorization on pricing of a risky asset. Frequent opportunities to trade can lead to large distortions in prices if some agents forecast future prices using a simplified model of the world that fails to distinguish between some states. In the limit as the period length vanishes, these distortions take a particular form: the price must be the same in any two states that a positive mass of agents categorize together. Price distortions therefore tend to be large when different agents categorize states in different ways, even if each individuals categorization is not very coarse.

Attention and Selection Effects

Who participates in transactions when information about the consequences must be learned? We show theoretically that decision makers for whom acquiring and processing information is more costly not only respond more strongly to changes in incentive payments for participating but also decide to participate based on worse information. With higher payments, the pool of participants consists of a larger proportion of individuals who have a worse understanding of the consequences of their decision. We conduct a behavioral experiment that confirms these predictions, both for experimental variation in the costs of information acquisition and for various measures of information costs, including school grades and cognitive ability. These findings are relevant for any transaction combining a payment for participation with uncertain yet learnable consequences.Who participates in transactions when information about their consequences must be learned? Theoretically, we show that decision makers for whom acquiring and processing information is more costly respond more strongly to changes in incentives for participating, and decide to participate based on worse information. Consequently, with higher incentives, the pool of participants consists of a larger fraction of individuals with a worse understanding of the consequences of their decision. Our behavioral experiment confirms these predictions, both for experimental variation in the costs of information acquisition, and for various measures of information costs including school grades and cognitive ability. These findings are relevant for any transaction that combines a price paid for participation with uncertain yet learnable consequences. Our results also clarify the relation between incentives and the ethical principle of informed consent, and thus help address ethical concerns with incentives. ∗Ambuehl: University of Toronto, UTSC and Rotman School of Management, 105 St George Street, Toronto, ON M5S 3E6, Canada, sandro.ambuehl@utoronto.ca. Ockenfels: University of Cologne, Department of Economics, Universitätsstrasse 22a, 50923 Cologne, Germany, ockenfels@uni-koeln.de. Stewart: University of Toronto, Department of Economics, 150 St. George Street, Toronto, ON M5S 3G7, Canada, colinbstewart@gmail.com. We are grateful to Roland Bénabou, Yoram Halevy, Collin Raymond, Roberto Weber and seminar and conference participants at Bonn, Calgary, Frankfurt, the FTC, Montreal, Ottawa, Purdue, Toronto, the CESifo Behavioural Economics Conference, the North American ESA Conference, SITE, and the Vienna Behavioral Public Economics Workshop for helpful comments and suggestions. This research has been approved by the University of Toronto’s Research Ethics Board in protocol 34310. Viola S. Ackfeld, Rami Abou-Seido and Ruizhi Zhu provided helpful research assistance. Ockenfels gratefully acknowledges support by the German Science Foundation through the DFG Research Unit Design & Behavior (FOR 1371). Ambuehl gratefully acknowledges support through a University of Toronto Connaught New Researcher Award and the Wynne and Bertil Plumptre Fellowship at the University of Toronto Scarborough. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 741409); the results reflect the authors’ view, the ERC is not responsible for any use that may be made of the information it contains.