The Wisdom of a Confused Crowd: Model-Based Inference
George J. Mailath and Larry Samuelson
January 16, 2019
“Crowds” are often regarded as “wiser” than individuals, and prediction markets are often regarded as effective methods for harnessing this wisdom. If the agents in prediction markets are Bayesians who share a common model and prior belief, then the no-trade theorem implies that we should see no trade in the market. But if the agents in the market are not Bayesians who share a common model and prior belief, then it is no longer obvious that the market outcome aggregates or conveys information. In this paper, we examine a stylized prediction market comprised of Bayesian agents whose inferences are based on different models of the underlying environment. We explore a basic tension—the differences in models that give rise to the possibility of trade generally preclude the possibility of perfect information aggregation.
The Curse of Long Horizons
V. Bhaskar and George J. Mailath
December 3, 2018 (original draft July 24, 2016)
We study a model of dynamic moral hazard with symmetric ex ante uncertainty about the difficulty of the job. Over time, both the principal and agent update their beliefs about the difficulty of the job as they observe output. Effort is private and so incentives must be provided for the agent to exert effort, and the principal can only make within period commitments. In consequence, the agent may have an additional incentive to shirk when the principal induces effort, because by shirking, the agent causes the principal to have incorrect beliefs. We show that this possibility can result in the contract that induces effort in every period needing incentives that become increasingly high powered as the length of the relationship increases. Thus it is never optimal to always induce effort in very long relationships.
A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games
V. Bhaskar, George J. Mailath, and Stephen Morris
October 29, 2012
We study perfect information games with an infinite horizon played by an arbitrary number of players. This class of games includes infinitely repeated perfect information games, repeated games with asynchronous moves, games with long and short run players, games with overlapping generations of players, and canonical non-cooperative models of bargaining. We consider two restrictions on equilibria. An equilibrium is purifiable if close by behavior is consistent with equilibrium when agents’ payoffs at each node are perturbed additively and independently. An equilibrium has bounded recall if there exists K such that at most one player’s strategy depends on what happened more than K periods earlier. We show that only Markov equilibria have bounded recall and are purifiable. Thus if a game has at most one long-run player, all purifiable equilibria are Markov. [This is essentially the January 5, 2010 version, with some typos corrected and two clarifications (the independence of payoff shocks across players made explicit and K-recall explicitly required in purifiability).]
Your Reputation Is Who You’re Not, Not Who You’d Like To Be
George J. Mailath and Larry Samuelson
August 7, 1998
We construct a model in which a firm’s reputation must be built gradually, is managed, and dissipates gradually unless appropriately maintained. Consumers purchase an experience good from a firm whose unobserved effort affects the probability distribution of consumer utilities. Consumers observe private, noisy signals (consumer utilities) of the behavior of the firm, yielding a game of imperfect private monitoring} The standard approach to reputations introduces some “good” or “Stackelberg” firms into the model, with consumers ignorant of the type of the firm they face and with ordinary firms acquiring their reputations by masquerading as Stackelberg firms. In contrast, the key ingredient of our reputation model is the continual possibility that the ordinary or “competent” firm might be replaced by a “bad” or “inept” firm who never chooses the Stackelberg action. Competent firms then acquire their reputations by convincing consumers that they are not inept. Building a reputation is an exercise in separating oneself from inept firms who one is not, rather than pooling with Stackelberg firms who one would like to be. We investigate how a firm manages such a reputation, showing, among other features, that a competent firm may not always choose the most efficient effort level to distinguish itself from an inept one.
Repeated Games with Imperfect Private Monitoring: Notes on a Coordination Perspective
George J. Mailath and Stephen Morris
July 3, 1998
In repeated games with imperfect public monitoring, players can use public signals to perfectly coordinate their behavior. Our study of repeated games with imperfect private monitoring focusses on the coordination problem that arises without public signals. We present three new observations. First, in a simple twice repeated game, we characterize the private signalling technologies that allow non-static Nash behavior in pure strategy equilibria. Our characterization uses the language of common p-belief due to Monderer and Samet (GEB, 1989). Second, we show that in the continuum action convention game of Shin and Williamson (GEB, 1996), for any full support private monitoring technology, equilibria of the finitely repeated convention game must involve only static Nash equilibria. By contrast, with sufficiently informative public monitoring, the multiplicity of Nash equilibria allows a finite folk theorem. Finally, for finite action games, we prove that there are full support private monitoring technologies for which a Nash reversion infinite horizon folk theorem holds.
A Reformulation of a Criticism of The Intuitive Criterion and Forward Induction
George J. Mailath
The intuitive criterion of Kreps has been criticized by Stiglitz (see Cho and Kreps (1987), Mailath, Okuno-Fujiwara, and Postlewaite (1993), and van Damme (1989)) for seeming inconsistencies in the way the reasoning is applied. Using the beer-quiche game as an example, this note recasts their criticism in a normal form argument which disputes the persuasiveness of the (naive) argument for not only the intuitive criterion, but also the requirement of robustness to elimination of never a weak best response (NWBR) strategies of Kohlberg and Mertens (1986)(a more general requirement which implies the intuitive criterion).
Updated February 15, 2017.