When and How the Punishment Must Fit the Crime
George J. Mailath, Volker Nocke, and Lucy White
February 15, 2015
In repeated normal-form (simultaneous-move) games, simple penal codes (Abreu, 1986, 1988) permit an elegant characterization of the set of subgame-perfect outcomes. We show that the logic of simple penal codes fails in repeated extensive-form games. By means of examples, we identify two types of settings in which a subgame-perfect outcome may be supported only by a profile with the property that the continuation play after a deviation is tailored not only to the identity of the deviator, but also to the nature of the deviation. (This is a major revision of "When the Punishment Must Fit the Crime: Remarks on the Failure of Simple Penal Codes in Extensive-Form Games," originally circulated in 2004.)
and Investments in Matching Markets
George J. Mailath, Andrew Postlewaite, and Larry Samuelson
August 15, 2014, revised October 4, 2015
We examine markets in which agents make investments and then match into pairs, creating surpluses that depend on their investments and that can be split between the matched agents. In general, each of the matched agents would "own" part of the surplus in the absence of interagent transfers. Most of the work in the large bargaining-and-matching literature ignores this initial ownership of the surplus. We show that when investments are not observable to potential partners, initial ownership affects the efficiency of equilibrium investments and affects the agents' payoffs. In particular, it is possible that reallocating initial ownership could increase welfare on both sides of the match.
By putting additional structure on the model studied in "Pricing and Investments in Matching Markets" (in particular, by only having one-sided investments, and studying a parametric model), we are able to obtain clean comparative statics with respect to premuneration values.
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.
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 October 9, 2015 .