All recent working papers,

as well as some working paper versions of forthcoming and published papers,

are available on SSRN.

as well as some working paper versions of forthcoming and published papers,

are available on SSRN.

- When and How the Punishment Must Fit the Crime, with Volker Nocke and Lucy White, February 15, 2015.
- Premuneration Values and Investments in Matching Markets, with Andrew Postlewaite and Larry Samuelson, October 4, 2015.
- A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games, with V. Bhaskar and Stephen Morris, October 29, 2012.
- Maintaining Authority, with Stephen Morris and Andrew Postlewaite, September 26, 2007.
- Laws and Authority, with Stephen Morris and Andrew Postlewaite, April 16, 2001.
- Your Reputation Is Who You're Not, Not Who You'd Like To Be, with Larry Samuelson, August 7, 1998.
- Repeated Games with Imperfect Private Monitoring: Notes on a Coordination Perspective, with Stephen Morris, July 3, 1998.
- A Reformulation of a Criticism of The Intuitive Criterion and Forward Induction, April 1988.

- The Impact of John Nash on Economics and Game Theory, a public lecture presented at the ANU, 22 July 2015. References.
- The Canonical Reputation Model and Reputation Effects, a lecture presented at the 26th Jerusalem School in Economic Theory, "Dynamic Games", June 24--July 3, 2015. Slides for the talk. See my Handbook chapter with Larry Samuelson for more.
- Repeated Games and Reputations, 9th Tinbergen Institute Conference: 70 Years of Games and Economic Behavior, June 26, 2014. Bibliography of talk.
- Premuneration Values, Investments, and Pricing in Matching Markets, McKenzie Lecture, University of Rochester, May 2, 2014.
- Reputations, Second Xiaokai Yang Memorial Lecture presented at the 35th Australian Conference of Economists, Perth, Australia, September 2006.
- Time Consistency, Reputations, and the Importance of Perpetual Uncertainty: Implications for Macroeconomics, Society for Economic Dynamics plenary talk, June 28, 2003, Paris.

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.)

Premuneration Values
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

purifiableif close by behavior is consistent with equilibrium when agents' payoffs at each node are perturbed additively and independently. An equilibrium hasbounded recallif there existsKsuch that at most one player's strategy depends on what happened more thanKperiods 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 andK-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 arenotinept. Building a reputation is an exercise in separating oneself from inept firmswho one is not, rather than pooling with Stackelberg firmswho 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

privatemonitoring 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 commonp-belief due to Monderer and Samet (GEB, 1989). Second, we show that in the continuum action convention game of Shin and Williamson (GEB, 1996), foranyfull 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

April 1988.

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 .