With Kareen Rozen

Abstract: We consider a team setting where forgetful players with limited memories have costly but socially efficient tasks to complete. Each teammate promises to complete some subset of the tasks, and strategically memorizes her own promises as well as a subset of her teammates' promises. She can be contractually punished for an unfulfilled promise only if another player remembers it. Hence the team's collective memory serves as a costly monitoring device.

We show that linear contracts are the optimal way to ensure that a player completes as many promises as she remembers, and characterize the optimal linear contract when players' memories differ in size and quality. Linear contracts are indeed optimal if players are not very forgetful. However, when players are more forgetful, an optimal equilibrium has empty promises; these are promises a player might not complete even if she remembers them. The corresponding optimal non-linear contract will "forgive" some failures. As players become more forgetful, they make more empty promises and devote more of their memories to monitoring.

Working paper 5/30/2009

Permalink

Tags: Optimal contracts, Behavioral economics, Mechanism design, Bounded memory, Cooperation

Note: Satoru Takahashi discovered an error in a previous version of this paper. I am working on figuring out how to correct it. For now, I am posting a shorter version that contains only the correct results. Please do not cite, circulate, or refer to any version of the paper dated prior to 2009.

Abstract: This paper proves folk theorems for repeated games with private information, communication, and monetary transfers, in which signal spaces may be arbitrary, signals may be statistically interdependent, and payoffs for each player may depend on the signals of other players.

Working paper 1/13/2009

Permalink

Tags: Repeated games, Private information, Mechanism design, Folk theorem

The New York TImes published a nice article today on David Kirsch and the Dot-Com Archive that he curates at the University of Maryland. The article briefly mentions a paper that David, Brent Goldfarb, and I published in the Journal of Financial Economics a few years ago. As the article mentions, our paper interprets the Dot-Com bubble as a strategy gone wrong — too many startup firms adopted "Get Big Fast" strategies (trying to emulate Yahoo!, Google, eBay, and Amazon), when they would have had better success targeting smaller niche markets.

However, the article does not mention that our paper also makes a broader contribution to the theory of investment bubbles and crashes in general — one that can help us interpret more recent events in markets like residential housing, public equities, and mortgage backed securities. The basic insight is that straightforward herding behavior among the relatively well-informed financial fund managers (like venture capitalists, hedge funds, and investment banks) can lead to a boom-bust cycle because these intermediaries are managing the funds of less informed investors (like pension funds, institutional investors, and individuals). A herd forms among the fund managers when enough of them decide that a certain kind of security or asset is a good investment that the rest find it optimal to "pile on" without investigating the fundamentals any further. Such a herd can be temporary and self-correcting, as the fund managers learn about the investment over time. However, investors on the outside, like you and me, don't know as much as the people we hired to manage our funds, and we don't fully trust them either because they're not playing with their own money. What Brent, David, and I showed in the paper is that once a bubble starts to pop, we (the investors) may find it optimal to withdraw our funds entirely, just as our fund managers have corrected their strategies to account for the collapse of the bubble.

In the current financial crisis, we can see these kinds of effects, as banks raise their interest rates and collateral requirements, investors "flee to quality" and seek refuge in treasury securities, and investment banks fail one after another. To make these ideas concrete in the context of a current crisis, we can think of AAA-rated corporate bonds (rather than equity shares in Dot-Com startups) as the overvalued security, mutual fund managers (instead of venture capitalists) as the well-informed intermediaries, and blindly trusting the bond rating agencies (rather than Get Big Fast) as the misguided strategy. According to our theory, once we see corporate bonds starting to crumble, we investors can find it optimal to withdraw from the corporate bond market in favor of Treasury bills, even though our mutual fund managers are learning to do a better job gauging the default risk of bond-issuing firms.

What does it take to get the market started again under this theory? We investors need to see some evidence that the financial intermediaries are investing wisely again. An infusion of government equity into the financial industry may help, if it gives the intermediaries a chance to demonstrate that they can be trusted once again. Otherwise we can get stuck in a bad equilibrium in which nobody invests because the intermediaries haven't demonstrated that they are trustworthy, and the intermediaries can't demonstrate that they are trustworthy because nobody is investing. So the theory suggests that the kinds of financial bailouts currently underway might actually be useful.

Permalink

Tags: Venture capital, Herding, Bubbles, Finance, Financial crisis

This fall I'll be presenting seminars at the following universities near you:

• September 25: Princeton University
• September 29: Columbia University
• October 6: University of Western Ontario
• October 7: University of Toronto
• October 17: Marshall School of Business, USC
• October 30: Georgetown University
• November 6: Harvard University (joint MIT seminar)
• November 18: Stern School of Business, NYU
• December 3: Yale UniversityPermalink

For the 2008-2009 school year, I will be visiting Yale University, specifically the Cowles Foundation and the Economics Department. I look forward to living in New England again after spending a decade in California!Permalink

With Nageeb Ali

Abstract: We endogenize social network formation and collective enforcement using a model in which players interact bilaterally and repeatedly along costly links. Cooperation is supported by the threat of collective punishments that spread through the network. Optimal networks are attainable in equilibrium. When the society is homogeneous, the optimal network consists of many separate cliques. Introducing heterogeneous match quality gives rise to more realistic "small worlds" networks, with connectedness, small distances, and high clustering.

Working paper coming soon

Permalink

Tags: Repeated games, Social Networks, Network Formation, Cooperation, Contagion, Small Worlds, Cliques

With Joel Watson

Abstract: We model repeated games with transferable utility and endogenous renegotiation, in which at the beginning of each period the players negotiate over their continuation play. Bargaining is cooperative, and depends on the endogenously generated outside options. We define the concept of negotiation equilibrium, in which the players' agreements are optimal subject to consistency and incentive compatibility constraints. A particular feature of negotiation equilibrium is that it allows for the players to disagree (which we view as a joint deviation), in which case they make no transfers in that period but still take actions that may depend on the history, and then anticipate agreeing again in the next period. This contrasts with renegotiation proofness, which does not allow for disagreement. We identify conditions under which all negotiation equilibria are efficient, as well as conditions under which optimal negotiation equilibria are inefficient. The actions that the players would choose under disagreement are key to supporting high payoffs under agreement.

Working paper coming soon

Permalink

Tags: Repeated games, Bargaining, Negotiation, Renegotiation proofness, Cooperation

Published in the European Economic Review, 52(3):387–412, April 2008 (lead article)

Abstract: This paper proposes a theoretical framework for studying the invention of new products when demand is uncertain. In this framework, under general conditions, the threat of ex post entry by a competitor can deter invention ex ante. Asymmetric market power in the ex post market exacerbates the problem. The implications of these general results are examined in a series of examples that represent important markets in the computer industry. The first is a model that shows how an operating system monopolist, by its mere presence, can deter the invention of complements, to its own detriment as well as that of society. The implications of policies such as patent protection, price regulation, and mandatory divestiture are considered. Three additional examples consider the ability of a monopolist in one market to commit to bundling an unrelated product, a pair of horizontally differentiated firms that can add a new feature to their products, and a platform leader that can be challenged in its base market by the supplier of a complementary product.

Working paper 8/24/2006 (older version but freely distributable)

Link to published version (ScienceDirect subscribers only)

Permalink

Tags: Industrial organization, Invention, Innovation, Demand uncertainty, Ex post entry, Intel, Microsoft, Netscape

Abstract: An ex post perfect public equilibrium (EPPPE) is a perfect public equilibrium that is robust to the possibility that players might observe unmodeled, payoff-irrelevant signals that are correlated with each others' contemporaneous private information. However, robustness comes at a cost to the players: in many games, efficient payoffs in the corresponding static mechanism design problem cannot be supported as average payoffs in an EPPPE, even when players are patient. In two-player repeated allocation games, an optimal EPPPE never employs a (static) efficient outcome function in any stage game. Instead, the players always prefer to give up some static efficiency by sometimes allocating to the player with the lower valuation. Under independent valuations, optimal equilibria are often stationary, but when valuations are globally interdependent, optimal equilibria are never stationary. Applied to the problem of collusion with hidden costs, these results yield new insights into the phenomenon of price wars in collusive equilibria.

Working paper 11/16/2007

Permalink

Tags: Repeated games, Private information, Mechanism design, Ex post incentive compatibility, Folk theorem, Collusion, Price wars

With Brent Goldfarb and David Kirsch

Published in the Journal of Financial Economics, 86(1):100-144, October 2007

Abstract: We present four stylized facts about the Dot Com Era: (1) there was a widespread belief in a "Get Big Fast" business strategy; (2) the increase and decrease in public and private equity investment was most prominent in the internet and information technology sectors; (3) the survival rate of dot com firms is on par or higher than other emerging industries; and (4) firm survival is independent of private equity funding. To connect these findings we offer a herding model that accommodates a divergence between the information and incentives of venture capitalists and their investors. A Get Big Fast belief cascade may have led to overly focused investment in too few internet startups and, as a result, too little entry.

Covered by The New York Times (Leslie Berlin, "Lessons of survival from the Dot-Com attic," p. BU4, 11/23/2008)

Covered by The Wall Street Journal (Lee Gomes, "The Dot-Com Bubble is reconsidered—and maybe relived," p. B1, 11/8/2006)

Covered by Inc.com (Leslie Taylor, "The dot-com bust? Not as bad as you think," 12/4/2006)

Working paper 12/13/2005 (older version but freely distributable)

Link to published version (ScienceDirect subscribers only)

Permalink

Tags: Venture capital, Herding, Bubbles, Finance