David A. Miller, Game Theorist

Several papers under revision… Check back soon!

d9miller@ucsd.edu — 2011-04-06T09:00:01-07:00

My four most current working papers, listed below, are all under active revision right now. Several of them may undergo a change of title as well. Check back later this spring for updates. If you really want the latest version of one of them right now, you may request it by email.

Robust collusion with private information (Updated 4/18/2011)
A theory of disagreement in repeated games (with Joel Watson)
Forgiveness with optimally empty promises (with Kareen Rozen)
Enforcing cooperation in networked societies (with Nageeb Ali)

Where to see me Spring 2010

d9miller@ucsd.edu — 2010-02-01T22:29:08-08:00

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

• March 15: Università Bocconi, Milan
• March 16: Collegio Carlo Alberto, Turin
• March 18: Universität Zürich
• March 23: European University Institute, Florence

Monitoring with collective memory: Forgiveness with optimally empty promises

d9miller@ucsd.edu — 2010-04-22T22:23:11-07:00

With Kareen Rozen

Abstract: We study optimal contracting in a team setting with moral hazard, where teammates promise to complete socially efficient but costly tasks. Teammates must monitor each other to provide incentives, but each team member has limited capacity to allocate between monitoring and productive tasks. Players incur contractual punishments for unfulfilled promises that are discovered. We show that optimal contracts are generally "forgiving" and players optimally make "empty promises" that they don't necessarily intend to fulfill. As uncertainty in task completion increases, players optimally make more empty promises but fewer total promises. A principal who hires a team of agents optimally implements a similar contract, with profit-sharing and employment-at-will. When agents differ in their productivity, the model suggests a "Dilbert principle" of supervision: less productive players optimally specialize in monitoring the more productive players' promises.

Working paper 4/22/2010

NY Times on the Dot-Com bubble, with lessons for today

d9miller@ucsd.edu — 2008-11-23T10:05:31-08:00

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.

Where to see me Fall 2008

d9miller@ucsd.edu — 2008-08-29T17:34:21-07:00

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 University

Visiting Yale, 2008-2009

d9miller@ucsd.edu — 2008-06-22T18:13:38-07:00

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!

Enforcing cooperation in networked societies

d9miller@ucsd.edu — 2010-02-01T22:23:03-08:00

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. Players observe only their own partners' actions, so collective punishments that support cooperation must spread endogenously through the network, as a contagion. Our model features asynchronous interaction, variable stakes in each relationship, and transferable utilities. With these properties, for any network there exists a contagion equilibrium in which incentive constraints bind along the equilibrium path. Among symmetric networks, the optimal network topology in a large society features many identical, independent cliques. We conjecture that such a network is also Pareto optimal among all (symmetric and asymmetric) networks. Our results formalize the notion that when collective enforcement is decentralized, the level of social cooperation, or "social capital," is maximized in tight-knit, highly clustered groups.

Working paper coming soon

A theory of disagreement in repeated games with renegotiation

d9miller@ucsd.edu — 2010-07-10T17:16:34-07:00

With Joel Watson

Abstract: This paper develops the concept of contractual equilibrium for repeated games with transferable utility, whereby the players negotiate cooperatively over their continuation strategies at the start of each period. Players may disagree in the negotiation phase, and continuation play may be suboptimal under disagreement. Under agreement, play is jointly optimal in the continuation game, and the players split the surplus (according to fixed bargaining weights) relative to what they would have attained under disagreement. Contractual equilibrium outcomes also arise from subgame perfect equilibria in a class of models with noncooperative bargaining, under some assumptions on the endogenous meaning of cheap-talk messages. Contractual equilibria exist for all discount factors, and for any given discount factor all contractual equilibria attain the same aggregate utility. Patient players attain efficiency under simple sufficient conditions; necessary and sufficient conditions are also provided. The allocation of bargaining power can dramatically affect aggregate utility. The theory extends naturally to games with more than two players, imperfect public monitoring, and heterogeneous discount factors.

Working paper 7/1/2010

Invention under uncertainty and the threat of ex post entry

d9miller@ucsd.edu — 2008-04-01T11:45:49-07:00

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)

Robust collusion with private information

d9miller@ucsd.edu — 2011-05-20T08:47:31-07:00

Accepted for publication in the Review of Economic Studies.

Abstract: The game-theoretic literature on collusion has been hard pressed to explain why a cartel should engage in price wars, without resorting to either impatience, symmetry restrictions, inability to communicate, or failure to optimize. This paper introduces a new explanation that relies on none of these assumptions: if the cartel's member firms have private information about their costs, price wars can be optimal in the face of complexity. Specifically, equilibria that are robust to payoff-irrelevant disruptions of the information environment generically cannot attain or approximate efficiency. An optimal robust equilibrium must allocate market shares inefficiently, and may call for price wars under certain conditions. For a two-firm cartel, cost interdependence is a sufficient condition for price wars to arise in an optimal robust equilibrium. That optimal equilibria are inefficient generically applies not only to collusion games, but also to the entire separable payoff environment (Chung & Ely 2006)---a class that includes most typical economic models.

Working paper 4/27/2011: This is a major update of the paper formerly titled "Optimal ex post incentive compatible equilibria in repeated games of private information” and “The dynamic cost of ex post incentive compatibility in repeated games of private information."

Attainable payoffs in repeated games with interdependent private information

d9miller@ucsd.edu — 2009-01-13T19:40:35-08:00

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

Was there too little entry during the Dot Com Era?

d9miller@ucsd.edu — 2007-10-01T11:29:01-07:00

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)

Efficiency in repeated trade with hidden valuations

d9miller@ucsd.edu — 2007-09-01T09:10:34-07:00

With Susan Athey

Published in Theoretical Economics, 2(3):299-354, September 2007

Abstract: We analyze the extent to which efficient trade is possible in an ongoing relationship between impatient agents with hidden valuations (i.i.d. over time), restricting attention to equilibria that satisfy ex post incentive constraints in each period. With ex ante budget balance, efficient trade can be supported in each period if the discount factor is at least one half. In contrast, when the budget must balance ex post, efficiency is not attainable, and furthermore for a wide range of probability distributions over their valuations, the traders can do no better than employing a posted price mechanism in each period. Between these extremes, we consider a "bank" that allows the traders to accumulate budget imbalances over time, but only within a bounded range. We construct non-stationary equilibria that allow traders to receive payoffs that approach efficiency as their discount factor approaches one, while the bank earns exactly zero expected profits. For some probability distributions there exist equilibria that yield exactly efficient payoffs for the players and zero profits for the bank, but such equilibria require high discount factors.

Published paper

"Token" equilibria in sensor networks with multiple sponsors

d9miller@ucsd.edu — 2006-05-06T08:57:57-07:00

With Sameer Tilak and Tony Fountain

Published in the Proceedings of the Workshop on Stochasticity in Distributed Systems (StoDiS'05), San Jose, CA, December 19, 2005

Abstract: When two sponsoring organizations, working towards separate goals, employ wireless sensor networks for a finite period of time, it can be efficiency-enhancing for the sponsors to program their sensors to cooperate. But if each sensor privately knows whether it can provide a favor in any particular period, and the sponsors cannot contract on ex post payments, then no favors are performed in any Nash equilibrium. Allowing the sponsors to contract on ex post payments, we construct equilibria based on the exchange of "tokens" that yield significant cooperation and increase expected sponsor payoffs. Increasing the sponsors' liability is beneficial because it enables them to use more tokens.

Working paper 5/22/2006 (newer and better than the StoDiS version)