Many economic problems are naturally modelled as a game of incomplete information, where a player's payoff depends on his own action, the actions of others, and some unknown economic fundamentals. Rational behavior in such environments clearly depends on a player's beliefs about economic fundamentals; but it also depends on "higher order beliefs," i.e., players' beliefs about other players beliefs, players' beliefs about other players' beliefs about other players' beliefs, and so on. While this dependence has been understood for a long time, it is only recently that a small theoretical literature in game theory has examined in more detail how the equilibria of incomplete information games vary with such higher order beliefs.
Conventional wisdom holds that such higher order beliefs may play an important role in some economic phenomena. It is reported that, following the Asian crisis, some of the investors who withdrew their capital from Brazil, did so not because they overestimated the economic linkages between Asia and Brazil, but because they thought others might do so. It is reported that negative shocks to some hedge fund portfolios led some lenders to make excessive margin calls and seek to liquidate collateral, not because they thought the fund was insolvent, but because they thought that other lenders might think so, and they had an incentive to get out early. It is reported that apparently irrelevant news about the economy leads some firms to reduce their investments (and thus to recession), not because they think that the news is relevant, but because they think others may think so. It is reported that some investors are currently paying inflated prices for internet stocks not because they believe that future dividends will be high enough to justify those prices, but because they believe that others believe so, and therefore there are short run speculative profits to be made.
Applied modelers have taken such reports very seriously. Yet the resulting
models have typically managed to avoid modelling higher order beliefs.
How? If economic fundamentals permit multiple equilibria and economic players
observe some payoff-irrelevant public signals ("sunspots"), then players
might happen to switch behavior contingent on the sunspot signal. Such
sunspot shifts are used in the academic literature to "explain" currency
crises, bank runs, recessions and other phenomena. Such sunspot explanations
are apparently intended as proxies for the true higher order beliefs explanations.
After all, it is common knowledge in the that the sunspots are payoff-irrelevant
(as are, presumably, literal sunspots). Yet the informal discussion accompanying
such sunspot explanations invariably appeal to "sunspots" that the modeler
may believe are payoff-irrelevant but for which there is clearly not common
knowledge of their irrelevance among economic agents (e.g., the Asian crisis
for Brazil).
In recent work with Hyun Song Shin, we have argued that it should be
possible to take higher order beliefs seriously in applied economic analysis,
exploiting the insights of the theoretical literature on higher order beliefs
in game theory. One fruitful way of doing so is to consider global
games models, first studied by Hans Carlsson and Eric van Damme.
Here it is assumed that each agent observes the true economic fundamentals
with a small amount of noise. This in turn implies that each agent
has a small amount of uncertainty about what others believe, and about
what others believe about him. This simple information structure generates
a rich structure of higher order beliefs and, in many instances, a unique
equilibrium as a function of agents' higher order beliefs where common
knowledge of fundamentals would have allowed multiple equilibria.
We survey all this work (applications of global games, the theory of global games and relation to the larger literature on higher order beliefs in game theory) in a recent survey prepared for the Eighth World Congress of the Econometric Society in Seattle.
Stephen Morris and Hyun Song Shin: Global Games: Theory and Applications.
On this web page, I have collected some of the key papers, with links. The list of papers is extremely incomplete (with a massive bias towards my own work). The references of the Global Games survey gives a slightly more complete listing of relevant papers. I hope to add papers and annotate the listing in due course. The web page is divided into four sections:
Rethinking Multiple Equilibria on Applied Models
Global Games Approach on Theoretical Work on Global Games
Higher Order Beliefs in Game Theory
Stephen Morris and Hyun Song Shin:Rethinking Multiple Equilibria in Macroeconomics.
Stephen Morris and Hyun Song Shin: Unique Equilibrium in a Model of Self-Fulfilling Attacks, American Economic Review, 88 (1998), 587-97.
Frank Heinemann: Unique Equilibrium in a Model of Self-Fulfilling Attacks, American Economic Review, forthcoming.
Stephen Morris and Hyun Song Shin: A Theory of the Onset of Currency Attacks, in Asian Financial Crisis: Causes, Contagion, and Consequences, edited by Agenor, Miller, Vines, and Weber, Cambridge University Press (1999).
Giancarlo Corsetti, Amil Dasgupta, Stephen Morris and Hyun Song Shin: Does One Soros Make a Difference? A Theory of Currency Crises with Large and Small Traders (1999).
Stephen Morris and Hyun Song Shin: Coordination Risk and the Price of Debt (1999).
Itay Goldstein and Ady Pauzner: Demand Deposit Contracts and the Probability of Banks Runs, (2000).
Amil Dasgupta: Financial Contagion through Capital Connections: A Model of the Origin and Spread of Bank Panics, (2000).
Hans Carlsson and Eric van Damme: Global Games and Equilibrium Selection, Econometrica 61 (1993), 989-1018.
Hans Carlsson and Eric van Damme: Equilibrium Selection in Stag Hunt Games, in Frontiers of GameTheory (K. Binmore, A. Kirman and A. Tani, Eds.). Cambridge, MA: MIT Press (1993).
Hans Carlsson and Mattias Ganslandt: Noisy Equilibrium Selection in Coordination Games, Economics Letters 60 (1998), 23-34.
Youngse Kim: Equilibrium Selection in N-Person Coordination Games, Games and Economic Behavior 15 (1996), 203-227.
David Frankel, Stephen Morris and Ady Pauzner: Equilibrium Selection in Global Games with Strategic Complementarities.
Ariel Rubinstein: The Electronic Mail Game: Strategic Behavior under Almost Common Knowledge, American Economic Review 79 (1989), 385-391.
Dov Monderer and Dov Samet: Approximating Common Knowledge with Common Beliefs, Games and Economic Behavior 1 (1989), 170-190.
Stephen Morris, Rafael Rob and Hyun Song Shin: p-Dominance and Belief Potential, Econometrica 63(1995), 145-157.
Stephen Morris and Hyun Song Shin: Approximate Common Knowledge and Co-ordination: Recent Lessons from Game Theory, Journal of Logic, Language and Information 6 (1997), 171-190.
Atsushi Kajii and Stephen Morris: The Robustness of Equilibria to Incomplete Information, Econometrica(1997), 1283-1309.
Atsushi Kajii and Stephen Morris: Refinements and Higher Order Beliefs: A Unified Survey, Center for Mathematical Studies in Economics and Management Science Discussion Paper #1197, Northwestern University.
Atsushi Kajii and Stephen Morris: Payoff Continuity in Incomplete Information Games, Journal of Economic Theory 82 (1998), 267-276.
Dov Monderer and Dov Samet:Proximity of Incomplete Information in Games with Common Beliefs, Mathematics of Operations Research 21, 707-725.
Hyun Song Shin and Tim Williamson: How Much Common Belief is Necessary for a Convention? Games and Economic Behavior 13 (1996), 252-268.
Takashi Ui: Robust Equilibria of Potential Games (1998)
Stephen Morris: Potential Methods in Interaction Games (1999)
Franklin Allen, Stephen Morris and Andrew Postlewaite: Finite Bubbles with Short Sales Constraints and Asymmetric Information, Journal of Economic Theory 61 (1993), 206-229.
Stephen Morris, Andrew Postlewaite and Hyun Song Shin: Depth of Knowledge and the Effect of Higher Order Uncertainty, Economic Theory 6 (1995), 453-467.
Franklin Allen and Stephen Morris: Game Theory and Finance Applications, Cowles Foundation Discussion Paper #1195; forthcoming in Advances in Business Applications of Game Theory, edited by Chatterjee and Samuelson. Kluwer Academic Press (1999).
Stephen Morris: Contagion, Review of Economic Studies 67 (2000), 57-78.
Stephen Morris: Interaction Games: A Unified Analysis of Incomplete Information, Local Interaction and Random Matching, Santa Fe Institute Working Paper #97-08-072 E.
Christophe Chamley: Coordinating Regime Switches, Quaterly Journal of Economics 114 (1999), 817-868.
K. Burdzy, David Frankel and Ady Pauzner: Fast Equilibrium Selection by Rational Players Living in a Changing World, forthcoming in Econometrica.
David Frankel and Ady Pauzner: Resolving Indeterminacy in Dynamic Settings: The Role of Shocks, Quarterly Journal of Economics 115 (2000), 285-304.
David Frankel: Dynamic Equilibrium Selection: A General Uniqueness Result.
Amil Dasgupta: Social Learning with Payoff Complementarities, November 1999, Yale University.
Atsushi Kajii and Stephen Morris: Common p-Belief: the General Case, Games and Economic Behavior 18 (1997), 73-82.