Correlated equilibria and local interactions

Summary This paper shows that Nash equilibria of a local-interaction game are equivalent to correlated equilibria of the underlying game.This work was done while George Mailath and Larry Samuelson were visiting the University of Bonn, whose hospitality is gratefully acknowledged. We thank Ken Binmore for helpful discussions. This is a revision of Section 2 of Mailath, Samuelson, and Shaked [6]. Financial support from the National Science Foundation and the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 303 at the University of Bonn, is gratefully acknowledged.     

Bounded rationality,neural network and folk theorem in repeated games with discounting

Summary The perfect folk theorem (Fudenberg and Maskin [1986]) need not rely on excessively complex strategies. We recover the perfect folk theorem for two person repeated games with discounting through neural networks (Hopfield [1982]) that have finitely many associative units. For any individually rational payoff vector, we need neural networks with at most 7 associative units, each of which can handle only elementary calculations such as maximum, minimum or threshold operation. The uniform upper bound of the complexity of equilibrium strategies differentiates this paer from Ben-Porath and Peleg [1987] in which we need to admit ever more complex strategies in order to expand the set of equilibrium outcomes.I would like to thank Hao Li and John Curran for excellent research assistance. Financial support from National Science Foundation (SES-9223483), Sloan Foundation and the Division of Social Sciences at the University of Chicago is gratefully acknowledged.     

Type interaction models and the rule of six

In this paper, I describe and analyze a class of type interaction models. In these models, an infinite population of agents with discrete types interact in groups of fixed size and possibly change their types as a function of those interactions. I then derive conditions for these models to produce multiple equilibria. These conditions demonstrate a trade off between the number of types and the size of the interacting groups. For deterministic interaction rules, I derive the rule of six: the number of agent types plus the group size must be at least six in order to support multiple equilibria given a spanning assumption.Troy Tassier provided help with early versions of this model. Ken Arrow, Bob Axelrod, Larry Blume, Steven Durlauf, David Harris, John Holland, Lu Hong, Mercedes Pascual, Rick Riolo, and Carl Simon provided input on earlier drafts of this research. Financial support from the National Science Foundation, the James S. McDonnell Foundation and the John D. and Catherine T. MacArthur Foundation is gratefully acknowledged.     

Testable Implications of Pareto Efficiency and Individualrationality

This paper investigates the testable implications of Pareto efficiency and individual rationality on finite data sets in exchange economies with finitely many commodities and agents. Efficiency alone provides no restrictions other than a trivial “no waste”-condition. Efficiency together with individual rationality implies robust restrictionsI appreciate the comments of Don Brown, Truman Bewley and Charles Steinhorn. I also thank seminar participants at Yale, Zuerich and Mainz, as well as conference participants at the 12th European General Equilibrium Workshop in Bielefeld. The generous support of the Cowles Foundation is gratefully acknowledged. The paper also benefited greatly from the comments of an anonymous referee     

Production, interest, and saving in deterministic economies with additive endowments

Stationary equilibria are constructed for a series of nonstochastic production economies in which the decisions of producers, wage earners, shareholders, and savers modulate, via a “production function”, the endowment variables in an additive manner. The efficiency of each model is compared to that of a single agent who produces for personal consumption.Most of this work was carried out during the spring of 2004, while Sudderth was visiting the Cowles Foundation at Yale University. The work of Karatzas was supported by the National Science Foundation under grant NSF-DMS-06-01774, and by the Institute for Mathematics and Its Applications (IMA) which made possible a visit to the University of Minnesota during a week in May 2004. The support of these foundations is gratefully acknowledged.     

Group contest success functions

This paper extends the axiomatic characterization of contest success functions of Skaperdas (Econ Theory 7:283–290, 1996) and Clark and Riis (Econ Theory 11:201–204, 1998) to contests between groups. Comments by Dan Kovenock significantly improved the paper and are gratefully acknowledged. I would also like to thank Pavlo Blavatskyy, Aron Kiss, Kai Konrad, Florian Morath, Dana Sisak, participants of the SFB/TR 15 meeting in Gummersbach 2004, the 2004 meeting of the Verein für Socialpolitik in Dresden, and two anonymous referees. Any errors are mine. Financial support from the Deutsche Forschungsgemeinschaft through SFB/TR 15 is gratefully acknowledged.     

Reputation with observed actions

Summary A single long-run player plays a fixed stage game (simultaneous orsequential move) against an infinite sequence of short-run opponents that play only once but can observe all past realized actions. Assuming that the probability distributions over types of long and short-run players have full support, we show that the long-run player can always establish a reputation for theStackelberg strategy and is therefore guaranteed almost his Stackelberg payoff in all Nash equilibria of the repeated game.The financial support of the National Science Foundation, Grant SES 90-7999, and of Consiglio Nazionale delle Ricerche is gratefully acknowledged. I wish to thank David Levine, Wolfgang Pesendorfer and Seminar Participants at UCLA, Universidad Carlos III de Madrid and University of Naples for useful discussions and suggestions.     

Firm reputation with hidden information

Summary. An adverse selection model of firm reputation is developed in which short-lived clients purchase services from firms operated by overlapping generations of agents. A firm's only asset is its name, or reputation, and trade of names is not observed by clients. As a result, names are traded in all equilibria regardless of the economy's horizon The general equilibrium analysis links the value of a name to the market for services. This causes a non-monotonicity that precludes higher types from sorting themselves through the market for names, and leads to “sensible” dynamics: reputations, and name prices, increase after success and decrease after failure. Received: July 31, 2001; revised version: December 20, 2001 RID="*" ID="*" I thank Jon Levin, Eric Maskin and Drew Fudenberg for valuable discussions, and Heski Bar-Isaac for comments on an earlier draft. Financial support from the National Science Foundation (NSF grants SBR-9818981 and SES-0079876) is gratefully acknowledged. This paper replaces an older (and incomplete) working paper titled “Reputation with Hidden Information”.     

A remark on the measurability of large games

A game with a continuum of players is described by a function assigning payoff functions to players and satisfying some measurability properties. In this note we establish the equivalence between several measurability assumptions that have been made in the literature. I thank an anonymous referee for very helpful comments and John Huffstot for editorial assistance. Financial support from a Nova Fórum grant is gratefully acknowledged.     

Speculative trade, asset prices and investment levels

Summary. In this paper I consider a dynamically complete market model without intrinsic uncertainty. Agents' beliefs are different, but correct in the limit. Some agents are more patient than others. I show that infinitely often share prices are low and the economy stagnates. Also, infinitely often share prices are high and the economy grows. The changes from growth to stagnation and from stagnation to growth are not caused by exogenous shocks. They are caused by speculative trade among agents with different propensities to save and invest. Received: January 8, 2001; revised version: April 11, 2002 RID="*" ID="*" I thank an anonymous referee for helpful comments. I gratefully acknowledge financial support from the National Science Foundation.     

Renegotiation in agency contracts, menus vs. simple contracts

The literature on contracts has shown that renegotiation in agency relationships generates efficiency losses when the principal leads the renegotiation. We show that contractual incompleteness may reduce such efficiency loss. This provides an explanation to the widespread use of simple contracts. We further point at the limited liability of the agent as a source of inefficiency when he leads the renegotiation; this latter result tempers the irrelevancy of contractual incompleteness demonstrated earlier in the literature. I thank E. Del Rey and the referees for their helpful comments and suggestions. Financial support from the EU RTN grant HPRN-CT-2000-00064 is gratefully acknowledged.     

The demand commitment bargaining and snowballing cooperation

Summary A multi-person bargaining model based on sequential demands is studied for coalitional games with increasing returns to scale for cooperation. We show that for such games the (subgame perfect) equilibrium behavior leads to a payoff distribution which approaches the Shapley value as the money unit approaches 0. Subgame consistency and strategic equilibria are the main tools used in the analysis. The model is then applied to study a problem of public good consumption.I wish to thank Reinhard Selten, who introduced me with the topic of non-cooperative coalition bargaining, for many constructive discussions. Al Roth's warm hospitality during the academic year 1990–1991, as well as many useful remarks are also gratefully acknowledged. Helpful discussions with Dieter Balkenborg, Tatsuro Ichiishi, Richard Mclean, Benny Moldovanu, Daniel Seidmann Avner Shaked are gratefully acknowledged as well. Part of this research was also supported by the Deutscheforschungsgemeinschaft SFB 303 at the University of Bonn.     

Stability of jurisdiction structures under the equal share and median rules

We consider a finite society with of individuals distributed along the real line. The individuals form jurisdictions to consume public projects, equally share their costs and, in addition, bear a transportation cost to the location of the project. We examine a core and Nash notions of stable jurisdiction structures and show that in hedonic games both solution sets could be empty. We demonstrate that in a quasi-hedonic set-up there is a Nash stable partition, but, in general, there are no core stable partitions. We then examine a subclass of societies that admits the existence of both types of stable partitions. Financial support through grants R98-0631 from the Economic Education and Research Consortium, # NSh-1939.2003.6 School Support, Russian Foundation for Basic Research No. 04-02-17227, and the Russian Science Support Foundation is gratefully acknowledged.     

Dynamic and stochastic structures in tourism demand modeling

In this paper we consider a model for international tourism demand. The point of departure of the analysis is a utility function that is both dynamic and stochastic. In the model the stochastic component is interpreted as random changes in preferences for goods and services, while the dynamic component can be seen as either habit formation or as interdependent preferences. The resulting demand functions are estimated as a multivariate state space model, where the stochastic components enter the model as stochastic seasonal and trend components. An application is constructed for different segments of the Swedish tourism market. The results indicate the importance of including both dynamic and stochastic components in the utility function, and the importance of using disaggregate data to enable investigation of each market segment.I am grateful to two anonymous referees for useful comments. Much of the research was done while I was a visiting scholar at University of California Berkeley. The hospitality of the RIPM division is gratefully acknowledged. The research was supported by grants from the Wallander Foundation.First version received: January 2003/Final version received: February 2004     

On the complexity of repeated principal agent games

Summary We examine an infinitely repeated principal agent game without discounting (Radner [1985]), in which the agent may engage in multiple projects. We focus on linear strategies that summarize each history into a linear function of public outcomes, and select an action according to a single threshold rule. We claim that linear strategies significantly simplify the computation needed to make strategic decisions following each history. Despite the simplicity of linear strategies, we can virtually recover the folk theorem. For any individually rational payoff vector in the interior of the set of feasible expected payoff vectors, there exists a pair of linear strategies that form a Nash equilibrium supporting the target payoff. The equilibrium strategies and the equilibrium payoff vectors form a globally stable solution (Smale [1980]).I would like to thank Andrew Atkeson and the anonymous referee for helpful comments. John Curran and Hao Li provided excellent research assistance. Financial support from the National Science Foundation, the Alfred P. Sloan Foundation and the Division of Social Sciences at the University of Chicago is gratefully acknowledged.     

On some topological properties of stable measures

Summary The paper shows that the set of stable probability measures and the set of Rational Beliefs relative to a given stationary measure are closed in the strong topology, but not closed in the topology of weak convergence. However, subsets of the set of stable probability measures which are characterized by uniformity of convergence of the empirical distribution are closed in the topology of weak convergence. It is demonstrated that such subsets exist. In particular, there is an increasing sequence of sets of SIDS measures who's union is the set of all SIDS measures generated by a particular system and such that each subset consists of stable measures. The uniformity requirement has a natural interpretation in terms of plausibility of Rational Beliefs.ncial support from The Carlsberg Foundation, The University of Copenhagen, and Danish Social Science Research Council is gratefully acknowledged. I would like to thank Trinidad Casasus, Mordecai Kurz, and Tiefeng Jiang for many useful suggestions for improving the paper, and Karl Vind for helpful discussions about parts of it.     

Fixed-prize tournaments versus first-price auctions in innovation contests

This paper analyzes a procurement setting with identical firms and stochastic innovations. In contrast to the previous literature, I show that a procurer who cannot charge entry fees may prefer a fixed-prize tournament to a first-price auction. The reason is that holding an auction may leave higher rents to firms when the innovation technology is subject to large random factors. I would like to thank Dominique Demougin and Carsten Helm for helpful comments and discussions. Financial support by the Deutsche Forschungsgemeinschaft through the SFB 649 “Economic Risk” is gratefully acknowledged.     

Auctioning incentive contracts: The common cost,independent types case

Laffont and Tirole (1987) analyzed the problem of a regulator that wants to select one ofn firms to carry out a single indivisible project when the firms have private and independent costs and have the possibility of an ex-post investment in (non-observable) effort to reduce the (observable) cost.This paper generalizes the analysis to a model of common costs, unknown at the bidding stage, while keeping the assumption of independent types. I show that the main characteristics of the private costs model are kept in a common cost framework. I provide two mechanisms that may be used to implement the optimal contract.This is a much revised version of a part of chapter one of my Ph.D. dissertation. I would like to thank Drew Fudenberg, Oliver Hart, and two anonymous referees for their comments. I am especially indebted to Jean Tirole, who suggested this problem to me. I have also benefited from presentations at MIT and the EARIE 93 Meeting. Financial support from INVOTAN (grant 3/88/PO) is gratefully acknowledged. Remaining errors are my own.     

OPEC behaviour and the price of petroleum

I thank Ernst Mohr and Horst Siebert for discussing earlier versions of the paper with me, and Susanne Krebs and Frank Schulz for carefully drawing the diagrams. Suggestions by three anonymous referees helped improve the paper. The usual disclaimer applies. Financial support by Deutsche Forschungsgemeinschaft (SFB 178) is gratefully acknowledged.     

On the convexity of the value function in Bayesian optimal control problems

Summary I study the question on the convexity of the value function and Blackwell (1951)'s Theorem and relate this to the uniqueness of optimal policies. The main results will conclude that strict convexity and a strict inequality in Blackwell's Theorem will hold if and only if from different priors different optimal actions may be chosen.Financial support from the C. V. Starr Center and the Research Challenge Fund at New York University is gratefully acknowledged. I thank Professor Tara Vishwanathan whose questioning resulted in this paper.