Exploring optimization through hierarchies and ratio scales

This paper explores the concept of optimization by solely using the AHP and compares outcomes with those obtained in traditional optimization theory without and with constraints. The difference is essentially in the absence of the traditional black box involving complex manipulations in algebra or the calculus on an assumed linear or nonlinear mathematical structure. This paper is an exploratory attempt to use an individual's understanding together with a way to convert his judgments to ratios to deal with optimization. At first sight it may go contrary to the reader's (learned) intuition, but in the end he must face the question of whether the magic of traditional manipulations gives rise to better answers than one's actual and complete understanding in which one does not abdicate judgmental control of the solution, and why. This idea is ripe for deeper and more detailed exploration.     

Competitive equilibrium when preferences change over time

Summary. We show the existence of a competitive equilibrium in an economy with many consumers whose preferences may change over time. The demand correspondence of an individual consumer is determined by the set of subgame-perfect equilibrium outcomes in his intrapersonal game. For additively separable preferences with concave period utility functions that are unbounded above, this demand correspondence will satisfy the usual boundary conditions. Whenever consumers can recall their own mixed actions, this correspondence is convex-valued. This ensures the existence of a symmetric competitive equilibrium.Received: 29 July 2004, Revised: 17 November 2004, JEL Classification Numbers: D51, D91, C73. Correspondence to: Thomas MariottiWe thank Michele Piccione for useful comments and suggestions. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.     

The rationality and efficacy of decisions under uncertainty and the value of an experiment

Summary A decision maker faces a known prior distribution over payoff relevant states. We compare the expected utility of this individual under two scenarios. In the first, the decision maker makes a choice without further information. In the second, the decision maker has access to an experiment before choosing an action. However, the decision maker does not know the true joint distribution over states and messages. The value of the experiment as measured by the difference in the two utility levels can be negative as well as positive. We give a condition which is necessary and sufficient for the experiment to be valuable in our sense, for any decision problem.An earlier version of this paper was circulated under the title Noisy Bayes Updating and the Value of Information. We have gained from the comments of Stephen Coate, John Geanakoplos, Larry Samuelson, Timothy Van Zandt and seminar participants at Harvard Business School, Princeton, Boston University, the international conference on game theory at Stony Brook 1992 and the Winter meeting of the Econometric Society at Anaheim 1993. The first author received support for this project from NSF grant #SES-9308515 and a University of Pennsylvania Research Foundation Grant.     

Time to default in the UK mortgage market

This paper employs duration analysis to investigate the timing of default in the UK mortgage market. Our analysis is performed on an ex ante basis, in that our explanatory variables are available to mortgage lenders when the loan is first made. We estimate both standard Weibull distributions and generalizations of the Weibull that permit non-monotonic hazard functions. The models fit the data well, suggesting that we have captured the major sources of variation in duration. We find that ‘cash flow’ variables, such as salary and interest rate paid, play the largest role. Surprisingly, loan-to-value ratios are either insignificant or influence default times in a counter-intuitive direction.     

Keynes' theory of money and his attack on the classical model

This paper centers on Keynes' theory of money and his attack on the classical model. Keynes criticized the self-correcting model of the British orthodoxy along two separate lines. In the first, in which Keynes' theory of money was crucial, he took the institutional variables as given and examined the functional relationships. Keynes' burden was to undermine what he termed the "classical dichotomy," where money was a veil, playing no role in determining output and employment. Two key features of the orthodox model were loanable funds and quantity theories, and Keynes' theory of money emerged from the rejection of these theories. The key to his attack on the classical dichotomy was the speculative demand for money, which he presented as an indirect, unstable function of the interest rate. Hence, Keynes linked money demand to the interest rate. The interest rate was thus determined by monetary variables rather than real factors, contrary to British orthodox opinion. Keynes then demonstrated that intended investment and saving need not be equal at a full employment equilibrium.A previous version of this paper was presented at the Fiftieth International Atlantic Economic Conference, October 15–18, 2000, Charleston, South Carolina. The authors are grateful to participants for their helpful suggestions. The authors are responsible for any remaining errors.     

Reputation and Perfection in Repeated Common Interest Games

We consider a wide class of repeated common interest games perturbed with one-sided incomplete information: one player (the informed player) might be a commitment type playing the Pareto dominant action. As discounting, which is assumed to be symmetric, and the prior probability of the commitment type go to zero, it is shown that the informed player can be held close to her minmax payoff even when perfection is imposed on the equilibrium.Journal of Economic LiteratureClassification Numbers: C73, D83.     

Social learning with private and common values

Summary. We consider an environment where individuals sequentially choose among several actions. The payoff to an individual depends on her action choice, the state of the world, and an idiosyncratic, privately observed preference shock. Under weak conditions, as the number of individuals increases, the sequence of choices always reveals the state of the world. This contrasts with the familiar result for pure common-value environments where the state is never learned, resulting in herds or informational cascades. The medium run dynamics to convergence can be very complex and non-monotone: posterior beliefs may be concentrated on a wrong state for a long time, shifting suddenly to the correct state.Received: 6 January 2005, Revised: 5 May 2005, JEL Classification Numbers: C72, D82.Jacob K. Goeree: Correspondence toFinancial support from the National Science Foundation NSF (SBR-0098400 and SES-0079301) and the Alfred P. Sloan Foundation is gratefully acknowledged. We thank Richard McKelvey posthumously for insights and conjectures about information aggregation that helped shape our thinking about the problem. We also acknowledge helpful comments from Kim Border, Tilman Börgers, Bogachen Celen, Luis Corchon, Matthew Jackson and seminar participants at University College London, the University of Arizona, Universitat Autonoma de Barcelona, the California Institute of Technology, the 2003 annual meeting of ESA in Pittsburgh, the 2003 Malaga Workshop on Social Choice and Welfare Economics, the 2003 SAET meetings in Rhodos, and the 2003 ESSET meetings in Gerzensee.