William Zame - Academia.edu (original) (raw)

Papers by William Zame

This paper studies the design of online exchange systems that are operated based on the exchange ... more This paper studies the design of online exchange systems that are operated based on the exchange of tokens, a simple internal currency which provides indirect reciprocity among agents for cooperation. The emphasis is on how the protocol designer should choose a protocol - a supply of tokens and suggested strategies - to maximize service provision, taking into account that impatient agents will comply with the protocol if and only if it is in their interests to do so. The protocol is designed in such a way that it is robust to (small) errors in the designer’s knowledge of the system parameters. We prove that robust protocols have a simple pure threshold structure and there is a unique optimal supply of tokens that balances the token distribution in the population and achieves the optimal eciency. In the meanwhile, we also emphasize that choosing the wrong token supply can result in an enormous eciency loss. 1

Machine Learning has proved its ability to produce accurate models but the deployment of these mo... more Machine Learning has proved its ability to produce accurate models but the deployment of these models outside the machine learning community has been hindered by the difficulties of interpreting these models. This paper proposes an algorithm that produces a continuous global interpretation of any given continuous black-box function. Our algorithm employs a variation of projection pursuit in which the ridge functions are chosen to be Meijer G-functions, rather than the usual polynomial splines. Because Meijer G-functions are differentiable in their parameters, we can tune the parameters of the representation by gradient descent; as a consequence, our algorithm is efficient. Using five familiar data sets from the UCI repository and two familiar machine learning algorithms, we demonstrate that our algorithm produces global interpretations that are both highly accurate and parsimonious (involve a small number of terms). Our interpretations permit easy understanding of the relative impor...

Review of Financial …, 2010

... Peter Bossaerts, Paolo Ghirardato, Serena Guarnaschelli and William Zame This version: March... more ... Peter Bossaerts, Paolo Ghirardato, Serena Guarnaschelli and William Zame This version: March 2007 ... Most obviously, the studies here are an outgrowth of Bossaerts, Plott and Zame (2007), which studies environments with pure risk. ...

Game equilibrium models

THE ALGEBRAIC GEOMETRY OF GAMES AND THE TRACING PROCEDURE Stephen H. Schanuel Leo K. Simon Willia... more THE ALGEBRAIC GEOMETRY OF GAMES AND THE TRACING PROCEDURE Stephen H. Schanuel Leo K. Simon William R ... set of triples (u,v,w) € IR3 such that the polynomial ut2 + vt ♦ w has two ... first order formulas whenever we specialize or bound the variable у ; ie, if r is any ...

Econometrica, 2002

WE THANK ANDREAS BLUME for pointing out an error in a claim that we made in Example 1, and Eric B... more WE THANK ANDREAS BLUME for pointing out an error in a claim that we made in Example 1, and Eric Balder for pointing out that the proof of a lemma contains an assertion that is far from obvious and that two steps of the main proof contain typos and misstatements that make the steps difficult to follow. We offer corrections here. In Example 1 we claim that no equilibrium exists for any type-independent tiebreaking rule. Andreas Blume has pointed out the following counterexample to that claim. Consider a tie-breaking rule where all ties are broken in favor of bidder 1. 1 Bidder 2 bids 3.5 for all types. Bidder 1 bids 3.5 if his type is .5 or higher, and bids 3 5 − εt 1 when of type t 1 < 5. For small ε > 0, this is an equilibrium. The error in our proof of the nonexistence claim comes in the assertion that if there exists an equilibrium, then there exists one in weakly increasing strategies. To justify that assertion, we appealed to Proposition 1 of Maskin and Riley (2002), to which the above is also a counterexample. 2 A slight modification of our Example 1 resurrects the claim that there does not exist an equilibrium for any type-independent tie-breaking rule. Consider exactly the same setting except for the following: with probability 1 − ε there is one item available that is awarded to the high bidder at the high price; and with probability 0 < ε < 1/200 there are two items available, in which case the auctioneer randomly draws a number x from a uniform distribution on [0 6] and gives an item to each bidder whose bid exceeds x at a price of 0. 3 With this modification, whenever there exists an equilibrium there also exists one in weakly increasing strategies. This follows from the observation that if one type of a bidder weakly prefers a high bid to a low one, then a higher type of the bidder will strictly prefer the higher bid to the lower one, as now any increase in bids increases the probability of obtaining an object. The remaining proof shows that in any equilibrium the bottoms of the supports of the bidding strategies must be identical and must be bid by both bidders with positive probability. A contradiction is then reached by showing that for any choice of this lowest bid that results in a positive probability of ties, at least one bidder would deviate. The (nontrivial) details can be found in "Supplement to Corrigendum to 'Communication and Equilibrium in Discontinuous Games of Incomplete Information' (

Econometrica, 1999

One of the central features of classical models of competitive markets is the generic determinacy... more One of the central features of classical models of competitive markets is the generic determinacy of competitive equilibria. For smooth economies with a finite number of com-modities and a finite number of consumers, almost all initial endowments admit only a finite number of ...

Journal of Mathematical Economics, Dec 31, 1989

In this paper we argue that indeterminacy of equilibrium is a possibility inherent in economies w... more In this paper we argue that indeterminacy of equilibrium is a possibility inherent in economies with a double infinity of agents and goods, large-square economies. We develop a framework that is quite different from the overlapping generations one and that is amenable to analysis by means of differential calculus in linear spaces. The commodity space is a separable, infinite-dimensional Hilbert space, and each of a continuum of consumers is described by means of an individual excess demand function defined on an ...

Transactions of the American Mathematical Society, 1987

We prove that every compact Lie group can be realized as the (full) automorphism group of a stric... more We prove that every compact Lie group can be realized as the (full) automorphism group of a strictly pseudoconvex domain and as the (full) isometry group of a compact, connected, smooth Riemannian manifold.

Journal of the London Mathematical Society, 1976

A commutative Banach algebra with identity is said to be quasi-simple if 0 is the only element wh... more A commutative Banach algebra with identity is said to be quasi-simple if 0 is the only element which belongs to every power of every maximal ideal. A strong uniqueness result is established for the functional calculus in quasi-simple algebras with no non-trivial idempotents. Related results on uniqueness and continuity of homomorphisms are also obtained.

Cal Tech Working Paper, 2000

The prices and allocations in two sets of asset markets experiments are studied. One set is the c... more The prices and allocations in two sets of asset markets experiments are studied. One set is the certainty equivalent of the other. In both sets, markets evidently price risk correctly (expected excess returns are proportional to covariance with aggregate risk) even when allocations are wrong (individual allocations do not reflect the portfolio separation predicted by theory). We explain this price-allocation paradox by adding perturbation terms to standard general equilibrium theory. Using data from the certainty-equivalent experiments, we show that the extent to which portfolio separation obtains is a poor measure of the efficiency of the final allocations. Instead, most of the utility losses stem from the wrong mix of riskfree versus risky securities. Price changes in both sets of experiments strongly correlate with a fully optimal aggregate excess demand. We also discover that allocational efficiency improves dramatically in the certainty equivalent experiments, yet find mixed evidence of this in the uncertainty experiments. Because utility losses all but disappear in the certainty equivalent experiments, the lack of allocational improvements in the uncertainty experiments cannot be attributed to poor incentives. We do find strong evidence, however, that subjects' behavior reflect understanding of mean-variance efficiency: given the volatility of their portfolio, subjects manage to improve expected return when potential improvements emerge. This explains why we find that price changes are significantly related to a mean-variance optimal aggregate excess demand, and why pricing tends towards the predictions of the Capital Asset Pricing Model (CAPM).

Journal of economic theory, 1993

Page 1. Journal of Economic Theory 91, 280 291 (2000) NOTES, COMMENTS, AND LETTERS TO THE EDITOR ... more Page 1. Journal of Economic Theory 91, 280 291 (2000) NOTES, COMMENTS, AND LETTERS TO THE EDITOR On Monitoring and Collusion in Hierarchies1 Anke S. Kessler Department of Economics, University of Bonn, Adenauerallee ...

PloS one, 2018

Risk prediction is crucial in many areas of medical practice, such as cardiac transplantation, bu... more Risk prediction is crucial in many areas of medical practice, such as cardiac transplantation, but existing clinical risk-scoring methods have suboptimal performance. We develop a novel risk prediction algorithm and test its performance on the database of all patients who were registered for cardiac transplantation in the United States during 1985-2015. We develop a new, interpretable, methodology (ToPs: Trees of Predictors) built on the principle that specific predictive (survival) models should be used for specific clusters within the patient population. ToPs discovers these specific clusters and the specific predictive model that performs best for each cluster. In comparison with existing clinical risk scoring methods and state-of-the-art machine learning methods, our method provides significant improvements in survival predictions, both post- and pre-cardiac transplantation. For instance: in terms of 3-month survival post-transplantation, our method achieves AUC of 0.660; the be...

Mathematical Social Sciences

Bristol Economics Discussion Papers, 2014

Department of Economics Ucb, May 1, 1995

ABSTRACT This paper takes steps toward integrating firm theory in the spirit of Alchian and Demse... more ABSTRACT This paper takes steps toward integrating firm theory in the spirit of Alchian and Demsetz (1972) and Grossman and Hart (1986), contract theory in the spirit of Holmstrom (1979), and general equilibrium theory in the spirit of Arrow and Debreu (1954) and McKenzie (1959). In the model presented here, the set of firms that form and the contractual arrangements that appear, the assignments of agents to firms, the prices faced by firms for inputs and outputs, and the incentives to agents are all determined endogenously at equilibrium. Agents choose consumption—but they also choose which firms to join, which roles to occupy in those firms, and which actions to take in those roles. Agents interact anonymously with the (large) market, but strategically within the (small) firms they join. The model accommodates moral hazard, adverse selection, signaling, and insurance. Equilibria may be Pareto ranked.