Dynamic price competition

We consider the model of price competition for a single buyer among many sellers in a dynamic environment. The surplus from each trade is allowed to depend on the path of previous purchases, and as a result, the model captures phenomena such as learning by doing and habit formation in consumption.We characterize Markovian equilibria for finite and infinite horizon versions of the model and show that the stationary infinite horizon version of the model possesses an efficient equilibrium where all the sellers receive an equilibrium payoff equal to their marginal contribution to the social welfare.     

Equilibria in large games with continuous procedures

We study existence of equilibria in large games where players use boundedly rational procedures. The equilibria are different from Nash equilibria; the difference persists even when players use procedures for which the observations gathered in any period are used to evaluate the payoff from different actions.     

Good news and bad news in two-armed bandits

This note provides a characterization of optimal policies in a class of two-armed bandits that allows for correlated arms. This characterization extends previously known results in the literature. In particular, it implies, under a mild continuity assumption, the optimality of cutoff belief strategies for this class of bandits. Cutoff beliefs are not unique, though.     

Act similarity in case-based decision theory

Summary Case-Based Decision Theory (CBDT) postulates that decision making under uncertainty is based on analogies to past cases. In its original version, it suggests that each of the available acts is ranked according to its own performance in similar decision problems encountered in the past.The purpose of this paper is to extend CBDT to deal with cases in which the evaluation of an act may also depend on past performance of different, but similar acts. To this end we provide a behavioral axiomatic definition of the similarity function over problem-act pairs (and not over problem pairs alone, as in the original model).We propose a model in which preferences are context-dependent. For each conceivable history of outcomes (to be thought of as the context of decision) there is a preference order over acts. If these context-dependent preference relations satisfy our consistency-across-contexts axioms, there is an essentially unique similarity function that represents these preferences via the (generalized) CBDT functional.We are grateful to Akihiko Matsui for the discussions that motivated this work. We also thank Enriqueta Aragones, Roger Myerson, Zvika Neeman, Ariel Rubinstein, Peyton Young, and an anonymous referee for their comments. Partial financial support from the Alfred Sloan Foundation is gratefully acknowledged.     

A subjective model of experimentation

Typically an experiment is defined by a set of possible signals and a likelihood function, and both are specified exogenously—they are taken to be observable by the analyst. This paper renders them subjective by showing that they may be derived from suitable choice behavior. This is done in the context of an axiomatic representation theorem for preference on a suitable domain.     

Trading mechanism selection with directed search when buyers are risk averse

We endogenize the trading mechanism selection in a model of directed search with risk averse buyers and show that the unique symmetric equilibrium entails all sellers using fixed price trading. Mechanisms that prescribe the sale price as a function of the realized demand (auctions, bargaining, discount pricing, etc.) expose buyers to the “price risk”, the uncertainty of not knowing how much to pay in advance. Fixed price trading eliminates the price risk, which is why risk averse customers accept paying more to shop at such stores.     

Conditional preferences and updating

This paper axiomatizes updating rules for preferences that are not necessarily in the expected utility class. Two sets of results are presented. The first is the axiomatization of conditional preferences. The second consists of the axiomatization of three updating rules: the traditional Bayes rule, the Dempster-Shafer rule, and the generalized Bayes rule. The last rule can be regarded as the updating rule for the multi-prior expected utility (Gilboa and Schmeidler, J. Math. Econom. 18 (1989) 141). Operationally, it is equivalent to updating each prior by the traditional Bayes rule.     

On the impossibility of achieving no regrets in repeated games

Regret-minimizing strategies for repeated games have been receiving increasing attention in the literature. These are simple adaptive behavior rules that lead to no regrets and, if followed by all players, exhibit nice convergence properties: the average play converges to correlated equilibrium, or even to Nash equilibrium in certain classes of games. However, the no-regret property relies on a strong assumption that each player treats her opponents as unresponsive and fully ignores the opponents’ possible reactions to her actions. We show that if at least one player is slightly responsive, it is impossible to achieve no regrets, and convergence results for regret minimization with responsive opponents are unknown.     

Robustness and ambiguity in continuous time

We use statistical detection theory in a continuous-time environment to provide a new perspective on calibrating a concern about robustness or an aversion to ambiguity. A decision maker repeatedly confronts uncertainty about state transition dynamics and a prior distribution over unobserved states or parameters. Two continuous-time formulations are counterparts of two discrete-time recursive specifications of Hansen and Sargent (2007) [16]. One formulation shares features of the smooth ambiguity model of Klibanoff et al. (2005) and (2009) [24] and [25]. Here our statistical detection calculations guide how to adjust contributions to entropy coming from hidden states as we take a continuous-time limit.     

Bayesian learning and convergence to Nash equilibria without common priors

Summary. Consider an infinitely repeated game where each player is characterized by a “type” which may be unknown to the other players in the game. Suppose further that each player's belief about others is independent of that player's type. Impose an absolute continuity condition on the ex ante beliefs of players (weaker than mutual absolute continuity). Then any limit point of beliefs of players about the future of the game conditional on the past lies in the set of Nash or Subjective equilibria. Our assumption does not require common priors so is weaker than Jordan (1991); however our conclusion is weaker, we obtain convergence to subjective and not necessarily Nash equilibria. Our model is a generalization of the Kalai and Lehrer (1993) model. Our assumption is weaker than theirs. However, our conclusion is also weaker, and shows that limit points of beliefs, and not actual play, are subjective equilibria. Received: March 3, 1995; revised version: February 17, 1997     

Search and Knightian uncertainty

Suppose that “uncertainty” about labor market conditions has increased. Does this change induce an unemployed worker to search longer, or shorter? This paper shows that the answer is drastically different depending on whether an increase in “uncertainty” is an increase in risk or that in true uncertainty in the sense of Frank Knight. We show in a general framework that, while an increase in risk (the mean-preserving spread of the wage distribution that the worker thinks she faces) increases the reservation wage, an increase in Knightian uncertainty (a decrease in her confidence about the wage distribution) reduces it.     

Market experience eliminates some anomalies—and creates new ones

We report two experiments which investigate whether experience of decision making in repeated markets purges behaviour of preference reversals. We investigate two behavioural mechanisms that may be shaping bids in repeated auctions: A tendency to adjust bids towards previously observed market prices, and a tendency to reduce bids following bad market outcomes. We find little support for the former but strong support for the latter. Also, whilst ‘just enough’ market exposure eliminates the typical preference reversal phenomenon, continued exposure fosters the mirror image anomaly. Therefore, although market experience shapes behaviour, in our experiments, it does not generally promote consistency with standard preference theory.     

The hot hand and the cold hand in professional golf

Previous studies have shown that people believe in the existence of the “hot hand” effect: recent good performances make one more confident and lead to more good performances. However, economists have found little evidence that such an effect is present. Motivated by models of momentum from psychology, this study examines hole-by-hole performances of four types of professional golfers, which is perhaps the ideal environment to evaluate whether such an effect exists. The results show that evidence consistent with the existence of hot hand and cold hand can be masked by looking only at overall mean impacts because the existence and magnitude of the effects can vary with the player's experience.     

Selecting equilibria in common agency games

We characterize equilibrium payoffs of a delegated common agency game in a public good context where principals use smooth contribution schedules. We prove that under complete information, payoff vectors of equilibria with truthful schedules coincide with the set of smooth equilibrium payoffs, including non-truthful schedules. We next consider whether the presence of arbitrarily small amounts of asymmetric information is enough to refine this payoff set. Providing that the extensions of the equilibrium schedules beyond the equilibrium point are flatter than truthful schedules, the set of equilibrium payoffs is strictly smaller than the set of smooth (equivalently, truthful) equilibrium payoffs. Interestingly, some forms of asymmetric information do not sufficiently constrain the slopes of the extensions and fail to refine the payoff set. In the case of a uniform distribution of types and arbitrary out-of-equilibrium contributions, the refinement has no bite. If, however, one restricts out-of-equilibrium behavior in a natural way, the refinement is effective. Alternatively, we may consider an exponential distribution with unbounded support (and hence no out-of-equilibrium choices) and we find that the refinement selects a unique equilibrium payoff vector equal to Lindahl prices.As a separate contribution, equilibria with forcing contracts are also considered both under complete and asymmetric information.     

Informational control and organizational design

This paper focuses on issues of allocating authority between an uninformed principal and an informed expert. We analyze the benefits of informational control—restricting the precision of the expert's information (without learning its content). In this case, the result of Dessein (2002) [8] that delegating decisions to a perfectly informed expert is better than communication when preferences between the expert and the principal are not too far apart is reversed. We demonstrate that these organizational forms—informational control and delegation—can be either complements or substitutes, depending on the principal's ability to affect the expert's discretion about the set of allowed policies.     

From private to public common agency

This note establishes that two propositions in the theory of private common agency by Laussel and Le Breton (J. Econ. Theory 100 (2001) 93) extend to a larger class of games, in which each principal's gross monetary payoff does not depend exclusively on the quantities she receives. A new result is offered to demonstrate that Proposition 4.3 is robust to the introduction of negative externalities. An existing result is reinterpreted to show that Proposition 4.2 is robust to the introduction of positive externalities.     

Preference for Flexibility and Dynamic Consistency

Dekel, Lipman, and Rustichini [3] characterize preferences over menus of lotteries that can be represented by the use of a unique subjective state space and a prior. We investigate what would be the appropriate version of Dynamic Consistency in such a setup. The condition we find, which we call Flexibility Consistency, is linked to a comparative theory of preference for flexibility. When the subjective state space is finite, we show that Flexibility Consistency is equivalent to a subjective version of Dynamic Consistency and that it implies that the decision maker is a subjective state space Bayesian updater. Later we characterize when a collection of signals can be interpreted as a partition of the subjective state space of the decision maker.     

Is diversity in Delphi panelist groups useful? Evidence from a French forecasting exercise on the future of nuclear energy

This paper further enhances the analytical power of Delphi methodology by identifying the advantages, disadvantages and challenges presented by increasing diversity among panel groups. Using Delphi survey data on the future of nuclear energy in France, we analyze the origins of the variety of judgments within and between two panels: one of experts and one of laypeople. We investigate the determinants of the stability of those opinions both in one given round and over several rounds of opinion-formation. We reach an apparently paradoxical conclusion: that non-expert judgment is less stable, but not necessarily less accurate, than that of experts, judgments on the part of experts sometimes being clouded by self-interest. Apart from highlighting some factors underlying the controversy over nuclear power, our paper calls for greater participatory democracy in Delphi panels, but also demonstrates the limits of such an extension.     

Dynamic variational preferences

We introduce and axiomatize dynamic variational preferences, the dynamic version of the variational preferences we axiomatized in [F. Maccheroni, M. Marinacci, A. Rustichini, Ambiguity aversion, robustness, and the variational representation of preferences, Mimeo, 2004], which generalize the multiple priors preferences of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141-153], and include the Multiplier Preferences inspired by robust control and first used in macroeconomics by Hansen and Sargent (see [L.P. Hansen, T.J. Sargent, Robust control and model uncertainty, Amer. Econ. Rev. 91 (2001) 60-66]), as well as the classic Mean Variance Preferences of Markovitz and Tobin. We provide a condition that makes dynamic variational preferences time consistent, and their representation recursive. This gives them the analytical tractability needed in macroeconomic and financial applications. A corollary of our results is that Multiplier Preferences are time consistent, but Mean Variance Preferences are not.     

Dynamic coordination with individual learning

We study coordination in dynamic global games with private learning. Players choose whether and when to invest irreversibly in a project whose success depends on its quality and the timing of investment. Players gradually learn about project quality. We identify conditions on temporal incentives under which, in sufficiently long games, players coordinate on investing whenever doing so is not dominated. Roughly speaking, this outcome occurs whenever players? payoffs are sufficiently tolerant of non-simultaneous coordination. We also identify conditions under which players coordinate on the risk-dominant action. We provide foundations for these results in terms of higher order beliefs.