Bayesian Conjoint Choice Designs for Measuring Willingness to Pay

In this paper, we propose a new criterion for selecting efficient conjoint choice designs when the interest is in quantifying willingness to pay (WTP). The new criterion, which we call the WTP-optimality criterion, is based on the c-optimality criterion which is often used in the optimal experimental design literature. We use a simulation study to evaluate the designs generated using the WTP-optimality criterion and discuss the design of a real-life conjoint experiment from the literature. The results show that the new criterion leads to designs that yield more precise estimates of the WTP than Bayesian D-optimal conjoint choice designs, which are increasingly being seen as the state-of-the-art designs for conjoint choice studies, and to a substantial reduction in the occurrence of unrealistically high WTP estimates.     

A Model of Product Recalls with Asymmetric Information

This paper presents a model of involuntary product recall in which a firm has private information on its ability to produce safety. The ex post regulation of safety is motivated through a parametric imperfection in the product liability system which results in a firm under internalizing expected liability expenses. We treat the problem as one of mechanism design, where the regulator designs a recall procedure. This framework illuminates the point that recall is an interesting blend of ex ante and ex post regulation. We characterize a perfect recall procedure, contrast this with real world imperfect procedures, and study the interaction of the recall and the liability systems. Further, we analyze the interaction between optimal recall policy and product market structure.     

Harassment, corruption and tax policy: A comment on Marjit, Mukherjee and Mukherjee [Eur. J. Political Economy 16 (2000) 75–94]

Our comment on Marjit et al. [Marjit, S., Mukherjee, V., Mukherjee, A., 2000. Harassment, corruption and tax policy. European Journal of Political Economy 16, 75–94.] addresses the equilibrium concept used in the game with imperfect information, Section 4 of the original paper. The solution represented in the original paper does not constitute a perfect Bayesian Nash-equilibrium. We develop an alternative solution of the game given the assumptions made by Marjit et al. [Marjit, S., Mukherjee, V., Mukherjee, A., 2000. Harassment, corruption and tax policy. European Journal of Political Economy 16, 75–94.] and find that the results concerning the optimal amount of over-evaluation of income and the existence of a pooling or separating equilibrium are altered.     

Unobserved heterogeneity and equilibrium: an experimental study of Bayesian and adaptive learning in normal form games

We describe an experiment based on a simple two-person game designed so that different learning models make different predictions. Econometric analysis of the experimental data reveals clear heterogeneity in the subjects’ learning behavior. But the subjects follow only a few decision rules for basing their play on their information, and these rules have simple cognitive interpretations. There is a unique equilibrium in pure strategies, and many equilibria in mixed strategies. We find that the only equilibrium consistent with the data is one of the mixed strategy equilibria. This equilibrium is shown, surprisingly, to be consistent with Jordan's Bayesian model.     

How to identify trust and reciprocity

This paper uses a three-games (or triadic) design to identify trusting and reciprocating behavior. A large literature on single-game trust and reciprocity experiments is based on the implicit assumption that subjects do not have altruistic or inequality-averse other-regarding preferences. Such experimental designs test compound hypotheses that include the hypothesis that other-regarding preferences do not affect behavior. In contrast, experiments with the triadic design do discriminate between transfers resulting from trust or reciprocity and transfers resulting from other-regarding preferences that are not conditional on the behavior of others. Decomposing trust from altruism and reciprocity from altruism or inequality aversion is critical to obtaining empirical information that can guide the process of constructing models that can increase the empirical validity of game theory.     

Reciprocal relationships and mechanism design

We study an incomplete information game in which players can coordinate their actions by contracting among themselves. We model this relationship as a reciprocal contracting procedure where each player has the ability to make commitments contingent on the other players' commitments. We differ from the rest of the literature on reciprocal contracting by assuming that punishments cannot be enforced in the event that cooperation breaks down. We fully characterize the outcomes that can be supported as perfect Bayesian equilibrium outcomes in such an environment. We use our characterization to show that the set of supportable outcomes with reciprocal contracting is larger than the set of outcomes available in a centralized mechanism design environment in which the mechanism designer is constrained by his inability to enforce punishments against non‐participants. The difference stems from the players' ability in our contracting game to convey partial information about their types at the time they offer contracts. We discuss the implications of our analysis for modelling collusion between multiple agents interacting with the same principal.     

Do people make strategic commitments? Experimental evidence on strategic information avoidance

Game theory predicts that players make strategic commitments that may appear counter-intuitive. We conducted an experiment to see if people make a counter-intuitive but strategically optimal decision to avoid information. The experiment is based on a sequential Nash demand game in which a responding player can commit ahead of the game not to see what a proposing player demanded. Our data show that subjects do, but only after substantial time, learn to make the optimal strategic commitment. We find only weak evidence of physical timing effects.     

Implications of trust, fear, and reciprocity for modeling economic behavior

This paper reports three experiments with triadic or dyadic designs. The experiments include the moonlighting game in which first-mover actions can elicit positively or negatively reciprocal reactions from second movers. First movers can be motivated by trust in positive reciprocity or fear of negative reciprocity, in addition to unconditional other-regarding preferences. Second movers can be motivated by unconditional other-regarding preferences as well as positive or negative reciprocity. The experimental designs include control treatments that discriminate among actions with alternative motivations. Data from our three experiments and a fourth one are used to explore methodological questions, including the effects on behavioral hypothesis tests of within-subjects vs. across-subjects designs, single-blind vs. double-blind payoffs, random vs. dictator first-mover control treatments, and strategy responses vs. sequential play. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C70, C91, D63, D64     

An experimental study of information and mixed-strategy play in the three-person matching-pennies game

Summary. Recent experiments on mixed-strategy play in experimental games reject the hypothesis that subjects play a mixed strategy even when that strategy is the unique Nash equilibrium prediction. However, in a three-person matching-pennies game played with perfect monitoring and complete payoff information, we cannot reject the hypothesis that subjects play the mixed-strategy Nash equilibrium. Given this support for mixed-strategy play, we then consider two qualitatively different learning theories (sophisticated Bayesian and naive Bayesian) which predict that the amount of information given to subjects will determine whether they can learn to play the predicted mixed strategies. We reject the hypothesis that subjects play the symmetric mixed-strategy Nash equilibrium when they do not have complete payoff information. This finding suggests that players did not use sophisticated Bayesian learning to reach the mixed-strategy Nash equilibrium. Received: August 9, 1996; revised version: October 21, 1998     

Learning in experimental games

Summary Experimental games typically involve subjects playing the same game a number of times. In the absence of perfect rationality by all players, the subjects may use the behavior of their opponents in early rounds to learn about the extent of irrationality in the population they face. This makes the problem of finding the Bayes-Nash equilibrium of the experimental game much more complicated than finding the game-theoretic solution to the ideal game without irrationality. We propose and implement a computationally intensive algorithm for finding the equilibria of complicated games with irrationality via the minimization of an appropriate multi-variate function. We propose two hypotheses about how agents learn when playing experimental games. The first posits that they tend to learn about each opponent as they play it repeatedly, but do not learn about the population parameters through their observations of random opponents (myopic learning). The second posits that both types of learning take place (sequential learning). We introduce a computationally intensive sequential procedure to decide on the informational value of conducting additional experiments. With the help of that procedure, we decided after 12 experiments that our original model of irrationality was unsatisfactory for the purpose of discriminating between our two hypotheses. We changed our models, allowing for two different types of irrationality, reanalyzed the old data, and conducted 7 more experiments. The new model successfully discriminated between our two hypotheses about learning. After only 7 more experiments, our approximately optimal stopping rule led us to stop sampling and accept the model where both types of learning occur.We acknowledge the financial support from NSF grant #SES9011828 to the California Institute of Technology. We also acknowledge the able research assistance of Mark Fey, Lynell Jackson and Jeffrey Prisbrey in setting up the experiments, recruiting subjects and running the experiments. We acknowledge the help of the Jet Propulsion Laboratory and its staff members for giving us access to their Cray XMP/18, and subsequently their Cray YMP2E/116.     

Conducting interactive experiments online

Online labor markets provide new opportunities for behavioral research, but conducting economic experiments online raises important methodological challenges. This particularly holds for interactive designs. In this paper, we provide a methodological discussion of the similarities and differences between interactive experiments conducted in the laboratory and online. To this end, we conduct a repeated public goods experiment with and without punishment using samples from the laboratory and the online platform Amazon Mechanical Turk. We chose to replicate this experiment because it is long and logistically complex. It therefore provides a good case study for discussing the methodological and practical challenges of online interactive experimentation. We find that basic behavioral patterns of cooperation and punishment in the laboratory are replicable online. The most important challenge of online interactive experiments is participant dropout. We discuss measures for reducing dropout and show that, for our case study, dropouts are exogenous to the experiment. We conclude that data quality for interactive experiments via the Internet is adequate and reliable, making online interactive experimentation a potentially valuable complement to laboratory studies.     

An experimental test of observational learning under imperfect information

Summary. Nearly all observational learning models assume that individuals can observe all the decisions that have previously been made. In reality, such perfect information is rarely available. To explore the difference between observational learning under perfect and imperfect information, this paper takes an experimental look at a situation in which individuals learn by observing the behavior of their immediate predecessors. Our experimental design uses the procedures of Çelen and Kariv [9] and is based on the theory of Çelen and Kariv [10]. We find that imitation is much less frequent when subjects have imperfect information, even less frequent than the theory predicts. Further, while we find strong evidence that under perfect information a form of generalized Bayesian behavior adequately explains behavior in the laboratory, under imperfect information behavior is not consistent even with this generalization of Bayesian behavior.Received: 29 January 2002, Revised: 12 May 2004, JEL Classification Numbers: C92, D8. Correspondence to: Boaçhan ÇelenWe completed most of this paper when we were both graduate students at New York University. This research was supported by the Center for Experimental Social Sciences (C.E.S.S.) and the C.V. Starr Center for Applied Economics at New York University. We are grateful to Andrew Schotter for his guidance and to an anonymous referee for his comments. We benefited from the expositional suggestions of William Baumol. We also acknowledge helpful discussions of Colin Camerer, Liran Einav, Xavier Gabaix, Douglas Gale, Charles Holt, David Laibson, and Matthew Rabin. We also benefited from suggestions by the participants of the 2002 International ESA Meeting and seminars at several universities.     

The tragedy of the commons revisited: The importance of group decision-making

We use a laboratory experiment to compare the way groups and individuals behave in an inter-temporal common pool dilemma. The experimental design distinguishes between a non-strategic problem where players (individuals or groups of three) make decisions without interaction and a strategic part where players harvest from a common pool. This allows us to correct for differences between individuals and groups in the quality of decisions when testing for differences in competitiveness. Group decisions are either made by majority rule or unanimity. The results show that groups are less myopic than individuals (i.e., they make qualitatively better decisions) but that they are more competitive than individuals when placed in a strategic setting. The net result for groups deciding by majority rule is that they make less efficient decisions in the strategic game than individuals do. We are able to show that this is caused by the median voter departing from her original preference in early periods with a shrinking pool. When groups have to make unanimous decisions they start playing the strategic game more efficiently then individuals do, but they rapidly become more competitive with repetition of the game.     

Positional learning with noise

We propose (and test experimentally) a model of observational learning in which players have social preferences. To this end, we design an experiment–based on a classic parlor game known as the Chinos Game–in which we vary (by way of an exogenous iid stochastic process) the probability of getting the prize in the event of a correct guess. By this design, we are able to estimate more efficiently players’ sensitivity to difference in payoffs (and how this sensitivity affects information decoding along the sequence). We also condition our estimates upon additional information on subjects’ socio-demographics, risk attitudes and cognitive reflection by way of a questionnaire that we collect at the end of each session.     

Equilibrium selection through incomplete information in coordination games: an experimental study

We perform an experiment on a pure coordination game with uncertainty about the payoffs. Our game is closely related to models that have been used in many macroeconomic and financial applications to solve problems of equilibrium indeterminacy. In our experiment, each subject receives a noisy signal about the true payoffs. This game (inspired by the “global” games of Carlsson and van Damme, Econometrica, 61, 989–1018, 1993) has a unique strategy profile that survives the iterative deletion of strictly dominated strategies (thus a unique Nash equilibrium). The equilibrium outcome coincides, on average, with the risk-dominant equilibrium outcome of the underlying coordination game. In the baseline game, the behavior of the subjects converges to the theoretical prediction after enough experience has been gained. The data (and the comments) suggest that this behavior can be explained by learning. To test this hypothesis, we use a different game with incomplete information, related to a complete information game where learning and prior experiments suggest a different behavior. Indeed, in the second treatment, the behavior did not converge to equilibrium within 50 periods in some of the sessions. We also run both games under complete information. The results are sufficiently similar between complete and incomplete information to suggest that risk-dominance is also an important part of the explanation.      

基于微观经济工程的我国流域水市场设计刍议

20世纪90年代以来,博弈论方法被微观经济学家(主要是博弈论学者)积极运用于制度设计,特别是市场设计。目前,实验检验制度的方法已应用于可交易的排污权与公共池塘资源领域。结合计算机手段,学者运用实验方法研究不同产业计算机支持市场的绩效。在以上研究基础上,J.J.Murphy等人发展了灵敏水市场技术。中国的流域市场是一个复杂的系统,其复杂性来自两个方面:(1)环境条件的复杂性;(2)相关人行为的复杂性。本文提出开发计算机支持的灵敏流域水市场,通过计算机技术、实验方法和博弈论的整合,开发SCAMW系统。     

An Experiment to Evaluate Bayesian Learning of Nash Equilibrium Play

We report on an experiment designed to evaluate the empirical implications of Jordan's model of Bayesian learning in games of incomplete information. A finite example is constructed in which the model generates unique predictions of subjects' choices in nearly all periods. When the “true” game defined by players' private information was one with a unique equilibrium in pure strategies, the experimental subjects' play converged to the equilibrium, as Jordan's theory predicts, even when the subjects had not attained complete information about one another. But when there were two pure strategy equilibria, the theory's predictions were not consistent with observed behavior. Journal of Economic Literature Classification numbers: D83, C72, C92.     

Commercial Policy Towards Multinational Corporations Under Imperfect Information*

This paper examines host country government (HCG) commercial policy towards imports resulting from intrafirm trade conducted by a multinational corporation (MNC). the effectiveness of the HCG's commercial policy is impaired by its limited information about the MNC's cost of production. the commercial policy consists of restrictions on intrafirm transactions. We construct and characterize the optimal commercial policy under imperfect information and find that under imperfect information the optimal policy entails a distorted transfer price and a lower level of intrafirm trade relative to the full information case. Welfare implications of commercial policy under imperfect information are also examined.     

Public choice and the development of modern laboratory experimental methods in economics and political science

The paper is an account of the development of laboratory experimental methods in the early 1970s as influenced by the fields of Public Choice and Social Choice. Just a few key experiments conducted during a period when no experimental markets research was taking place, provide a bridge with the subsequent, rapid, growth of experimental economics. A new focus on public goods and externalities, as opposed to private goods traditionally used in economics experiments, required new representations of the commodity space and preference inducement methods. The importance of voting and collective decision making processes dictated the testing of equilibrium concepts from political science and cooperative game theory as opposed to the competitive equilibrium and Nash equilibria found in economics. The existence of many theories from multiple disciplines required new experimental designs and experimental tests. The Public Choice and Social Choice emphasis on comparing the performance of different types of collective decision processes induced early experiments related to institutional design and testing.     

Belief in the opponentsʼ future rationality

For dynamic games we consider the idea that a player, at every stage of the game, will always believe that his opponents will choose rationally in the future. This is the basis for the concept of common belief in future rationality, which we formalize within an epistemic model. We present an iterative procedure, backward dominance, that proceeds by eliminating strategies from the game, based on strict dominance arguments. We show that the backward dominance procedure selects precisely those strategies that can rationally be chosen under common belief in future rationality if we would not impose (common belief in) Bayesian updating.