An experiment on partnership protocols for bilateral trade with incomplete information

We study experimentally partnership protocols of the sort proposed by Kalai and Kalai (2010), for bilateral trade games with incomplete information. We utilize the familiar game analyzed by Chatterjee and Samuelson (1983) and Myerson and Sattherwaite (1983), with a buyer and seller with value and cost independently distributed uniformly on (0,100). The usual rules of the game are for the buyer and seller to submit price bids and asks, and for trade to occur if and only if the buyer's bid price exceeds the seller's ask price, in which case trade occurs at the average of the bid and the ask price. We compare the efficiency of trade and the nature of bid functions in this standard game to those in other versions of the game, including games in which cheap talk is allowed prior to trade (either before or after the traders know their own information, but without knowing each others' information), games with the formal mechanisms proposed by Kalai and Kalai available as an option for the traders to use, and games with both the mechanisms and cheap talk available. We consider both ex ante and interim mechanisms. That is, traders simultaneously choose whether to opt in to the mechanism either prior to knowing their own information, or after knowing their own information. In the last two versions of the game, cheap talk takes place prior to the opt-in decision. We find that the formal mechanisms significantly increase the efficiency of trade in both the ex ante and interim cases. Specifically, in the baseline game, traders captured 73% of the available surplus (compared to a theoretical maximum of 84% possible with optimal strategies). Efficiency rises to 87% and 82% for the ex ante and interim mechanisms, respectively, and further rises to 90% and 84% when cheap talk is also allowed with the mechanisms. When only cheap talk is allowed, traders capture 81% (for ex ante talk), but only 70% (for interim talk). On average, 55% of trading pairs opt in to mechanisms when they are available

A Deeper Look at Hyperbolic Discounting

We conduct an experiment to investigate the degree to which deviations from exponential discounting can be accounted for by the hypothesis of hyperbolic discounting. Subjects are asked to choose between an earlier or later payoff in a series of 40 choice questions. Each question consists of a pair of monetary amounts determined by com- pounding a given base amount at a constant rate per period. Two bases (8 and 20 dollars), three compounding rates (low, medium and high) and three delays (2, 4, and 6 weeks) are each used. There are also 2 initial periods (Today and 2 weeks) and there are two separate questionnaires, one with lower “realistic” compounding rates and the other with higher compounding rates, typical of those used in previous studies. We ana- lyze the detailed patterns of choice in 6 groups of 6 related questions each (in which the base and rate is fixed but the initial period and delay varies), documenting the frequency of patterns consistent with exponen- tial discounting and with hyperbolic discounting. We find that exponen- tial discounting is the clear modal choice pattern in virtually all cases. Hyperbolic discounting is never the modal pattern (except in the sense that constant discounting is a special case of hyperbolic discounting). We also estimate a linear probability model that takes account of individual heterogeneity. The estimates show substantial increases in the probabil- ity of choosing the later option when the compounding rate increases, as one would expect. There are small, sometimes significant, increases in this probability when the delay is increased or the initial period is in the future. Such behavior is consistent with hyperbolic discounting, but can account for only a small proportion of choices. Overall, deviations from exponential discounting appear to be due to error, or to other effects not accounted for by hyperbolic discounting. Principal among these is an increase in later choices when the base is larger.

Learning in Tournaments with Inter-Generational Advice

We study learning in a simulated tournament using an inter-generational framework. Here a group of subjects are recruited into the lab and play the stage game for 10 rounds. After his participation is over, each player is replaced by another player, his laboratory descendant, who then plays the game for another 10 rounds as a member of a fresh group of subjects. A particular player in generation t+1 can (1) see the history of choices by his generation t predecessor and (2) receive advice from that predecessor via free-form messages that generation t players leave for their generation t+1 successors. We find that the presence of advice makes a difference in that the experimental groups who get advice perform better – their decisions are closer to the Nash equilibrium – compared to a control group of subjects that plays the game with no recourse to such advice.Advice

An Experimental Test for Stability of the Transformation Function in Rank-Dependent Expected Utility Theory and Order-Dependent Present Value Theory

We propose and analyze a generalization of present value maximization, 'time-order dependent present value (TODPV),' for intertemporal income choice. The model is analagous to the rank dependent expected utility model (RDEU) for choice under risk. The main feature of interest in the model is the 'payment transformation function,' which operates on proportions of a fixed total of payments just as the probability weighting function in RDEU operates on probabilities. These models can accomodate many choice patterns, for both risky and intertemporal choice, so we conduct experiments in an attempt to (i) measure the structure of preferences over lotteries and intertemporal income streams and (ii) test for stability of the probability and payment transformation functions over different choice sets. The design is based on manipulations of the 'probability triangle' and the 'intertemporal choice triangle.' If, as in many previous studies of the RDEU model, a representative agent approach is taken, then the average preference structure in both the domain of risky choice and the domain of intertermporal choice can be characterized as 'homothetic' in the respective choice triangles. This implies a strictly concave transformation function, and is at odds witht the finding of an 'inverted S' shaped function that many researchers have suggested for the RDEU model. Individual analysis reveals considerable heterogeneity of preferences. A disaggregated analysis in which we classify subjects according to which transformation function is most consistent with their revealed choice behavior shows that a linear and a strictly concave transformation function are the most common for both risky choice and for intertemporal choice. Direct estimation of the transformation function is consistent with this classification. In particular, there is no evidence of an inverted S-shaped transformation function for choice under risk, contrary to several previous studies. The difference between our results and those of previous studies can be mainly attributed to the choice of functional forms used in estimating the transformation function, or to the limited space of lotteries upon which estimates have been based

Advice and behavior in intergenerational: Ultimatum games: An experimental approach

In the real world, when people play games, they often receive advice from those that have played it before them. Such advice can facilitate the creation of a convention of behavior. This paper studies the impact of advice on the behavior subjects who engage in a non-overlapping generational Ultimatum game where after a subject plays he is replaced by another subject to whom he can offer advice. Our results document the fact that allowing advice has a dramatic impact on the behavior of subjects. It diminishes the variance of offers made over time, lowers their mean, and causes Receivers to reject low offers with higher probability. In addition, by reading the advice offered we conclude that arguments of fairness are rarely used to justify the offers of Senders but are relied upon to justify rejections by Receivers

Information transparency, fairness and labor market efficiency

The paper studies the role of information transparency on fairness concerns, welfare and efficiency. When the firm's productivity and ultimately profits are revealed, wage offers induce relatively fair divisions of potential gains and workers respond with higher performance. Workers respond not only to wages but also to firms' intentions concerning fairness. Information transparency serves as a mechanism that promotes fairness and performance while the lack of transparency results in reduced earnings for workers and market inefficiency

Consistency and aggregation in individual choice under uncertainty

It is common in studies of individual choice behavior to report averages of the behavior under consideration. In the social sciences the mean is, indeed, often the quantity of interest, but at times focusing on the mean can be misleading. For example, it is well known in labor economics that failure to account for individual differences may lead to incorrect inference about the nature of hazard functions for unemployment duration. If all workers have constant hazard functions independent of duration, simple aggregation will nonetheless lead to the inference that the hazard function is state-dependent, with the hazard of leaving unemployment declining with duration of unemployment. Similarly, a recent study in psychology has shown that the learning curve a monotonically increasing function of response to a stimuli, is better understood as an average representation of individual response functions that are, in fact, more step-function-like. As such, the learning curve as commonly understood is a misleading representation of the behavior of any one individual