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

Social Learning and Coordination Conventions in Inter-Generational Games: An Experimental Study

This is a paper on the creation and evolution of conventions of behavior in "inter-generational games". In these games a sequence of nonoverlapping "generations" of players play a stage game for a finite number of periods and are then replaced by other agents who continue the game in their role for an identical length of time. Players in generation t are allowed to see the history of the game played by all (or some subset) of the generations who played it before them and can communicate with their successors in generation t+1 and advise them on how they should behave. What we find is that word-of-mouth social learning (in the form of advice from laboratory "parents" to laboratory "children") can be a strong force in the creation of social conventions, far stronger than the type of learning subjects seem capable of doing simply by learning the lessons of history without the guidance o¥ered by such advice.

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.

Creating Culture in the Lab: Equilibrium Conventions in Inter-Generational Ultimatum Games

The Ultimatum Game and the experiments surrounding it, have presented economists with a puzzle that they have struggled to explain. But as Robert Aumann has pointed out, while there may be only one sub-game perfect equilibrium to the Ultimatum Game, there are an infinite number of Nash equilibria. All that is needed to maintain a non-sub-game perfect equilibrium is a set of Sender beliefs that the offer contemplated is the minimum that would be accepted and behavior on the part of the Receivers that confirms these beliefs. The only puzzle is how such a set of mutually consistent beliefs developed in the first place and how they are passed on from one generation of player to the next. Using an inter-generational game experimental setting, this paper investigates how "culture" serves as the selection mechanism which solves this puzzle. Culture is then simply a system of beliefs and self-confirming actions which support any one of these non-sub-game perfect Nash equilibria as the accepted solution to the game being played. The outcome is, as Robert Aumann has called it a "perfectly good" Nash equilibrium convention which is just not perfect.

Coupled rotor/airframe vibration analysis program manual manual. Volume 1: User's and programmer's instructions

user instruction and software descriptions for the base program of the coupled rotor/airframe vibration analysis are provided. The functional capabilities and procedures for running the program are provided. Interfaces with external programs are discussed. The procedure of synthesizing a dynamic system and the various solution methods are described. Input data and output results are presented. Detailed information is provided on the program structure. Sample test case results for five representative dynamic configurations are provided and discussed. System response are plotted to demonstrate the plots capabilities available. Instructions to install and execute SIMVIB on the CDC computer system are provided

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

The Challenge to Home Economists...

Home Economics majors are pulled in many directions. Some of us go into business, others into education. We work in research labs, advertising agencies and department stores. How can we tell whether we measure up to the standards of our profession