In this experiment of learning, subjects were asked to choose one of two weighted voting games repeatedly. The payoffs for subjects were determined by a latent stochastic payoffgenerating function. The vote apportionments and quotas of those games were hidden from them in windows on their computer screens. We mouse-tracked what information subjects viewed on the screens. After subjects had experienced a binary choice problem in rounds for learning something, we examined whether those subjects increased the number of choosing the answer which would give a higher expected payoff (subjects meaningfully learned the underlying structure of weighted voting) in a similar but different binary choice problem in the subsequent rounds. Our main results are as follows. (1) The information on subjects’ cumulative payoffs might promote meaningful learning, whereas the information on their own current payoffs did not, or even hindered it. (2) It would be plausible that even if subjects paid more attention to their cumulative payoff, they would fail in meaningful learning when they chose the runs of options randomly, unlike algorithms in machine learning.

It might be a promising idea to use the Shapley value and its variants as pricing schemes of information due to their tractability of variables that constitute the data and the traditional interpretation as a fair distribution of the total surplus generated in the market by the data. As a particular example of information trading, this paper studies asymptotic bargaining outcomes in licensing a patented technology of an external patent holder to firms that operate in general Cournot markets. Our main results are as follows. When the number of firms that operate in the Cournot markets is relatively small, the Aumann-Drèze-Shapley (ADS) value may provide at least as much payoff for the patent holder as a stable standard of behavior shared among players. However, the same result never holds when the number of firms becomes sufficiently large, and the von Neumann-Morgenstern stable sets distribute twice as much payoff to the patent holder as the ADS value.

It is necessary to extract some patterns of human behavior from events observed in subject experiments in order to choose particular parameters for computer experiments on trades of information. Many experimental sites are, however, faced with practical problems due to their small subject pools. In conducting a subject experiment at multiple sites for avoiding those problems, homogeneity of subjects’ behavior is important for integrating the data collected at separate sites. Ideally, preliminary test results on the homogeneity are needed in planning the experiment. This paper clarifies a condition under which subjects’ behavior in a bandit experiment with the context of weighted voting can be homogenized across different subject pools in five universities in Japan by covariate adjustment with their cognitive ability scores on Raven’s APM test. Among experimental sites located in different regions, we could not obtain homogeneity of subjects’ behavior by covariate adjustment with their cognitive ability scores in addition to their attribute information, although it was not difficult to obtain the homogeneity across the experimental sites located in the same region.

In a simple model of the market for transactions of data proposed by [9], this note examines the effects of budget constraints on the prices of data and the gains from trades of data produced with their constituent variables in a subject experiment. In the model, the prices of variables are exogenously set at the initial round, and then updated for the next round immediately according to the demand for the data traded in the current round. Data are traded freely among agents and the prices are determined through transactions among agents. Resale of data is permitted among agents. The initial prices of variables are computed assuming the results of sequential trades of data. Each subject was faced with budget constraints, but surplus budgets cannot be carried over to subsequent rounds. In the subject experiment, the prices of variables fluctuated, but the prices of data determined by the initial owners under budget constraints remained relatively stable without a drastic increase compared with the prices of data determined under no budget constraints. The efficiency rates in transactions made under budget constraints were not lower than those in transactions made under no budget constraints.

This note presents two remarks about the specifications of the subject experiment designed and conducted by [4] regarding the problem of assigning students to schools as a large-scale data processing problem. We compared the efficiency of assignments under two mechanisms the Boston mechanism (Bos) and the deferred acceptance mechanism (DA). First, we first conducted a subject experiment in which subjects were categorized into two groups according to their scores of the Raven Advanced Progressive Matrices (APM) test, which measures cognitive ability. Subjects needed to compute their priority orders for schools from a queue of numbers. Next, we input the behavioral data observed in the early rounds of the subject experiment to the subjects’ submission of their preferences for schools and generated assignments under the Bos and the DA in order to create a virtual situation where subjects believed that the priority orders were actually unchanged, although those orders had been changed. Our main observations are as follows. (1) We should control the subjects’ cognitive ability scores and the mixtures of subjects with those scores in the experimental sessions in order to obtain the same result as the one observed by [4]. (2) Subjects might not compute the priority orders of students for schools exactly. Future research should further examine the conditions necessary to reproduce the experimental results of [4], based on the remarks clarified in this note,

For multiple-item auctions with unitary demands, the approximate Demange-Gale-Sotomayor (DGS) algorithm has an easy-to-understand rule but it needs a considerably longer time to settle, as compared with the Vickrey-Clarke-Groves (VCG) mechanism. A possible way to make the time shorter is to raise asking prices in larger increments, but concerns about deterioration of allocative efficiency and the seller’s revenue arise when the increments are large. In a subject experiment, we observed under the approximate DGS algorithm that there was an appropriate increment in asking prices by which the seller’s revenue and allocative efficiency did not significantly differ from those in a smaller increment. The theoretical approximation boundaries of the winning prices were not necessarily satisfied because human subjects did not choose sincere bidding.

This note presents a simple model of pricing data and their constituent variables traded in two-sided markets, where resale of data is allowed. The prices of those variables are exogenously set at the initial round, and in each round those prices are updated for the next round immediately at the end of the round, based on the outcomes of data transactions. If traders behave in accordance with the backward induction, then the initial prices never move in any rounds. In the subject experiment, this property was not observed but the average prices of those variables were not far from the initial values. We also examined whether information provision of the gross profits the user and non-user receive from data transactions affects the social welfare measured by the amounts of producer surplus.

In a two-armed bandit experiment with the contextual information on weighted voting, we investigated whether subjects who had experienced a binary choice problem for many periods increased the number of choosing the answer which would give a higher expected payoff when they were faced with a similar but different binary choice problem in the subsequent periods (or meaningfully learned the correct answer). Receiving both cumulative payoff and current payoffs as the feedback information, subjects learned the correct answers of three binary choice problems we examined, but for any binary choice problem they did not meaningfully learn it from their experience in a similar but different one. Compared with the previous study where subjects received only current payoffs as the feedback information, the additional feedback information on cumulative payoff might induce subjects to learn the correct answers but would not promote their meaningful learning of the latent feature of the contextual information in this experiment.

Prime contractors often solicit estimates for part of their work from potential subcontractors who can perform that work on their behalf with lower costs, prior to submitting their own estimates in procurement auctions. In a simple model for capturing this aspect of procurement auctions, this note clarifies through a numerical study with experimental data an important factor for obtaining clearer results in the experimental sessions. It was shown that unclear results observed in the sessions conducted previously would be due to the presence of extreme patterns in the distributions of risk aversion rates among the participants. We need to control the extreme risk aversion rates of participants for designing the experiment for future research.