When Does Learning in Games Generate Convergence to Nash Equilibria? The Role of Supermodularity in an Experimental Setting

This study clarifies the conditions under which learning in games produces convergence to Nash equilibria in practice. Previous work has identified theoretical conditions under which various stylized learning processes achieve convergence. One technical condition is supermodularity, which is closely related to the more familiar concept of strategic complementarities. We experimentally investigate the role of supermodularity in achieving convergence through learning. Using a game from the literature on solutions to externalities, we systematically vary a free parameter below, close to, at and beyond the threshold of supermodularity to assess its effects on convergence. We find that supermodular and ¡°near-supermodular¡± games converge significantly better than those far below the threshold. From a little below the threshold to the threshold, the improvement is statistically insignificant. Within the class of supermodular games, increasing the parameter far beyond the threshold does not significantly improve convergence. Simulation shows that while most experimental results persist in the long run, some become more pronounced.learning, supermodular games

Ambiguous Solicitation: Ambiguous Prescription

We conduct a two-phase laboratory experiment, separated by several weeks. In the first phase, we conduct urn games intended to measure ambiguity aversion on a representative population of undergraduate students. In the second phase, we invite the students back with four different solicitation treatments, varying in the ambiguity of information regarding the task and the payout of the laboratory experiment. We find that those who return do not differ from the overall pool with respect to their ambiguity version. However, no solicitation treatment generates a representative sample. The ambiguous task treatment drives away the ambiguity averse disproportionally, and the detailed task treatment draws in the ambiguity averse disproportionally.laboratory experimental methods, experimental economics, laboratory selection effects

Pricing and Bundling Electronic Information Goods: Field Evidence

Dramatic increases in the capabilities and decreases in the costs of computers and communication networks have fomented revolutionary thoughts in the scholarly publishing community. In one dimension, traditional pricing schemes and product packages are being modified or replaced. We designed and undertook a large-scale field experiment in pricing and bundling for electronic access to scholarly journals: PEAK. We provided Internet-based delivery of content from 1200 Elsevier Science journals to users at multiple campuses and commercial facilities. Our primary research objective was to generate rich empirical evidence on user behavior when faced with various bundling schemes and price structures. In this article we report initial results. We found that although there is a steep initial learning curve, decision-makers rapidly comprehended our innovative pricing schemes. We also found that our novel and flexible "generalized subscription" was successful at balancing paid usage with easy access to a larger body of content than was previously available to participating institutions. Finally, we found that both monetary and non-monetary user costs have a significant impact on the demand for electronic access.

User cost, usage and library purchasing of electronically-accessed journals

http://deepblue.lib.umich.edu/bitstream/2027.42/63447/3/gazzale-jmm-user-cost-peak-book.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/63447/2/gazzale-jmm-peak-usercost_files.ziphttp://deepblue.lib.umich.edu/bitstream/2027.42/63447/1/gazzale-jmm-peak-usercost.htm

Improving Learning Performance by Applying Economic Knowledge

Digital information economies require information goods producers to learn how to position themselves within a potentially vast product space. Further, the topography of this space is often nonstationary, due to the interactive dynamics of multiple producers changing their positions as they try to learn the distribution of consumer preferences and other features of the problem's economic structure. This presents a producer or its agent with a difficult learning problem: how to locate profitable niches in a very large space. In this paper, we present a model of an information goods duopoly and show that, under complete information, producers would prefer not to compete, instead acting as local monopolists and targeting separate niches in the consumer population. However, when producers have no information about the problem they are solving, it can be quite difficult for them to converge on this solution. We show how a modest amount of economic knowledge about the problem can make it much easier, either by reducing the search space, starting in a useful area of the space, or by introducing a gradient. These experiments support the hypothesis that a producer using some knowledge of a problem's (economic) structure can outperform a producer that is performing a naive, knowledge-free form of learning.http://deepblue.lib.umich.edu/bitstream/2027.42/50435/1/improving-amec03-lncs04.pd

Model Selection in an Information Economy: Choosing what to Learn

In an economy in which a producer must learn the preferences of a consumer population, it is faced with a classic decision problem: when to explore and when to exploit. If the producer has a limited number of chances to experiment, it must explicitly consider the cost of learning (in terms of foregone profit) against the value of the information acquired. Information goods add an additional dimension to this problem; due to their flexibility, they can be bundled and priced according to a number of different price schedules. An optimizing producer should consider the profit each price schedule can extract, as well as the difficulty of learning of this schedule. In this paper, we demonstrate the tradeoff between complexity and profitability for a number of common price schedules. We begin with a one-shot decision as to which schedule to learn. Schedules with moderate complexity are preferred in the short and medium term, as they are learned quickly, yet extract a significant fraction of the available profit. We then turn to the repeated version of this one-shot decision and show that moderate complexity schedules, in particular two-part tariff, perform well when the producer must adapt to nonstationarity in the consumer population. When a producer can dynamically change schedules as it learns, it can use an explicit decision-theoretic formulation to greedily select the schedule which appears to yield the greatest profit in the next period.http://deepblue.lib.umich.edu/bitstream/2027.42/50438/1/comp-intel.pd

Information Bundling in a Dynamic Environment

Markets for digital information goods provide the possibility of exploring new and more complex pricing schemes, due to information goods' flexibility and negligible marginal cost. In this paper we compare the dynamic performance of price schedules of varying complexity under two different specifications of consumer demand shifts.http://deepblue.lib.umich.edu/bitstream/2027.42/50442/1/sce_dynamic_bundling.pd

Endogenous Differentiation of Information Goods under Uncertainty

Information goods can be reconfigured at low cost. Therefore, firms can choose how to differentiate their products at a frequency comparable to price changes. However, doing so effectively is complicated by uncertainty about customer preferences, compounded by the fact that the search for a good product niche is carried out in competition with other searching firms. We study two firms that differentiate their information goods. The firms simultaneously compete in product configuration and price. We assume a non-uniform distribution of consumers:the largest number prefer a product located at a “sweet spot, ” but the rate at which the customer density falls off away from this product configuration is unknown. Our characterization reflects the standard tradeoff between exploitation (current profit) and exploration (learning to enhance future profit). In our model firms balance current profits from competing for a mass and a niche market, while learning about the profitability of these alternative strategies. We show that the amount of learning that firms will undertake depends on the convexity or concavity of the profit function in the rate of demand fall-off. In our model firms have an incentive to learn, and can use both price and product configuration in order to explore. We show that the ability to explore in product characteristic space leads to a previously unidentified consequence of learning:attenuation of competition. The incentive to learn induces firms to differentiate their products more than they would if the value of learning were ignored. This leads to decreased direct com-∗ MacKie-Mason gratefully acknowledges support from a