🤖 AI Summary
This paper addresses the robustness of information aggregation among partially informed traders in dynamic trading, extending Ostrovsky (2012) by introducing a periodic paid-signal acquisition mechanism to analyze how declining information acquisition costs affect market aggregation efficiency. Methodologically, it integrates a dynamic rational expectations model, Market Scoring Rule incentives, a Shannon entropy-based cost function, and Bayesian equilibrium analysis. The paper introduces the novel concept of “k-separability” and proves it is both necessary and sufficient for full information aggregation. It shows that as signal costs approach zero, almost all securities satisfy k-separability, enabling full equilibrium aggregation even before costs vanish. Furthermore, it establishes that “unique-state-payoff” securities achieve efficient aggregation with probability one and yield strictly higher precision than equally informative opinion polls—demonstrating a nonlinear precision leap. These results deepen understanding of cost-driven aggregation thresholds and structural conditions for efficient market learning.
📝 Abstract
This paper examines whether the ability to acquire costly signals during trading can make markets more efficient at aggregating information. This question becomes more relevant as the continuous improvements in information technology have created an abundance of available information, which is now cheaper than ever to acquire, analyze, and act upon. We use the dynamic trading model of [Ostrovsky, 2012] with infinitely many periods and payoffs given by the Market Scoring Rule (MSR) [Hanson, 2003, 2007]. We first characterize the class of securities which are always separable, irrespective of who trades and what is their information structure. This class is very small and uninformative. This means that information may not aggregate in 'most' markets. Does the availability of cheap information alleviate this problem? To study this question, we enhance the model by enabling traders to buy a costly signal structure in each period, before trading. We allow for a large class of information cost functions k, including the Shannon entropy. We define the class of k separable securities and show that they are necessary and sufficient for information aggregation, when the cost of information is k, thus generalizing [Ostrovsky, 2012]. As information acquisition costs decrease, the securities that eventually become k separable, and therefore aggregate information in all equilibria and for all information structures, have a very simple structure: they specify a different payoff at each state. This class of securities with unique values is generic. Hence, the main message of the paper is that the availability of cheap information makes 'most' markets aggregate information. If we can decrease the cost of information as much as we want, do we even need markets to aggregate information through prices? Each trader could buy the necessary signals and then bid very close to the true value. We argue that this intuition is incorrect because markets become even more important in an environment with information acquisition. As cost k decreases, a security switches discontinuously from non-separable to k separable, hence even a slight reduction can enable a market to aggregate information. This is in contrast to the average of the traders' opinions after receiving the information, or a poll, because its predictive accuracy improves smoothly as costs decrease. Hence, the availability of cheap information leverages the value of the markets, enabling them to aggregate information long before the cost goes to zero. Moreover, we show that a security is k separable if and only if the market is more accurate than a poll, for all priors. Finally, even with myopic traders, cheaper information may accelerate or decelerate information aggregation for all but Arrow-Debreu securities. A full version of this paper can be found at https://ssrn.com/abstract=4569284