Dávid Kopányi’s research while affiliated with University of Amsterdam and other places

Expectations of future returns are pivotal for investors’ trading decisions, and are therefore an important determinant of the evolution of actual returns. Evidence from individual choice experiments with exogenously given time series of returns suggests that subjects’ return forecasts are substantially affected by how they are elicited and by the format in which subjects receive information about past asset performance. In order to understand the impact of these effects found at the individual level on market dynamics, we consider a learning to forecast experiment where prices and returns are endogenously determined and depend directly upon subjects’ forecasts. We vary both the variable (prices or returns) subjects observe and the variable (prices or returns) they have to forecast, with the same underlying data generating process for each treatment. Although there is no significant effect of the presentation format of past information, we do find that markets are significantly more unstable when subjects have to forecast returns instead of prices. Our results therefore show that the elicitation format may exacerbate, or even create, bubbles and crashes in financial markets.

We conduct a learning to forecast asset pricing experiment that assumes that financial advisors and professional forecasters attract more investors when their price forecasts are more accurate. The competition between forecasters implies that the impact of their forecasts on realized market prices evolves endogenously. We investigate how these endogenous impacts affect price dispersion and mispricing relative to the fundamental price. Our results show that the effect of endogenous impacts depends on (i) the type of market dynamics (stable/unstable) and (ii) the sensitivity of impacts with respect to forecast accuracy (low/high). Compared to the baseline treatment, where impacts are constant and independent of forecast accuracy, price dispersion and mispricing is somewhat lower in stable markets when impacts are moderately sensitive to forecast accuracy. In contrast, impacts that are strongly sensitive to forecast accuracy can further destabilize unstable markets, amplifying price dispersion and mispricing.

The paper studies an oligopoly game, where firms can choose between price-taking and price-making strategies. On a mixed market price takers are always better off than price makers, though the profits of both types decline in the number of price takers. We investigate and confront two possibilities of firms’ decisions about their types: forward-looking equilibrium reasoning and backward-looking individual learning. We find that the Cournot outcome is the only equilibrium prediction and it is learnable if firms are sufficiently sensitive to profit differences. However, with a larger number of firms, a unilateral deviation from Cournot behavior becomes profitable. Under learning this incentive creates a space for permanent oscillations over different markets with a positive but low number of price takers.

In this paper we consider firms that learn about market conditions by estimating the demand function using past market data. We show that learning may lead to suboptimal outcomes even when the estimated demand function perfectly fits the observations used in the regression and firms thus perceive to have learned the demand function correctly. We consider the Salop model with three firms and two types of consumers that differ in their sensitivity to product differences. Firms do not know the demand structure and they apply least squares learning to learn the demand function. In each period, firms estimate a linear perceived demand function and they play the perceived best response to the previous-period price of the other firms. This learning rule can lead to three different outcomes: a self-sustaining equilibrium, the Nash equilibrium or an asymmetric learning-equilibrium. In this last equilibrium one firm underestimates the demand for low prices and it attracts consumers with high sensitivity only. This type of equilibrium has not been found in the literature on least squares learning before. Both the Nash equilibrium and the asymmetric learning-equilibrium are locally stable therefore the model has coexisting stable equilibria.

This paper stresses the importance of heterogeneity in learning. We consider a Bertrand oligopoly with firms using either least squares learning or gradient learning for determining the price. We demonstrate that convergence properties of the rules are strongly affected by heterogeneity. In particular, gradient learning may become unstable as the number of gradient learners increases. Endogenous choice between the learning rules may induce cyclical switching. Stable gradient learning gives higher average profit than least squares learning, making firms switch to gradient learning. This can destabilize gradient learning which, because of decreasing profits, makes firms switch back to least squares learning.

This paper stresses that the coexistence of different learning methods can have a substantial effect on the convergence properties of these methods. We consider a Bertrand oligopoly with differentiated goods in which firms either use least squares learning or gradient learning for determining the price for a given period. These methods are well-established in oligopoly models but, up till now, are used mainly in homogeneous setups. We illustrate that the stability of gradient learning depends on the distribution of learning methods over firms: as the number of gradient learners increases, the method may lose stability and become less profitable. We introduce competition between the learning methods and show that a cyclical switching between the methods may occur.