Models of human behavior with applications to finance and pricing
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This thesis presents two classes of models of boundedly rational decision makers - one with application to finance and the other to pricing. It consists of three parts. The first part of the thesis investigates the impact of investors' boundedly rational forecasting on asset price bubbles. We present a class of models, called extrapolation-correction models, of boundedly rational investor behavior. That is, the investors in our model, quite reasonably, use data available to them, i.e. past price data, to form forecasts about future prices. We relate the model parameters to various behavioral aspects like investor memory, caution/confidence, and panic. We present the resulting dynamical system model of asset price bubbles and relate the behavior of the dynamical system to the parameters capturing investor forecasting behavior. We show that, depending on the behavioral parameters, the associated dynamical system can converge to the fundamental value, go into predictable price cycles, or go into unpredictable price cycles. In particular, we find that the greater the weight investors' forecasts put on the most recent observations, the greater the tendency for the asset prices to exhibit cycles, forming positive and negative bubbles. We also find that when forecasts are strongly affected by recent prices, the price process becomes chaotic and it becomes increasingly difficult to forecast future prices accurately. The second part of the thesis addresses the question: How do investors make their price forecasts? We present the design of an experiment where investors participate in a virtual asset market run over a computer network. During the course of the experiment, the participants report their price forecasts and enter buy and sell orders. The computer software determines the market clearing prices. Despite full disclosure of the assets' dividends and the fundamental value, the price trajectories in all three experimental sessions exhibited cycles. We calibrated various models, including rational expectations based models and the extrapolation-correction family of models presented in the first part of the thesis. The results indicate that rational expectations hypothesis does not provide an accurate model of forecast formation. Moreover, a simple one-parameter exponential smoothing model is much better at modeling forecast formation, with the extrapolation-correction models making the fit slightly better. The third part of the thesis explores a different aspect of customer rationality - that of customer impatience - and its effect on pricing of product versions. We consider a setting in which impatient customers are faced with frequent product introductions, for example, products like Apple iPhones. This raises the following questions regarding customers: Given the pricing strategy of the firm, what are the optimal buying behaviors of the customers? How does customer buying behavior change in relation to impatience? We consider two settings. In the first setting, the firm offers a trade-in price for existing customers and a higher full price for new customers. In the second setting, the firm offers the same prices to new and existing customers, however there is an introductory full price and a discounted price later in the product cycle. We model the customer's problem in these two settings and characterize their optimal actions as a function of the price parameters. We also analyze the bilevel program for the firm's pricing decisions. We see that in both settings considered there are certain well-defined regions in the price space wherein the firm's optimal decision lies. We also provide some numerical computations to study the behavior of the optimal prices as the cost per unit increases.