Sven Rady

Strategic Experimentation with Exponential Bandits

This paper studies a game of strategic experimentation with two-armed bandits whose risky arm might yield a payoff only after some exponentially distributed random time. Because of free-riding, there is an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies with posterior beliefs as the state variable. After characterizing the unique symmetric Markovian equilibrium of the game, which is in mixed strategies, we construct a variety of pure-strategy equilibria. There is no equilibrium where all players use simple cut-off strategies. Equilibria where players switch finitely often between the roles of experimenter and free-rider all lead to the same pattern of information acquisition; the efficiency of these equilibria depends on the way players share the burden of experimentation among them. In equilibria where players switch roles infinitely often, they can acquire an approximately efficient amount of information, but the rate at which it is acquired still remains inefficient; moreover, the expected payoff of an experimenter exhibits the novel feature that it rises as players become more pessimistic. Finally, over the range of beliefs where players use both arms a positive fraction of the time, the symmetric equilibrium is dominated by any asymmetric one in terms of aggregate payoffs.

Tenure choice and the riskiness of non-housing consumption

This paper analyzes a households choice of housing tenure within a dynamic utility maximization model that yields simple analytical results under uncertainty of income, housing prices and rents. Given a housing consumption plan, we show that a decrease in the covariance between a households earnings and housing rents increases the likelihood of ownership. A household who plans to remain in its home over a long period is more likely to own; a household who plans to remain in its home over a short period is more likely to rent. The higher the covariance between the user cost of a home and that of other properties a household is likely to consider in the future, the more likely the household is to own this home. These predictions of our model find support in recent empirical studies.

Housing Market Fluctuations in a Life-Cycle Economy with Credit Constraints

This paper presents a first step towards a new theory of housing market fluctuations. We develop a life-cycle model where agents face credit constraints and their housing consumption is restricted to a discrete set of possibilities. The market interaction of young credit constrained agents climbing the property ladder with old agents trading down, generates co-movements of aggregate house prices, volume of transactions and income, consistent with the patterns observed in the U.S. and the U.K. Under plausible assumptions, the model reproduces the slight lead of transaction volume over the other two series as documented in the data. Our theory asserts that the fluctuations in housing prices depend crucially on fluctuations in the current income of young households (the first-time buyers). Thus, it sheds light on why housing prices are more volatile than GDP, and why they exhibit some degree of predictability in a market where households optimize over the timing of their transactions.

Option Pricing in the Presence of Natural Boundaries and a Quadratic Diffusion Term

Abstract. This paper uses a probabilistic change-of-numeraire technique to compute closed-form prices of European options to exchange one asset against another when the relative price of the underlying assets follows a diffusion process with natural boundaries and a quadratic diffusion coefficient. The paper shows in particular how to interpret the option price formula in terms of exercise probabilities which are calculated under the martingale measures associated with two specific numeraire portfolios. An application to the pricing of bond options and certain interest rate derivatives illustrates the main results.

Strategic Experimentation with Private Payoffs

We consider a game of strategic experimentation in which players face identical discrete-time bandit problems with a safe and a risky arm. In any period, the risky arm yields either a success or a failure, and the first success reveals the risky arm to dominate the safe one. When payoffs are public information, the ensuing free-rider problem is so severe that equilibrium experimentation ceases at the same threshold belief at which a single agent would stop, even if players can coordinate their actions through mediated communication. When payoffs are private information and the success probability on the risky arm is not too high, however, the socially optimal symmetric experimentation profile can be supported as a perfect Bayesian equilibrium for sufficiently optimistic prior beliefs, even if players can only communicate via binary cheap-talk messages.

Strongly Symmetric Equilibria in Bandit Games

This paper studies strongly symmetric equilibria (SSE) in continuous-time games of strategic experimentation with Poisson bandits. SSE payoffs can be studied via two functional equations similar to the HJB equation used for Markov equilibria. This is valuable for three reasons. First, these equations retain the tractability of Markov equilibrium, while allowing for punishments and rewards: the best and worst equilibrium payoff are explicitly solved for. Second, they capture behavior of the discrete-time game: as the period length goes to zero in the discretized game, the SSE payoff set converges to their solution. Third, they encompass a large payoff set: there is no perfect Bayesian equilibrium in the discrete-time game with frequent interactions with higher asymptotic efficiency.