Breakdowns

We study a continuous-time game of strategic experimentation in which the players try to assess the failure rate of some new equipment or technology. Breakdowns occur at the jump times of a Poisson process whose unknown intensity is either high or low. In marked contrast to existing models, we find that the cooperative value function does not exhibit smooth pasting at the efficient cut-off belief. This finding extends to the boundaries between continuation and stopping regions in Markov perfect equilibria. We characterize the unique symmetric equilibrium, construct a class of asymmetric equilibria, and elucidate the impact of bad versus good Poisson news on equilibrium outcomes

Rethinking Jagiello Hungary 1490-1526

Extensive Hungarian-language summary and commentary by Laszlo Szabolcs Gulyas in Klio 2006/2 (University of Debrecen). Electronic version available at http://www.c3.hu/~klio/klio062/klio040.htm

Negatively Correlated Bandits

We analyze a two-player game of strategic experimentation with two-armed bandits. Each player has to decide in continuous time whether to use a safe arm with a known payoff or a risky arm whose likelihood of delivering payoffs is initially unknown. The quality of the risky arms is perfectly negatively correlated between players. In marked contrast to the case where both risky arms are of the same type, we find that learn- ing will be complete in any Markov perfect equilibrium if the stakes exceed a certain threshold, and that all equilibria are in cutoff strategies. For low stakes, the equilib- rium is unique, symmetric, and coincides with the planner's solution. For high stakes, the equilibrium is unique, symmetric, and tantamount to myopic behavior. For inter- mediate stakes, there is a continuum of equilibria.Strategic Experimentation; Two-Armed Bandit; Exponential Distribution; Poisson Process; Bayesian Learning; Markov Perfect Equilibrium

Strategic Experimentation with Poisson Bandits

We study a game of strategic experimentation with two-armed bandits where the risky arm distributes lump-sum payoffs according to a Poisson process. Its intensity is either high or low, and unknown to the players. We consider Markov perfect equilibria with beliefs as the state variable. As the belief process is piecewise deterministic, payoff functions solve differential-difference equations. There is no equilibrium where all players use cut-off strategies, and all equilibria exhibit an `encouragement effect' relative to the single-agent optimum. We construct asymmetric equilibria in which players have symmetric continuation values at sufficiently optimistic beliefs yet take turns playing the risky arm before all experimentation stops. Owing to the encouragement effect, these equilibria Pareto dominate the unique symmetric one for sufficiently frequent turns. Rewarding the last experimenter with a higher continuation value increases the range of beliefs where players experiment, but may reduce average payoffs at more optimistic beliefs. Some equilibria exhibit an `anticipation effect': as beliefs become more pessimistic, the continuation value of a single experimenter increases over some range because a lower belief means a shorter wait until another player takes over.Strategic Experimentation; Two-Armed Bandit; Poisson Process; Bayesian Learning; Piecewise Deterministic Process; Markov Perfect Equilibrium; Differential-Difference Equation

Experimentation in Two-Sided Markets

We study optimal experimentation by a monopolistic platform in a two-sided market framework. The platform provider faces uncertainty about the strength of the externality each side is exerting on the other. It maximizes the expected present value of its profit stream in a continuous-time infinite-horizon framework by setting participation fees or quantities on both sides. We show that a price-setting platform provider sets a fee lower than the myopically optimal level on at least one side of the market, and on both sides if the two externalities are of approximately equal strenght. If the externality that one side exerts is sufficiently weaker than the externality it experiences, the optimal fee on this side exceeds the myopically optimal level. We obtain analogous results for expected prives when the platform provider chooses quantities. While the optimal policy does not admin closed-form representations in general, we identify special cases in which the undiscounted limit of the model can be solved in closed form

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

Homeownership: Low Household Mobility, Volatile Housing Prices, High Income Dispersion

We develop a dynamic stochastic equilibrium model of two locations within a city where heterogeneous households make joint location and tenure mode decisions. To investigate the effect of homeownership on equilibrium prices and allocations, we compare the response of this model economy to a labor shock with that of a rental-only version. This comparison yields three results. First, homeownership enables more households to remain in the more desirable location at the expense of newcomers. Second, homeownership adds to the volatility of the housing market. Third, homeownership may amplify the dispersion of household income within a location. Homeownership raises distributional issues. The households who consume the most housing gain the most from the ability to own their home. Newcomers to the city are the main losers.

Heterogeneity within Communities: A Stochastic Model with Tenure Choice

Standard explanations for the observed income heterogeneity within communities rely on differences of preferences across households and heterogeneity of the housing stock. We propose a dynamic stochastic model of location choice where households differ according to income only, and homes are identical within locations. Households choose whether to own or rent their home motivated by concerns over housing expenditure risk. The model highlights how differences in the timing of moves generate income heterogeneity across homeowners within neighborhoods, in particular in cities that experience strong positive demand shocks. US Census data provides evidence in favor of the income mixing mechanism we identify. In communities that have experienced strong price growth, the heterogeneity of homeowners’ incomes is positively correlated with the heterogeneity of the times since they bought their homes. Homeowners who moved in more recently earn higher incomes than homeowners who bought earlier, more so in cities with strong housing price growth. These relationships do not hold for renters.

Homeownership

We develop a dynamic stochastic equilibrium model of two locations within a city where heterogeneous households make joint location and tenure mode decisions. To investigate the effect of homeownership on equilibrium prices and allocations, we compare the response of this model economy to a labor shock with that of a rental-only version. This comparison yields three results. First, homeownership enables more households to remain in the more desirable location at the expense of newcomers. Second, homeownership adds to the volatility of the housing market. Third, homeownership may amplify the dispersion of household income within a location. Homeownership raises distributional issues. The households who consume the most housing gain the most from the ability to own their home. Newcomers to the city are the main losers.

Housing Market Dynamics: On the Contribution of Income Shocks and Credit Constraints (Revised Version)

We propose a life-cycle model of the housing market with a property ladder and a credit constraint. We focus on equilibria which replicate the facts that credit constraints delay some households' first home purchase and force other households to buy a home smaller than they would like. The model helps us identify a powerful driver of the housing market: the ability of young households to afford the down payment on a starter home, and in particular their income. The model also highlights a channel whereby changes in income may yield housing price overshooting, with prices of trade-up homes displaying the most volatility, and a positive correlation between housing prices and transactions. This channel relies on the capital gains or losses on starter homes incurred by credit-constrained owners. We provide empirical support for our arguments with evidence from both the U.K. and the U.S.Housing Demand ; Income Fluctuations ; Overlapping Generations ; Collateral Constraint