Subgame-Perfect Equilibria in Stochastic Timing Games

We introduce a notion of subgames for stochastic timing games and the related notion of subgame-perfect equilibrium in possibly mixed strategies. While a good notion of subgame-perfect equilibrium for continuous-time games is not available in general, we argue that our model is the appropriate version for timing games. We show that the notion coincides with the usual one for discrete-time games. Many timing games in continuous time have only equilibria in mixed strategies -- in particular preemption games, which often occur in the strategic real option literature. We provide a sound foundation for some workhorse equilibria of that literature, which has been lacking as we show. We obtain a general constructive existence result for subgame-perfect equilibria in preemption games and illustrate our findings by several explicit applications.Comment: 27 pages, 1 figur

Is the Endangered Species Act Endangering Species?

We develop theory and present a suite of theoretically consistent empirical measures to explore the extent to which market intervention inadvertently alters resource allocation in a sequentialmove principal/agent game. We showcase our approach empirically by exploring the extent to which the U.S. Endangered Species Act has altered land development patterns. We report evidence indicating significant acceleration of development directly after each of several events deemed likely to raise fears among owners of habitat land. Our preferred estimate suggests an overall acceleration of land development by roughly one year. We also find from complementary hedonic regression models that habitat parcels declined in value when the habitat map was published, which is consistent with our estimates of the degree of preemption. These results have clear implications for policymakers, who continue to discuss alternative regulatory frameworks for species preservation. More generally, our modeling strategies can be widely applied -- from any particular economic environment that has a sequential-move nature to the narrower case of the political economy of regulation.

Truth and Regret in Online Scheduling

We consider a scheduling problem where a cloud service provider has multiple units of a resource available over time. Selfish clients submit jobs, each with an arrival time, deadline, length, and value. The service provider's goal is to implement a truthful online mechanism for scheduling jobs so as to maximize the social welfare of the schedule. Recent work shows that under a stochastic assumption on job arrivals, there is a single-parameter family of mechanisms that achieves near-optimal social welfare. We show that given any such family of near-optimal online mechanisms, there exists an online mechanism that in the worst case performs nearly as well as the best of the given mechanisms. Our mechanism is truthful whenever the mechanisms in the given family are truthful and prompt, and achieves optimal (within constant factors) regret. We model the problem of competing against a family of online scheduling mechanisms as one of learning from expert advice. A primary challenge is that any scheduling decisions we make affect not only the payoff at the current step, but also the resource availability and payoffs in future steps. Furthermore, switching from one algorithm (a.k.a. expert) to another in an online fashion is challenging both because it requires synchronization with the state of the latter algorithm as well as because it affects the incentive structure of the algorithms. We further show how to adapt our algorithm to a non-clairvoyant setting where job lengths are unknown until jobs are run to completion. Once again, in this setting, we obtain truthfulness along with asymptotically optimal regret (within poly-logarithmic factors)

Non-clairvoyant Scheduling Games

In a scheduling game, each player owns a job and chooses a machine to execute it. While the social cost is the maximal load over all machines (makespan), the cost (disutility) of each player is the completion time of its own job. In the game, players may follow selfish strategies to optimize their cost and therefore their behaviors do not necessarily lead the game to an equilibrium. Even in the case there is an equilibrium, its makespan might be much larger than the social optimum, and this inefficiency is measured by the price of anarchy -- the worst ratio between the makespan of an equilibrium and the optimum. Coordination mechanisms aim to reduce the price of anarchy by designing scheduling policies that specify how jobs assigned to a same machine are to be scheduled. Typically these policies define the schedule according to the processing times as announced by the jobs. One could wonder if there are policies that do not require this knowledge, and still provide a good price of anarchy. This would make the processing times be private information and avoid the problem of truthfulness. In this paper we study these so-called non-clairvoyant policies. In particular, we study the RANDOM policy that schedules the jobs in a random order without preemption, and the EQUI policy that schedules the jobs in parallel using time-multiplexing, assigning each job an equal fraction of CPU time

On the Timing of Vertical Relationships

We show that the standard analysis of vertical relationships transposes directly to investment timing. Thus, when a firm undertaking a project requires an outside supplier (e.g. an equipment manufacturer) to provide it with a discrete input, and if the supplier has market power, investment occurs too late from an industry standpoint. The distortion in firm decisions is characterized by a Lerner index, which is related to the parameters of a stochastic downstream demand. When feasible, vertical restraints restore efficiency. For instance, the upstream firm can induce entry at the correct investment threshold by selling a call option on the input. Otherwise, competition may substitute for vertical restraints. In particular, if two firms are engaged in a preemption race downstream, the upstream firm sells the input to the first investor at a discount that is chosen in such a way that the race to preempt exactly offsets the vertical externality, and this leader invests at the optimal market threshold.

Coordination and Cooperation in Investment Timing with Externalities ?

We characterize sequential (preemption) and simultaneous (coordination) equilibria, as well as joint-value maximizing (cooperation) solutions, in a model of investment timing allowing for externalities in both flow pro...ts and investment costs. For two ex-ante symmetric ...rms, either preemption or attrition occur depending on the size of the investment externality. Coordination is less likely with more discounting, as in a repeated game, and more likely with higher growth and volatility. Optimal cooperation involves either monopoly or duopoly investment, the latter being either symmetric or asymmetric. Finally, these characterizations are validated by applications to standard speci...cations of capacity accumulation and of R&D investment. In the former setup, coordination is likelier if installed capacities and lumpy investments are both large. With R&D input choices, if investment synergies are large, coordination and cooperation result in the same outcomes.Investment Timing; Real Options; Simultaneous Equilibrium; Joint-Value Maximization; Cooperation; Investment Externalities

Scheduling with Predictions and the Price of Misprediction

In many traditional job scheduling settings, it is assumed that one knows the time it will take for a job to complete service. In such cases, strategies such as shortest job first can be used to improve performance in terms of measures such as the average time a job waits in the system. We consider the setting where the service time is not known, but is predicted by for example a machine learning algorithm. Our main result is the derivation, under natural assumptions, of formulae for the performance of several strategies for queueing systems that use predictions for service times in order to schedule jobs. As part of our analysis, we suggest the framework of the "price of misprediction," which offers a measure of the cost of using predicted information