Browsing by Author "Sun, Peng"

We present two game theoretic models on resource allocation in epidemic control and waiting time competition in service management.

The first model considers the drug allocation problem when facing the outbreak of an international influenza pandemic. The drugs are for prophylactic use. Since drug stockpiles are presently scattered in different countries, the outbreak of an epidemic gives rise to a game in which each country must make decisions about how best to allocate its own stockpile in order to protect its population. We develop a two-period multivariate Reed-Frost model to represent the spread of the epidemic within and across countries at its onset. We show that for small probability of between-country infections, the underlying game is supermodular and that a unique Pareto optimal Nash equilibrium exists. Further, we identify sufficient conditions under which the optimal solution of a central planner constitutes a Pareto improvement over the decentralized equilibrium.

The second model investigates the impact of reference effect on firms' waiting

time competition. We consider two firms (modeled as M/M/1 queueing facilities)

announcing the expected waiting times to attract customers. Customers' joining

decisions depend not only on the announced waiting times, but also on the reference effect, as demonstrated by the psychology literature. Reference effect, modeled in the spirit of prospect theory, is a "kinked" function of the gap between customers' expectation and perception of the waiting time, where the expectation is formed by both firms'announcements. We prove the existence of a unique (Pareto optimal) Nash equilibrium in the presence of reference effect. We show that comparing to the no reference effect case, the equilibrium waiting times are shorter and firms tend to announce a same waiting time.

In this dissertation, we study settings where a principal repeatedly determines the allocation of a single resource to i) a single agent, ii) one of two agents, and iii) one of n agents without monetary transfers over an infinite horizon with discounting. In all settings, the value of each agent for the resource in each period is private and the value distribution is common knowledge. For these settings, we design dynamic mechanisms that induce agents to report their values truthfully in each period via promises/threats of future favorable/unfavorable allocations. We show that our mechanisms asymptotically achieve the first-best efficient allocation (the welfare-maximizing allocation as if values are public) as the discount factor increases. Our results provide sharp characterizations of

convergence rates to first best as a function of the discount factor.

In the single-agent setting, the principal incurs a positive cost from allocating the resource to the agent. We first consider the case in which the allocation cost is random in each period with a known distribution. Next, we extend the model such that the allocation cost follows one of two possible probability distributions. The principal and the agent share the same belief about the true cost distribution and update their beliefs in each period using Bayes’ rule. In both cases, we provide mechanisms whose convergence rates are optimal, i.e., no other mechanism can converge faster to first best. In the settings with two or more agents, we do not consider allocation cost. We study the two-agent case before extending it to n agents. For two agents, we prove that the convergence rate of our mechanism is optimal. For n agents, we provide the convergence rate of our mechanism as a function of n.

This dissertation studies dynamic tournaments and their economic and managerial implications from two different perspectives. The first half focuses on the optimal timing of information release when a tournament uses a feedback scheme, while the other half investigates the impact of the use of mercy rule in a dynamic tournament on the economic output and other system wide characteristics.

In Chapter 2, we study dynamic tournaments in which time is modeled explicitly, as opposed to with the abstract notion of ``periods.'' By doing so, we characterize the effects of the ex-ante-designated timing of an interim progress report. Whether or not a policy of reporting increases total expected effort does not depend on the release time of the report, however the magnitude of the effect does. We demonstrate that total expected effort is single-peaked or single-troughed in the report's release time depending on parameters, with the peak/tough located at a time strictly more than halfway through the tournament. However, a policy of releasing information always harms the expected utility of the tournament's participants. Implications for tournament design are discussed.

Chaper 3 explores dynamic tournaments in a continuous space and continuous

time framework, in which contestants can observe their opponents' progresses

in real time and have the opportunity to end the contest early when one's

lead over the other is larger than some pre-determined threshold (a.k.a a

mercy rule). We first show that the game has a unique equilibrium, then characterize

the equilibrium numerically, and investigate the impacts of mercy rules on

tournament design. By doing so, we find that there exists an optimal mercy

rule that induces the best economic output, even though players always prefer a

tournament without a mercy rule. Depending on the cost and noises

parameters, a non-monotonic mercy rule may perform better. We also consider

the scenario in which players prefer to end the game early because of

outside options and have the choice to drop out. Given an exogenous mercy

rule, this drop-out option endogenizes another boundary. And surprisingly,

the endogenous mercy rule is not always dominated by the exogenous rule in

terms of inducing efforts.

This dissertation studies the optimal control of two different dynamic systems with learning: (i) diagnostic service systems, and (ii) green incentive policy design. In both cases, analytical models have been developed to improve our understanding of the system, and managerial insights are gained on its optimal management.

We first consider a diagnostic service system in a queueing framework, where the service is in the form of sequential hypothesis testing. The agent should dynamically weigh the benefit of performing an additional test on the current task to improve the accuracy of her judgment against the incurred delay cost for the accumulated workload. We analyze the accuracy/congestion tradeoff in this setting and fully characterize the structure of the optimal policy. Further, we allow for admission control (dismissing tasks from the queue without processing) in the system, and derive its implications on the structure of the optimal policy and system's performance.

We then study Feed-in-Tariff (FIT) policies, which are incentive mechanisms by governments to promote renewable energy technologies. We focus on two key network externalities that govern the evolution of a new technology in the market over time: (i) technological learning, and (ii) social learning. By developing an intertemporal model that captures these dynamics, we investigate how lawmakers should leverage on such effects to make FIT policies more efficient. We contrast our findings against the current practice of FIT-implementing jurisdictions, and also determine how the FIT regimes should depend on specific technology and market characteristics.

We propose an approximation scheme for single-product periodic-review inventory systems with L-natural-convex structure. We lay out three well-studied inventory models, namely the lost-sales system, the perishable inventory system, and the joint inventory-pricing problem. We approximate the value functions for these models by the class of L-natural-convex quadratic functions, through the technique of linear programming approach to approximate dynamic programming. A series of heuristics are derived based on the quadratic approximation, and their performances are evaluated by comparison with existing heuristics. We present the numerical results and show that our heuristics outperform the benchmarks for majority of cases and scale well with long lead times. In this dissertation we also discuss the alternative strategies we have tried but with unsatisfactory result.

This dissertation studies the use of information design to reduce the spread of an infection. In particular, I investigate whether central planners (senders) with more information can leverage the information advantage to improve social welfare. In the first chapter, I analyze a single sender's best information revelation policy when individuals (receivers) have heterogeneous social activity levels and decide their binary protection levels, which further determine a transmission network over which the infection spreads. I establish that it is optimal to obfuscate information only for intermediate transmission rates and for small initial infection probabilities. In the second chapter, I further explore the use of information when there are multiple senders, each caring their own population. I characterize the population's equilibrium actions given any information and the equilibrium information disclosure policies between two senders. I establish that the two senders will disclose no information when they are either heavily economically concerned with high economic costs and a low prior belief about the disease, or health concerned with low economic costs. The senders will disclose partial information when one sender is heavily economically concerned with high economic costs and a high prior belief about the disease, while the other sender is either heavily economically concerned with high economic costs or health concerned with low economic costs. The senders will disclose full information when at least one sender is either concerned but not extremely concerned about the economy or health concerned with high economic costs.

This dissertation considers practical operational settings, in which a decision maker needs to either coordinate preferences or to align incentives among different parties. We formulate these issues into stochastic optimization problems and use a variety of techniques from the theories of applied probability, queueing and dynamic programming.

First, we study a stochastic matching problem. We consider matching over time with short and long-lived players who are very sensitive to mismatch, and propose a novel method to characterize the mismatch. In particular, players' preferences are uniformly distributed on a circle, so the mismatch between two players is characterized by the one-dimensional circular angle between them. This framework allows us to capture matching processes in applications ranging from ride sharing to job hunting. Our analytical framework relies on threshold matching policies, and is focused on a limiting regime where players demonstrate low tolerance towards mismatch. This framework yields closed-form optimal matching thresholds. If the matching process is controlled by a centralized social planner (e.g. an online matching platform), the matching threshold reflects the trade-off between matching rate and matching quality. The corresponding optimal matching threshold is smaller than myopic matching threshold, which helps building market thickness. We further compare the centralized system with decentralized systems, where players decide their matching partners. We find that matching controlled by either side of the market may achieve optimal social welfare.

Second, we consider a dynamic incentive management problem in which a principal induces effort from an agent to reduce the arrival rate of a Poisson process of adverse events. The effort is costly to the agent, and unobservable to the principal, unless the principal is monitoring the agent. Monitoring ensures effort but is costly to the principal. The optimal contract involves monetary payments and monitoring sessions that depend on past arrival times. We formulate the problem as a stochastic optimal control model and solve the problem analytically. The optimal schedules of payment and monitoring demonstrate different structures depending on model parameters. Overall, the optimal dynamic contracts are simple to describe, easy to compute and implement, and intuitive to explain.

This dissertation studies dynamic pricing in service systems where the system state is defined as the wait time. The first essay studies a single-server queue where customers arrive according to a Poisson process. The service provider announces the price rate and current system wait time to incoming customers, who decide whether to join the queue and determine their service duration. The objective is to maximize either the long-run average revenue or social welfare. The problem is formulated as a continuous-time control model, and we develop an innovative method to obtain the optimal control policy. The optimal dynamic pricing policy reveals the compensation effect, where the service provider lowers the price rate when the wait time exceeds a threshold, in addition to the usual congestion effect. A numerical study demonstrates the superiority of the revenue-maximizing pricing policy over static pricing policies, especially for low arrival rates and impatient customers. The extension to nonlinear pricing and heterogeneous customers yields similar policy insights, showcasing the value of considering customer characteristics in dynamic pricing models. The proposed model can be utilized to design dynamic pricing schemes for fast-charging stations.

The second essay addresses a mechanism design problem for a single-server queue with customers arriving according to a Poisson process and possessing private information about their wait time sensitivity. Following a direct mechanism, where the service provider announces the system wait time and offers a menu of options to each arriving customer. By choosing an option or opting out, customers aim to maximize their utility. The objective is to design a mechanism that maximizes the long-run average revenue. The optimal mechanism is wait-time dependent and admits customers with lower wait-time sensitivities. The model reveals strategic complementarity between admission decisions and service times which became the admission threshold, and offered service time decreases as the wait time increases. Comparisons with simpler heuristic mechanisms quantify the value of the optimal mechanism, showing significantly higher revenue generation, particularly for moderate service costs and arrival rates. Modifying service times becomes crucial when considering the different customer types and their interaction with wait time.

The third essay investigates a queueing system where the firm strategically determines the release time of each arriving request. We consider a first-come-first-serve single-server system, with customer requests arriving according to a Poisson process. The base model includes two types of customers: impatient and patient, characterized by their privately known service valuations and time sensitivities. The chapter explores the potential of strategically delaying the release of products to improve system performance. It reveals that such a delay occurs when the proportion of impatient customers is high and the system wait time is shorter than the threshold. Importantly, the optimal inflated release time does not vary with the system wait time, facilitating practical implementation. The extension to continuous-type customers confirms the tangible impact of strategic delay on revenue improvement, particularly when faced with uncertainty in the types of arriving requests.