Design of Scheduling Algorithms Using Game Theoretic Ideas

Scheduling a set of jobs over a collection of machines to optimize a certain quality-of-service measure is one of the most important research topics in both computer science theory and practice. In this thesis, we design algorithms that optimize {\em flow-time} (or delay) of jobs for scheduling problems that arise in a wide range of applications. We consider the classical model of unrelated machine scheduling and resolve several long standing open problems; we introduce new models that capture the novel algorithmic challenges in scheduling jobs in data centers or large clusters; we study the effect of selfish behavior in distributed and decentralized environments; we design algorithms that strive to balance the energy consumption and performance.

The technically interesting aspect of our work is the surprising connections we establish between approximation and online algorithms, economics, game theory, and queuing theory. It is the interplay of ideas from these different areas that lies at the heart of most of the algorithms presented in this thesis.

The main contributions of the thesis can be placed in one of the following categories.

1. Classical Unrelated Machine Scheduling: We give the first polygorithmic approximation algorithms for minimizing the average flow-time and minimizing the maximum flow-time in the offline setting. In the online and non-clairvoyant setting, we design the first non-clairvoyant algorithm for minimizing the weighted flow-time in the resource augmentation model. Our work introduces iterated rounding technique for the offline flow-time optimization, and gives the first framework to analyze non-clairvoyant algorithms for unrelated machines.

2. Polytope Scheduling Problem: To capture the multidimensional nature of the scheduling problems that arise in practice, we introduce Polytope Scheduling Problem (\psp). The \psp problem generalizes almost all classical scheduling models, and also captures hitherto unstudied scheduling problems such as routing multi-commodity flows, routing multicast (video-on-demand) trees, and multi-dimensional resource allocation. We design several competitive algorithms for the \psp problem and its variants for the objectives of minimizing the flow-time and completion time. Our work establishes many interesting connections between scheduling and market equilibrium concepts, fairness and non-clairvoyant scheduling, and queuing theoretic notion of stability and resource augmentation analysis.

3. Energy Efficient Scheduling: We give the first non-clairvoyant algorithm for minimizing the total flow-time + energy in the online and resource augmentation model for the most general setting of unrelated machines.

4. Selfish Scheduling: We study the effect of selfish behavior in scheduling and routing problems. We define a fairness index for scheduling policies called {\em bounded stretch}, and show that for the objective of minimizing the average (weighted) completion time, policies with small stretch lead to equilibrium outcomes with small price of anarchy. Our work gives the first linear/ convex programming duality based framework to bound the price of anarchy for general equilibrium concepts such as coarse correlated equilibrium.

Game-Theoretically Allocating Resources to Catch Evaders and Payments to Stabilize Teams

Allocating resources optimally is a nontrivial task, especially when multiple

self-interested agents with conflicting goals are involved. This dissertation

uses techniques from game theory to study two classes of such problems:

allocating resources to catch agents that attempt to evade them, and allocating

payments to agents in a team in order to stabilize it. Besides discussing what

allocations are optimal from various game-theoretic perspectives, we also study

how to efficiently compute them, and if no such algorithms are found, what

computational hardness results can be proved.

The first class of problems is inspired by real-world applications such as the

TOEFL iBT test, course final exams, driver's license tests, and airport security

patrols. We call them test games and security games. This dissertation first

studies test games separately, and then proposes a framework of Catcher-Evader

games (CE games) that generalizes both test games and security games. We show

that the optimal test strategy can be efficiently computed for scored test

games, but it is hard to compute for many binary test games. Optimal Stackelberg

strategies are hard to compute for CE games, but we give an empirically

efficient algorithm for computing their Nash equilibria. We also prove that the

Nash equilibria of a CE game are interchangeable.

The second class of problems involves how to split a reward that is collectively

obtained by a team. For example, how should a startup distribute its shares, and

what salary should an enterprise pay to its employees. Several stability-based

solution concepts in cooperative game theory, such as the core, the least core,

and the nucleolus, are well suited to this purpose when the goal is to avoid

coalitions of agents breaking off. We show that some of these solution concepts

can be justified as the most stable payments under noise. Moreover, by adjusting

the noise models (to be arguably more realistic), we obtain new solution

concepts including the partial nucleolus, the multiplicative least core, and the

multiplicative nucleolus. We then study the computational complexity of those

solution concepts under the constraint of superadditivity. Our result is based

on what we call Small-Issues-Large-Team games and it applies to popular

representation schemes such as MC-nets.

Reference groups and product line decisions: An experimental investigation of limited editions and product proliferation

Some luxury goods manufacturers offer limited editions of their products, whereas some others market multiple product lines. Researchers have found that reference groups shape consumer evaluations of these product categories. Yet little empirical research has examined how reference groups affect the product line decisions of firms. Indeed, in a field setting it is quite a challenge to isolate reference group effects from contextual effects and correlated effects. In this paper, we propose a parsimonious model that allows us to study how reference groups influence firm behavior and that lends itself to experimental analysis. With the aid of the model we investigate the behavior of consumers in a laboratory setting where we can focus on the reference group effects after controlling for the contextual and correlated effects. The experimental results show that in the presence of strong reference group effects, limited editions and multiple products can help improve firms' profits. Furthermore, the trends in the purchase decisions of our participants point to the possibility that they are capable of introspecting close to two steps of thinking at the outset of the game and then learning through reinforcement mechanisms. © 2010 INFORMS.

On the Regulation of Small Actors: Three Experimental Essays about Policies based on Voluntary Compliance and Decentralized Monitoring

Monitoring and enforcement are perhaps the biggest challenges in the design and implementation of environmental policies in developing countries where the actions of many small informal actors cause significant impacts on the ecosystem services and where the transaction costs for the state to regulate them could be enormous. This dissertation studies the potential of innovative institutions based on decentralized coordination and enforcement to induce better environmental outcomes. Such policies have in common that the state plays the role of providing the incentives for organization but the process of compliance happens through decentralized agreements, trust building, signaling and monitoring. I draw from the literatures in collective action, common-pool resources, game-theory and non-point source pollution to develop the instruments proposed here. To test the different conditions in which such policies could be implemented I designed two field-experiments that I conducted with small-scale gold miners in the Colombian Pacific and with users and providers of ecosystem services in the states of Veracruz, Quintana Roo and Yucatan in Mexico. This dissertation is organized in three essays.

The first essay, “Collective Incentives for Cleaner Small-Scale Gold Mining on the Frontier: Experimental Tests of Compliance with Group Incentives given Limited State Monitoring”, examines whether collective incentives, i.e. incentives provided to a group conditional on collective compliance, could “outsource” the required local monitoring, i.e. induce group interactions that extend the reach of the state that can observe only aggregate consequences in the context of small-scale gold mining. I employed a framed field-lab experiment in which the miners make decisions regarding mining intensity. The state sets a collective target for an environmental outcome, verifies compliance and provides a group reward for compliance which is split equally among members. Since the target set by the state transforms the situation into a coordination game, outcomes depend on expectations of what others will do. I conducted this experiment with 640 participants in a mining region of the Colombian Pacific and I examine different levels of policy severity and their ordering. The findings of the experiment suggest that such instruments can induce compliance but this regulation involves tradeoffs. For most severe targets – with rewards just above costs – raise gains if successful but can collapse rapidly and completely. In terms of group interactions, better outcomes are found when severity initially is lower suggesting learning.

The second essay, “Collective Compliance can be Efficient and Inequitable: Impacts of Leaders among Small-Scale Gold Miners in Colombia”, explores the channels through which communication help groups to coordinate in presence of collective incentives and whether the reached solutions are equitable or not. Also in the context of small-scale gold mining in the Colombian Pacific, I test the effect of communication in compliance with a collective environmental target. The results suggest that communication, as expected, helps to solve coordination challenges but still some groups reach agreements involving unequal outcomes. By examining the agreements that took place in each group, I observe that the main coordination mechanism was the presence of leaders that help other group members to clarify the situation. Interestingly, leaders not only helped groups to reach efficiency but also played a key role in equity by defining how the costs of compliance would be distributed among group members.

The third essay, “Creating Local PES Institutions and Increasing Impacts of PES in Mexico: A real-Time Watershed-Level Framed Field Experiment on Coordination and Conditionality”, considers the creation of a local payments for ecosystem services (PES) mechanism as an assurance game that requires the coordination between two groups of participants: upstream and downstream. Based on this assurance interaction, I explore the effect of allowing peer-sanctions on upstream behavior in the functioning of the mechanism. This field-lab experiment was implemented in three real cases of the Mexican Fondos Concurrentes (matching funds) program in the states of Veracruz, Quintana Roo and Yucatan, where 240 real users and 240 real providers of hydrological services were recruited and interacted with each other in real time. The experimental results suggest that initial trust-game behaviors align with participants’ perceptions and predicts baseline giving in assurance game. For upstream providers, i.e. those who get sanctioned, the threat and the use of sanctions increase contributions. Downstream users contribute less when offered the option to sanction – as if that option signal an uncooperative upstream – then the contributions rise in line with the complementarity in payments of the assurance game.