Academic Commons

Theses Doctoral

Optimization in Strategic Environments

Feigenbaum, Itai Izhak

This work considers the problem faced by a decision maker (planner) trying to optimize over incomplete data. The missing data is privately held by agents whose objectives are dierent from the planner's, and who can falsely report it in order to advance their objectives. The goal is to design optimization mechanisms (algorithms) that achieve "good" results when agents' reports follow a game-theoretic equilibrium. In the first part of this work, the goal is to design mechanisms that provide a small worst-case approximation ratio (guarantee a large fraction of the optimal value in all instances) at equilibrium. The emphasis is on strategyproof mechanisms|where truthfulness is a dominant strategy equilibrium|and on the approximation ratio at that equilibrium. Two problems are considered|variants of knapsack and facility location problems. In the knapsack problem, items are privately owned by agents, who can hide items or report fake ones; each agent's utility equals the total value of their own items included in the knapsack, while the planner wishes to choose the items that maximize the sum of utilities. In the facility location problem, agents have private linear single sinked/peaked preferences regarding the location of a facility on an interval, while the planner wishes to locate the facility in a way that maximizes one of several objectives. A variety of mechanisms and lower bounds are provided for these problems. The second part of this work explores the problem of reassigning students to schools. Students have privately known preferences over the schools. After an initial assignment is made, the students' preferences change, get reported again, and a reassignment must be obtained. The goal is to design a reassignment mechanism that incentivizes truthfulness, provides high student welfare, transfers relatively few students from their initial assignment, and respects student priorities at schools. The class of mechanisms considered is permuted lottery deferred acceptance (PLDA) mechanisms, which is a natural class of mechanisms based on permuting the lottery numbers students initially draw to decide the initial assignment. Both theoretical and experimental evidence is provided to support the use of a PLDA mechanism called reversed lottery deferred acceptance (RLDA). The evidence suggests that under some conditions, all PLDA mechanisms generate roughly equal welfare, and that RLDA minimizes transfers among PLDA mechanisms.

Files

  • thumnail for Feigenbaum_columbia_0054D_13645.pdf Feigenbaum_columbia_0054D_13645.pdf binary/octet-stream 732 KB Download File

More About This Work

Academic Units
Industrial Engineering and Operations Research
Thesis Advisors
Sethuraman, Jaychandran
Degree
Ph.D., Columbia University
Published Here
October 14, 2016
Academic Commons provides global access to research and scholarship produced at Columbia University, Barnard College, Teachers College, Union Theological Seminary and Jewish Theological Seminary. Academic Commons is managed by the Columbia University Libraries.