Two-way Greedy: Algorithms for Imperfect Rationality

The realization that selfish interests need to be accounted for in the design of algorithms has produced many contributions in computer science under the umbrella of algorithmic mechanism design. Novel algorithmic properties and paradigms have been identified and studied. Our work stems from the observation that selfishness is different from rationality; agents will attempt to strategize whenever they perceive it to be convenient according to their imperfect rationality. Recent work has focused on a particular notion of imperfect rationality, namely absence of contingent reasoning skills, and defined obvious strategyproofness (OSP) as a way to deal with the selfishness of these agents. Essentially, this definition states that to care for the incentives of these agents, we need not only pay attention about the relationship between input and output, but also about the way the algorithm is run. However, it is not clear what algorithmic approaches must be used for OSP. In this paper, we show that, for binary allocation problems, OSP is fully captured by a combination of two well-known algorithmic techniques: forward and reverse greedy. We call two-way greedy this algorithmic design paradigm. Our main technical contribution establishes the connection between OSP and two-way greedy. We build upon the recently introduced cycle monotonicity technique for OSP. By means of novel structural properties of cycles and queries of OSP mechanisms, we fully characterize these mechanisms in terms of extremal implementations. These are protocols that ask each agent to consistently separate one extreme of their domain at the current history from the rest. Through the connection with the greedy paradigm, we are able to import a host of approximation bounds to OSP and strengthen the strategic properties of this family of algorithms. Finally, we begin exploring the power of two-way greedy for set systems

Complexity Theory, Game Theory, and Economics: The Barbados Lectures

This document collects the lecture notes from my mini-course "Complexity Theory, Game Theory, and Economics," taught at the Bellairs Research Institute of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th McGill Invitational Workshop on Computational Complexity. The goal of this mini-course is twofold: (i) to explain how complexity theory has helped illuminate several barriers in economics and game theory; and (ii) to illustrate how game-theoretic questions have led to new and interesting complexity theory, including recent several breakthroughs. It consists of two five-lecture sequences: the Solar Lectures, focusing on the communication and computational complexity of computing equilibria; and the Lunar Lectures, focusing on applications of complexity theory in game theory and economics. No background in game theory is assumed.Comment: Revised v2 from December 2019 corrects some errors in and adds some recent citations to v1 Revised v3 corrects a few typos in v