Computer Science and Game Theory: A Brief Survey

There has been a remarkable increase in work at the interface of computer science and game theory in the past decade. In this article I survey some of the main themes of work in the area, with a focus on the work in computer science. Given the length constraints, I make no attempt at being comprehensive, especially since other surveys are also available, and a comprehensive survey book will appear shortly.Comment: To appear; Palgrave Dictionary of Economic

A Sufficient Condition for Gaining Belief in Byzantine Fault-Tolerant Distributed Systems

Existing protocols for byzantine fault tolerant distributed systems usually rely on the correct agents' ability to detect faulty agents and/or to detect the occurrence of some event or action on some correct agent. In this paper, we provide sufficient conditions that allow an agent to infer the appropriate beliefs from its history, and a procedure that allows these conditions to be checked in finite time. Our results thus provide essential stepping stones for developing efficient protocols and proving them correct.Comment: In Proceedings TARK 2023, arXiv:2307.0400

A computer scientist looks at game theory

I consider issues in distributed computation that should be of relevance to game theory. In particular, I focus on (a) representing knowledge and uncertainty, (b) dealing with failures, and (c) specification of mechanisms.Comment: To appear, Games and Economic Behavior. JEL classification numbers: D80, D8

Nonrational Belief Paradoxes as Byzantine Failures

David Christensen and others argue that Dutch Strategies are more like peer disagreements than Dutch Books, and should not count against agents’ conformity to ideal rationality. I review these arguments, then show that Dutch Books, Dutch Strategies, and peer disagreements are only possible in the case of what computer scientists call Byzantine Failures—uncorrected Byzantine Faults which update arbitrary values. Yet such Byzantine Failures make agents equally vulnerable to all three kinds of epistemic inconsistencies, so there is no principled basis for claiming that only avoidance of true Dutch Books characterizes ideally rational agents. Agents without Byzantine Failures can be ideally rational in a very strong sense, but are not normative for humans. Bounded rationality in the presence of Byzantine Faults remains an unsolved problem

A note on knowledge-based programs and specifications

Knowledge-based program are programs with explicit tests for knowledge. They have been used successfully in a number of applications. Sanders has pointed out what seem to be a counterintuitive property of knowledge-based programs. Roughly speaking, they do not satisfy a certain monotonicity property, while standard programs (ones without tests for knowledge) do. It is shown that there are two ways of defining the monotonicity property, which agree for standard programs. Knowledge-based programs satisfy the first, but do not satisfy the second. It is further argued by example that the fact that they do not satisfy the second is actually a feature, not a problem. Moreover, once we allow the more general class of knowledge-based specifications, standard programs do not satisfy the monotonicity property either.Comment: To appear, Distributed Computin

Nonrational Belief Paradoxes as Byzantine Failures

David Christensen and others argue that Dutch Strategies are more like peer disagreements than Dutch Books, and should not count against agents’ conformity to ideal rationality. I review these arguments, then show that Dutch Books, Dutch Strategies, and peer disagreements are only possible in the case of what computer scientists call Byzantine Failures—uncorrected Byzantine Faults which update arbitrary values. Yet such Byzantine Failures make agents equally vulnerable to all three kinds of epistemic inconsistencies, so there is no principled basis for claiming that only avoidance of true Dutch Books characterizes ideally rational agents. Agents without Byzantine Failures can be ideally rational in a very strong sense, but are not normative for humans. Bounded rationality in the presence of Byzantine Faults remains an unsolved problem