Lower Bounds on Implementing Robust and Resilient Mediators

We consider games that have (k,t)-robust equilibria when played with a mediator, where an equilibrium is (k,t)-robust if it tolerates deviations by coalitions of size up to k and deviations by up to $t$ players with unknown utilities. We prove lower bounds that match upper bounds on the ability to implement such mediators using cheap talk (that is, just allowing communication among the players). The bounds depend on (a) the relationship between k, t, and n, the total number of players in the system; (b) whether players know the exact utilities of other players; (c) whether there are broadcast channels or just point-to-point channels; (d) whether cryptography is available; and (e) whether the game has a $k+t)-punishment strategy; that is, a strategy that, if used by all but at most$k+t$ players, guarantees that every player gets a worse outcome than they do with the equilibrium strategy

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

Breaking the O(n^2) Bit Barrier: Scalable Byzantine agreement with an Adaptive Adversary

We describe an algorithm for Byzantine agreement that is scalable in the sense that each processor sends only $\tilde{O}(\sqrt{n})$ bits, where $n$ is the total number of processors. Our algorithm succeeds with high probability against an \emph{adaptive adversary}, which can take over processors at any time during the protocol, up to the point of taking over arbitrarily close to a 1/3 fraction. We assume synchronous communication but a \emph{rushing} adversary. Moreover, our algorithm works in the presence of flooding: processors controlled by the adversary can send out any number of messages. We assume the existence of private channels between all pairs of processors but make no other cryptographic assumptions. Finally, our algorithm has latency that is polylogarithmic in $n$. To the best of our knowledge, ours is the first algorithm to solve Byzantine agreement against an adaptive adversary, while requiring $o(n^{2})$ total bits of communication

The power of mediation in an extended El Farol game

A mediator implements a correlated equilibrium when it pro- poses a strategy to each player con dentially such that the mediator's proposal is the best interest for every player to follow. In this paper, we present a mediator that implements the best correlated equilibrium for an extended El Farol game with symmetric players. The extended El Farol game we consider incorporates both negative and positive network e ffects. We study the degree to which this type of mediator can decrease the overall social cost. In particular, we give an exact characterization of Mediation Value (MV) and Enforcement Value (EV) for this game. MV is the ratio of the minimum social cost over all Nash equilibria to the minimum social cost over all mediators of this type, and EV is the ratio of the minimum social cost over all mediators of this type to the optimal social cost. This sort of exact characterization is uncommon for games with both kinds of network e ffects. An interesting outcome of our results is that both the MV and EV values can be unbounded for our game

Implementation of Communication Equilibria by Correlated Cheap Talk: The Two-Player Case

We show that essentially every communication equilibrium of any finite Bayesian game with two players can be implemented as a strategic form correlated equilibrium of an extended game, in which before choosing actions as in the Bayesian game, the players engage in a pos-sibly infinitely long (but in equilibrium almost surely finite), direct, cheap talk.Bayesian game, cheap talk, communication equilibrium, correlated equilibrium, pre-play communication

Distributed computing building blocks for rational agents

Following [4] we extend and generalize the game-theoretic model of distributed computing, identifying different utility functions that encompass different potential preferences of players in a distributed system. A good distributed algorithm in the game-theoretic context is one that prohibits the agents (processors with interests) from de-viating from the protocol; any deviation would result in the agent losing, i.e., reducing its utility at the end of the algorithm. We dis-tinguish between different utility functions in the context of dis-tributed algorithms, e.g., utilities based on communication prefer-ence, solution preference, and output preference. Given these pref-erences we construct two basic building blocks for game theoretic distributed algorithms, a wake-up building block resilient to any preference and in particular to the communication preference (to which previous wake-up solutions were not resilient), and a knowl-edge sharing building block that is resilient to any and in partic-ular to solution and output preferences. Using the building blocks we present several new algorithms for consensus, and renaming as well as a modular presentation of the leader election algorithm of [4]

Communication, correlation and cheap-talk in games with public information

This paper studies extensive form games with perfect information and simultaneous moves, henceforth called games with public information. On this class, we prove that all communication equilibrium payoffs can be obtained without mediator by cheap-talk procedures. The result encompasses repeated games and stochastic games

Fair Leader Election for Rational Agents in Asynchronous Rings and Networks

We study a game theoretic model where a coalition of processors might collude to bias the outcome of the protocol, where we assume that the processors always prefer any legitimate outcome over a non-legitimate one. We show that the problems of Fair Leader Election and Fair Coin Toss are equivalent, and focus on Fair Leader Election. Our main focus is on a directed asynchronous ring of $n$ processors, where we investigate the protocol proposed by Abraham et al. \cite{abraham2013distributed} and studied in Afek et al. \cite{afek2014distributed}. We show that in general the protocol is resilient only to sub-linear size coalitions. Specifically, we show that $\Omega(\sqrt{n\log n})$ randomly located processors or $\Omega(\sqrt[3]{n})$ adversarially located processors can force any outcome. We complement this by showing that the protocol is resilient to any adversarial coalition of size $O(\sqrt[4]{n})$. We propose a modification to the protocol, and show that it is resilient to every coalition of size $\Theta(\sqrt{n})$, by exhibiting both an attack and a resilience result. For every $k \geq 1$, we define a family of graphs ${\mathcal{G}}_{k}$ that can be simulated by trees where each node in the tree simulates at most $k$ processors. We show that for every graph in ${\mathcal{G}}_{k}$, there is no fair leader election protocol that is resilient to coalitions of size $k$. Our result generalizes a previous result of Abraham et al. \cite{abraham2013distributed} that states that for every graph, there is no fair leader election protocol which is resilient to coalitions of size $\lceil \frac{n}{2} \rceil$.Comment: 48 pages, PODC 201