Ronen Gradwohl

Fault tolerance in large games

A Nash equilibrium is an optimal strategy for each player under the assumption that others play according to their respective Nash strategies. In the presence of irrational players or coalitions of colluding players, however, it provides no guarantees. Some recent literature has focused on measuring the potential damage caused by the presence of faulty behavior, as well as designing mechanisms that are resilient against such faults. In this paper we show that large games are naturally fault tolerant. We first quantify the ways in which two subclasses of large games -- λ-continuous games and anonymous games -- are resilient against Byzantine faults (i.e. irrational behavior), coalitions, and asynchronous play. We then show that general large games also have some non-trivial resilience against faults.

Random selection with an adversarial majority

We consider the problem of random selection, where p players follow a protocol to jointly select a random element of a universe of size n. However, some of the players may be adversarial and collude to force the output to lie in a small subset of the universe. We describe essentially the first protocols that solve this problem in the presence of a dishonest majority in the full-information model (where the adversary is computationally unbounded and all communication is via non-simultaneous broadcast). Our protocols are nearly optimal in several parameters, including the round complexity (as a function of n), the randomness complexity, the communication complexity, and the tradeoffs between the fraction of honest players, the probability that the output lies in a small subset of the universe, and the density of this subset.

Partial exposure in large games

In this work we introduce the notion of partial exposure, in which the players of a simultaneous-move Bayesian game are exposed to the realized types and chosen actions of a subset of the other players. We show that in any large simultaneous-move game, each player has very little regret even after being partially exposed to other players. If players are given the opportunity to be exposed to others at the expense of a small decrease in utility, players will decline this opportunity, and the original Nash equilibria of the game will survive.

Privacy in implementation

In most implementation frameworks agents care only about the outcome, and not at all about the way in which it was obtained. Additionally, typical mechanisms for full implementation involve the complete revelation of all private information to the planner. In this paper I consider the problem of full implementation with agents who may prefer to protect their privacy. I analyze the extent to which privacy-protecting mechanisms can be constructed under various assumptions about agents’ predilection for privacy and the permissible game forms.

Rationality in the full-information model

We study rationality in protocol design for the full-information model, a model characterized by computationally unbounded adversaries, no private communication, and no simultaneity within rounds. Assuming that players derive some utility from the outcomes of an interaction, we wish to design protocols that are faithful: following the protocol should be an optimal strategy for every player, for various definitions of “optimal” and under various assumptions about the behavior of others and the presence, size, and incentives of coalitions. We first focus on leader election for players who only care about whether or not they are elected. We seek protocols that are both faithful and resilient, and for some notions of faithfulness we provide protocols, whereas for others we prove impossibility results. We then proceed to random sampling, in which the aim is for the players to jointly sample from a set of m items with a distribution that is a function of players’ preferences over them. We construct protocols for m≥3 that are faithful and resilient when players are single-minded. We also show that there are no such protocols for 2 items or for complex preferences.

t-Wise independence with local dependencies

In this note we prove a large deviation bound on the sum of random variables with the following dependency structure: there is a dependency graph G with a bounded chromatic number, in which each vertex represents a random variable. Variables that are represented by neighboring vertices may be arbitrarily dependent, but collections of variables that form an independent set in G are t-wise independent.

Perception Games and Privacy

Players have privacy concerns that may affect their choice of actions in strategic settings. We use a variant of signaling games to model this effect and study its relation to pooling behavior, misrepresentation of information, and inefficiency.

Voting in the Limelight

When committees make decisions, voting rules are coupled with one of three disclosure rules: open voting, in which each committee members individual vote is revealed; anonymous voting, in which only an anonymized tally is publicized; and secret voting, in which only the outcome is disclosed. I focus on strategic voters who have a preference for strategic ambiguity, and show that the amount of disclosure may have a non-monotonic effect on both the accuracy of the decision and the welfare of the voters. In particular, anonymous voting can yield both lower accuracy and higher welfare than both open and secret voting.

On the error parameter of dispersers

Optimal dispersers have better dependence on the error than optimal extractors. In this paper we give explicit disperser constructions that beat the best possible extractors in some parameters. Our constructions are not strong, but we show that having such explicit strong constructions implies a solution to the Ramsey graph construction problem.

How to Buy Advice with Limited Instruments

A decision maker, whose payoff is influenced by an unknown stochastic process, seeks the advice of an advisor, who may be informed about the process. We establish that there exists a strategy of the decision maker that will yield him an almost first-best payoff in every period when interacting with an informed advisor. An important feature of this strategy is that it only requires a fixed budget - regardless of the realizations of the stochastic process and whether or not the advisor is actually informed about it, the total payoff to the decision maker will never fall below a fixed threshold. The strategy also has the property that per-period compensation to the advisor is independent of the present realization of the process, and depends solely on the expected value of the advice as reported by the advisor.