Fault Tolerant Implementation

Abstract

In this paper we investigate the implementation problem arising when some of the players are "faulty" in the sense that they fail to act optimally. The planner and the non-faulty players only know that there can be at most k faulty players in the population. However, they know neither the identity of the faulty players, their exact number nor how faulty players behave. We define a solution concept which requires a player to optimally respond to the non-faulty players regardless of the identity and actions of the faulty players. We introduce a notion of fault tolerant implementation, which unlike standard notions of full implementation, also requires robustness to deviations from the equilibrium. The main result of this paper establishes that under symmetric information any choice rule that satisfies two properties-kmonotonicity and no veto power-can be implemented by a strategic game form if there are at least three players and the number of faulty players is less than 1 2 n − 1. As an application of our result we present examples of simple mechanisms that implement the constrained Walrasian function and a choice rule for the efficient allocation of an indivisible good.

Model Checking Nash Equilibria in MAD Distributed Systems

“…Accordingly, in Sect. VII we give a definition of mechanism Nash equilibrium accounting for the presence of up to f Byzantine players (along the lines of [21]) and for agent tolerance to small (ε > 0) differences in rewards (along the classical lines of, e.g. [23], [26]).…”

“…[49], [45], [13]). Design methods for BAR protocols have been investigated in [1], [36], [15], [21]. We differ from such works since our focus here is on automatic verification of Nash equilibria for finite state BAR systems rather than on design principles for them.…”

“…Our notion of Nash equilibrium for a mechanism combines those in [23], [21]. Intuitively, a mechanism M is ε-f -Nash, if as long as the number of Byzantine agents is no more than f (e.g.…”

“…Intuitively, a mechanism M is ε-f -Nash, if as long as the number of Byzantine agents is no more than f (e.g. see [21]), no rational agent has an interest greater than ε (e.g. see [23], [26]) in deviating from the proposed protocol in M.…”

“…Furthermore, stretching Def. 4 by setting ε = 0, we see that 0-f -Nash is the f -Nash equilibrium defined in [21] whereas 0-0-Nash is the classical Nash equilibrium (e.g., see [26]). …”