Lower Bounds on Implementing Mediators in Asynchronous Systems with Rational and Malicious Agents

Abstract

Abraham, Dolev, Geffner, and Halpern [1] proved that, in asynchronous systems, a ( k , t )-robust equilibrium for n players and a trusted mediator can be implemented without the mediator as long as n > 4( k + t ), where an equilibrium is ( k , t )-robust if, roughly speaking, no coalition of t players can decrease the payoff of any of the other players, and no coalition of k players can increase their payoff by deviating. We prove that this bound is tight, in the sense that if n ≤ 4( k + t ) there exist ( k , t )-robust equilibria with a mediator that cannot be implemented by the players alone. Even though implementing ( k , t )-robust mediators seems closely related to implementing asynchronous multiparty ( k + t )-secure computation [6], to the best of our knowledge there is no known straightforward reduction from one problem to another. Nevertheless, we show that there is a non-trivial reduction from a slightly weaker notion of ( k + t )-secure computation, which we call ( k + t )-strict secure computation , to implementing ( k , t )-robust mediators. We prove the desired lower bound by showing that there are functions on n variables that cannot be ( k + t )-strictly securely computed if n ≤ 4( k + t ). This also provides a simple alternative proof for the well-known lower bound of 4 t + 1 on asynchronous secure computation in the presence of up to t malicious agents [4, 8, 10].

Reflections on the asymmetry of causation

“…16 I am reverting to the ordinary convention of not capitalizing 'macrostate' even though using it specifically in the remainder of the paper to refer to the thermodynamic coarse-graining. 17 The existence of emergent macroregularities robust under the kinds of noisy conditions we find out in the wild is already highly non-generic, but what happens to these laws along a thermodynamic gradient is what supports information-gathering and utilization with a long horizon. In denying that that the macroscopic coarsegraining has a special metaphysical status, I mean anything that requires ontological distinction not captured by these dynamical considerations.…”

“…But if one is searching in the assembled architecture of the world for a stratum that will support information-gathering and utilization, the pattern that emerges under the macroscopic coarse-graining will stand forth as special indeed. 17 Suppose that we were suddenly given eyes that could see the world in full microscopic detail. We can ask whether adding microscopic information would increase future macropredictability.…”

“…It is the interventionist pathways that are the target for analysis of the causal asymmetry. 3 On the comparison between the probability calculus and interventionist formalism see [16,17]. 4 See [18].…”

Mediated Cheap Talk Design

“…Ben-Porath [10] gave a way to simulate mediated communication using long cheap talk if players have a punishment strategy. This work was later generalized by Abraham et al [2,3,1], and Geffner and Halpern [16,15], who gave a way to simulate mediated communication even in the presence of coalitions up to a certain size. A direct consequence of these results is that, if we consider information transmission games with several senders (these games are sometimes referred to as information aggregation games [25,4]), the value of mediation is 1 with respect to any welfare function if the number of senders is large enough.…”