4 research outputs found
Limits on the Power of Cryptographic Cheap Talk
We revisit the question of whether cryptographic protocols can replace correlated equilibria mediators in two-player strategic games. This problem was first addressed by Dodis, Halevi and Rabin (CRYPTO 2000), who suggested replacing the mediator with a secure protocol and proved that their solution is stable in the Nash equilibrium (NE) sense, provided that the players are computationally bounded.
We show that there exist two-player games for which no cryptographic protocol can implement the mediator in a sequentially rational way; that is, without introducing empty threats. This explains why all solutions so far were either sequentially unstable, or were restricted to a limited class of correlated equilibria (specifically, those that do not dominate any NE, and hence playing them does not offer a clear advantage over playing any NE).
In the context of computational NE, we classify necessary and sufficient cryptographic assumptions for implementing a mediator that allows to achieve a given utility profile of a correlated equilibrium. The picture that emerges is somewhat different than the one arising in semi-honest secure two-party computation. Specifically, while in the latter case every functionality is either “complete (i.e., implies Oblivious Transfer) or “trivial (i.e., can be securely computed unconditionally), in the former there exist some “intermediate utility profiles whose implementation is equivalent to the existence of one-way functions
Computational Extensive-Form Games
We define solution concepts appropriate for computationally bounded players
playing a fixed finite game. To do so, we need to define what it means for a
\emph{computational game}, which is a sequence of games that get larger in some
appropriate sense, to represent a single finite underlying extensive-form game.
Roughly speaking, we require all the games in the sequence to have essentially
the same structure as the underlying game, except that two histories that are
indistinguishable (i.e., in the same information set) in the underlying game
may correspond to histories that are only computationally indistinguishable in
the computational game. We define a computational version of both Nash
equilibrium and sequential equilibrium for computational games, and show that
every Nash (resp., sequential) equilibrium in the underlying game corresponds
to a computational Nash (resp., sequential) equilibrium in the computational
game. One advantage of our approach is that if a cryptographic protocol
represents an abstract game, then we can analyze its strategic behavior in the
abstract game, and thus separate the cryptographic analysis of the protocol
from the strategic analysis