Computationally restricted unmediated talk under incomplete information

Abstract

We show the role of unmediated talk with computational complexity bounds as both an information transmission and a coordination device for the class of two-player games with incomplete information and rational parameters. We prove that any communication equilibrium payoff of such games can be reached as a Bayesian-Nash equilibrium payoff of the game extended by a two phase universal mechanism of interim computationally restricted pre-play communication. The communication protocols are designed with the help of modern cryptographic tools. A familiar context in which our results could be applied is bilateral trading with incomplete information. Copyright Springer-Verlag Berlin/Heidelberg 2004Computational complexity, Unmediated communication, Correlated equilibrium, Bayesian-Nash equilibrium.,

Distributed Protocols for Leader Election: A Game-Theoretic Perspective

“…For one thing, work has continued on secret sharing and multiparty computation, taking faulty and rational behavior into account (e.g., [Abraham, Dolev, Gonen, and Halpern 2006;Dani, Movahedi, Rodriguez, and Saia 2011;Fuchsbauer, Katz, and Naccache 2010;Gordon and Katz 2006;Lysyanskaya and Triandopoulos 2006]). There has also been work on when and whether a problem that can be solved with a trusted third party can be converted to one that can be solved using cheap talk, without a third party, a problem that has also attracted the attention of game theorists (e.g., [Abraham, Dolev, Gonen, and Halpern 2006;Abraham, Dolev, and Halpern 2008;Barany 1992;Ben-Porath 2003;Dodis, Halevi, and Rabin 2000;Forges 1990;Heller 2005;Izmalkov, Lepinski, and Micali 2011;Lepinski, Micali, Peikert, and Shelat 2004;McGrew, Porter, and Shoham 2003;Shoham and Tennenholtz 2005;Urbano and Vila 2002;Urbano and Vila 2004]). This is relevant because there are a number of well-known distributed computing problems that can be solved easily by means of a "trusted" mediator.…”

Distributed computing building blocks for rational agents

“…At the same time, another line of research has shown applicative and theoretical results for cooperative services for what is known as the BAR model (Byzantine, acquiescent [33] and rational) [5,26,33] . Another related line of research asks whether a problem that can be solved with a mediator can be converted to a cheap talk based solution [2,3,6,7,9,11,21,22,24,29,30,31]. This approach is very strong because there are many results that are based on a mediator, which other players cannot trust under the rationality assumption, if we can convert mediator based protocols to be based on cheap talk, many of the previous works that do not assume rationality may become relevant under this assumption.…”

Implementation of communication equilibria by correlated cheap talk: The two-player case

“…Ben-Porath (1998) does not rely on any cryptographic tool, but obtains a similar result by allowing the players to make use of urns or envelopes while they talk. Generalizations to games with incomplete information are proposed by Krishna (2007) and Izmalkov et al (2011) for the latter approach, and by Urbano and Vila (2004) for the cryptographic approach. The common feature of these solutions (as opposed to ours) is that at every stage, cheap talk is relaxed in some way: limited computational ability or physical hard devices are used to exchange messages at every stage.…”