Computational Complexity and Communication: Coordination in Two-Player Games

Abstract

The main contribution of this paper is the development and application of cryptographic techniques to the design of strategic communication mechanisms. One of the main assumptions in cryptography is the limitation of the computational power available to agents. We introduce the concept of limited computational complexity, and by borrowing results from cryptography, we construct a communication protocol to establish that every correlated equilibrium of a two-person game with rational payoffs can be achieved by means of computationally restricted unmediated communication. This result provides an example in game theory where limitations of computational abilities of players are helpful in solving implementation problems. More specifically, it is possible to construct mechanisms with the property that profitable deviations are too complicated to compute.

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.…”

Optimal Use of Communication Resources

“…Starting with Forges (1990) and Bárány (1992), a body of literature, including Urbano and Vila (2002), Ben-Porath (2003), and Gerardi (2004), studies models of decentralized communication. An important conclusion of this literature is that-under various assumptions-all communication equilibria can be implemented through preplay decentralized communication procedures.…”

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.…”