1 Cryptography and Game Theory

The Cryptographic and Game Theory worlds seem to have an intersection in that they both deal with an interaction between mutually distrustful parties which has some end result. In the cryptographic setting the multiparty interaction takes the shape of a set of parties communicating for the purpose of evaluating a function on their inputs, where each party receives at the end some output of the computation. In the game theoretic setting parties interact in a game which guarantees some payoff for the participants according to their joint actions of all the parties, while the parties wish to maximize their own payoff. In the past few years the relationship between these two areas has been investigated with the hope of having cross fertilization and synergy. In this chapter we describe the two areas, the similarities and differences, and some of the new results stemming from their interaction. The first and second section will describe the cryptographic and the game theory settings (respectively). In the third section we contrast the two settings, and in the last sections we detail some of the existing results. Cryptography is a vast subject requiring its own book. Therefore, in the following we will only give a high-level overview of the problem of Multi-Party Computation (MPC), ignoring most of the lower-level details and concentrating only on aspects relevant to Game Theory. MPC deals with the following problem. There are n ≥ 2 parties P 1 , ..., P n where party P i holds input t i , 1 ≤ i ≤ n, and they wish to compute together a function s = f (t 1 , ..., t n) on their inputs. The goal is that each party will learn the output of the function, s, yet with the restriction that P i will not learn any additional information about the input of the other parties aside from what can be deduced from the pair (t i , s). Clearly it is the secrecy restriction which adds complexity to the problem, as without it each party could announce its input to all other parties, and each party would locally compute the value of the function. Thus, the goal of MPC is to achieve the 1