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**2022/1762**

**Title:**

On the impossibility of surviving (iterated) deletion of weakly dominated strategies in rational MPC

**Authors:**
Johannes Blömer, Jan Bobolz, Henrik Bröcher

**Abstract:**

Rational multiparty computation (rational MPC) provides a framework for analyzing MPC protocols through the lens of game theory. One way to judge whether an MPC protocol is rational is through weak domination: Rational players would not adhere to an MPC protocol if deviating never decreases their utility, but sometimes increases it.

Secret reconstruction protocols are of particular importance in this setting because they represent the last phase of most (rational) MPC protocols. We show that most secret reconstruction protocols from the literature are not, in fact, rationally sound with respect to weak domination. Furthermore, we formally prove that (under certain assumptions) it is impossible to design a rationally sound secret reconstruction protocol if (1) shares are authenticated or (2) half of all players may form a coalition.

**ePrint:**
https://eprint.iacr.org/2022/1762

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