Abraham, Dolev, Geffner, and Halpern proved that, in asynchronous systems, a$(k,t)$-robust equilibrium for $n$ players and a trusted mediator can beimplemented without the mediator as long as $n > 4(k+t)$. We prove that this bound istight, in the sense that if $n \le 4(K+T)$ there exist . there exist $(k)$ – with a mediator that cannot be implemented by the players alone . This also provides a simple alternative proof for the well-known lowerbound of $4t+1$ on . asynchronous secure computation in the presence of up to $t$malicious agents . We show that there is a non-trivialreduction from a slightly weaker notion of $(k/t) $4-secure computation, which we call $(k+)$

Author(s) : Ivan Geffner, Joseph Y. Halpern

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Keywords : asynchronous - mediator - exist - secure - computation -

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