Based on this paper a protocol is secure if and only if it satisfies secrecy and resiliency. Most of the papers in ecnomic and computer since deal with the following problem. They consider the case where $n$ parties with private information $s1,...,s_n$ wish to compute any function $f(s_1,...,s_n) = (y_1,...,y_n)$ in such a way that no party $i=1,2,...,n$ learns more than their input $s_1$ and output $y_i$. They construct a protocol such that for any coalition of players of size less than $n/3$, any joint deviation by the coalition produces no additional information and does not disrupt the messages received by the remaining players.
$\textbf{Question 1:}$ Does this function $f(s_1,...,s_n) = (y_1,...,y_n)$ gives the recommendations to the players about what strategy to follow and hence the correlated strategy? Furthermore, the paper that I refer here, uses also the connectivity notion why is this so important?
$\textbf{Question 2:}$ In case a mediator exists, to caclulate $f$ without learning somehting more that the private input or outpout is easy as cited in Heller et al (2012). However, in case the players communicate directly to each other with a cheap talk phase how can someone prove that a protocol is secure if and only if it satisfies secrecy and resiliency?
$\textbf{Question 3:}$When we have a cheap talk scheme of comminication we replace the device or mediator that has full information about the players private information with another. The latter mediator makes only suggestions about how the players should communicate in a plain conversation scheme and remains fully ignorant of the players' private info so as they can keep their privasey. My laset question is the following. How can the plaeyrs replicate somehow the central mediator with cheap talk and after exchanging messages they are only aware only for their private inptuts and outpouts and nothing more than the information of one another?
