A social choice rule (SCR) $F$ maps preference profiles to lotteries over some finite set of outcomes. $F$ is virtually implementable in (pure and mixed) Nash equilibria provided that for all $\epsilon 0$, there exists a mechanism such that for each preference profile $\theta$, its set of Nash...

In a market with indivisibilities, Roth and Postlewaite (1977) show that the (weak) core can suffer from instability problems, in the sense that groups of individuals might upset the equilibrium by recontracting among themselves. By contrast, the strong core is stable. Following the seminal...