Consider again the auction of Justin Timberlake's left-over toast, which has utility value of 4 to each bidder. There are 15 individual whose bids, $b_i$, must be a strictly positive integer. Alternatively, an individual can also choose not to make a bid. The individual with the highest bid wins. If two or more make the same bid, then each of the highest bidder receives Justin Timberlake's toast with equal probability. Thus, if $s$ many individuals make the same highest bid, then each of them receives a payoff of $(4-b)/s$, where $b$ is the highest bid. An individual who does not win the auction receives a payoff of zero.
What is the minimum number of individuals that have to make a bid that wins the toast with strictly positive probability so that there exists a Nash equilibrium in which all bidders' payoffs are zero?