IP addresses face exhaustion, at the least those under the standard IPv4 format, and by some reports they should have been all used up already. What has helped delay the inevitable is probably the fact that there is now a market for IP addresses, yet it is not clear that the market is working efficiently. The reason is that IP addresses are allocated in blocks, and fragmenting the big IP allocation table makes it more difficult to manage it. For technical reasons, each allocation needs to be a square in the table. Thus, if a square is partially unused, it can only be split in multiple squares, increasing their number. Routers need to keep each possible square in memory, and their multiplication slows routing. And as IP addresses are privately owned and managed, there is no way to control this negative externality.
Benjamin Edelman and Michael Schwarz propose a market mechanism that should make the allocation of IP addresses more efficient. They suggest a "spartan rule:" in each bilateral trade, one of the two traders is designated as "extinguished," i.e., as prohibited from trading with other extinguished ones. As one can be extinguished only once, this implies that the number of cuts N in the IP table is limited to the number of initial holders of IP blocks. The analysis is static and under certainty, implying that the implicit rental price of an IP is zero as long as there is still a free one. But with the proposed rule, I do not see how one could necessarily reach exhaustion after the N cuts. It all depends on the initial allocation: one can end up with free IP addresses and no possible moves. In addition, once we add uncertainty and dynamics, there is going to be strategic behavior as being extinguished is a potentially costly absorbing state. I am thus not convinced of the arguments in this paper.
Of course, the easiest would be for everyone to switch to IPv6, which would give a sufficient number of IP addresses to last for a long time. But IPv6 devices cannot communicate with IPv4 devices (large scale IPv4 to IPv6 translation is cumbersome), which gives little incentive to switch until there is substantial critical mass. In other words, another situation like Y2K is approaching, and nobody has an incentive to do something about it. The more efficient market allocation will delay this, but also will make it even more urgent when it happens, because more addresses will need to switch, and they will have less time for it.