Core global bond markets--led by German Bunds and US Treasuries--have been trending lower fairly reliably.  For European bonds, that rally has occupied most of the month whereas the US version is only really a week old.  The latter is also heavily reliant on the stock market.  Here's how all of these trends look on a chart:

Breaking the charts out individually is a bit misleading.  Sure, we can see that stocks and Treasuries share more correlation, but we don't really get a sense for the magnitude of stock losses that have been required to fuel the bond rally.  If we set the y-axis scaling based on September's highs/lows, here's how October looks by comparison:

So, the question of "who blinks first" is really a question of "when will stocks blink?"  In answering that question, this week's earnings releases may be the biggest game in town.  That was certainly the case last week.  This time around, however, there will be much stiffer competition from a slew of top tier economic data.  ADP Employment, ISM Manufacturing and Friday's NFP data are the big 3.  Notably, some of the week's biggest earnings releases will be occurring on the 3 days where those economic reports are coming out.

All of the above does nothing to guarantee the direction of the next move in bonds, but it does a lot to suggest volatility.