In Lake Wobegone there are 1+n firms. The first firm raises or lowers its price by a mean-zero random amount, e. The remaining n identical firms wait to see what the first firm has done, then raise their prices by B times the average expected inflation rate, or lower their prices by B times the average expected deflation rate.
In rational expectations equilibrium, the Lake Wobegone inflation rate p is determined by:
p = Bp[n/(n+1)] + e/(n+1)
Which gives us:
p = e/(n(1-B)+1)
If 0 < B < 1+(1/n) this equilibrium looks sensible. A positive random shock at the first firm causes positive inflation, but the effect gets smaller as n gets larger.
If B > 1+(1/n) this equilibrium looks strange. A positive random shock at the first firm causes negative inflation.
The first equilibrium is the standard equilibrium in a New Keynesian model, where the central bank follows the Howitt-Taylor principle, promising to raise the nominal interest rate by enough, if expected inflation rises above target, to make each firm want to raise its price by less than expected inflation.
That second equilibrium is the Neo-Fisherian equilibrium in a New Keynesian model, where the central bank holds the nominal interest rate fixed at the (real) natural rate of interest, so if expected inflation rises above target, each firm wants to raise its price by more than expected inflation.
Empirically, that second equilibrium doesn't look very plausible to me. When the government raises taxes on smokes, for example, we normally see a small temporary increase in inflation, not a decrease.