The viability of a market impact model is usually considered to be equivalent to the absence
of price manipulation strategies in the sense of Huberman & Stanzl (2004). By analyzing a model
with linear instantaneous, transient, and permanent impact components, we discover a new class of
irregularities, which we call transaction-triggered price manipulation strategies. We prove that price
impact must decay as a convex decreasing function of time to exclude these market irregularities along
with standard price manipulation.