  A large body of empirical literature has shown that market impact of
financial prices is transient. However, from a theoretical standpoint, the
origin of this temporary nature is still unclear. We show that an implied
transient impact arises from the Nash equilibrium between a directional trader
and one arbitrageur in a market impact game with fixed and permanent impact.
The implied impact is the one that can be empirically inferred from the
directional trader's trading profile and price reaction to order flow.
Specifically, we propose two approaches to derive the functional form of the
decay kernel of the Transient Impact Model, one of the most popular empirical
models for transient impact, from the behaviour of the directional trader at
the Nash equilibrium. The first is based on the relationship between past order
flow and future price change, while in the second we solve an inverse optimal
execution problem. We show that in the first approach the implied kernel is
unique, while in the second case infinite solutions exist and a linear kernel
can always be inferred.
