The demise of constant price impact functions and single-time step   models of speculation
  Constant and symmetric price impact functions, most commonly used in agent-based market modelling, are shown to give rise to paradoxical and inconsistent outcomes in the simplest case of arbitrage exploitation when open-hold-close actions are considered. The solution of the paradox lies in the non-constant nature of real-life price impact functions. A simple model that includes explicit position opening, holding, and closing is briefly introduced and its information ecology discussed, shedding new light on the relevance of the Minority Game to the study of financial markets. 
Damien Challet