In this paper, we introduce a Transactionally Efficient Market Model, which evolves from the standard efficient market  model, encompassing both transaction costs and bid-ask prices. Hence, we delve into how arbitrage makes its way within this complex setting. The main outgrowth of the analysis is the “trap set”, which is the place where most of price trajectories should enter to put an end to supernormal profits, although the underlying dynamics seems far from coming to a halt, and becomes bewildering instead. Bid-ask arbitrage gaps will prove useful to track down those adjustments of current prices, transaction costs and fundamental values. At this point, we define a transactionally efficacious market. Furthermore, a non linear dynamics whose environment gives room to mediator and microstructure, will lead us to prove the existence of a vectorial arbitrage gap mapping which becomes operational at managing the transactional efficiency of the market, in a complex surroundings with chaotic patterns eventually. Summing up: transactionally efficient markets are those markets which are informative efficient and transactionally efficacious.