What is the influence of short-term memory enhancement on the emergence of grammatical agreement systems in multi-agent language games? Agreement systems suppose that at least two words share some features with each other, such as gender, number, or case. Previous work, within the multi-agent language-game framework, has recently proposed models stressing the hypothesis that the emergence of a grammatical agreement system arises from the minimization of semantic ambiguity. On the other hand, neurobiological evidence argues for the hypothesis that language evolution has mainly related to an increasing of short-term memory capacity, which has allowed the online manipulation of words and meanings participating particularly in grammatical agreement systems. Here, the main aim is to propose a multi-agent language game for the emergence of a grammatical agreement system, under measurable long-range relations depending on the short-term memory capacity. Computer simulations, based on a parameter that measures the amount of short-term memory capacity, suggest that agreement marker systems arise in a population of agents equipped at least with a critical short-term memory capacity.