The effect of spatial structure has been proved very relevant in repeated games. In this work we propose an agent based
model where a fixed finite population of tagged agents play iteratively the Nash demand game in a regular lattice. The
model extends the multiagent bargaining model by Axtell, Epstein and Young  modifying the assumption of global
interaction. Each agent is endowed with a memory and plays the best reply against the opponent’s most frequent demand.
We focus our analysis on the transient dynamics of the system, studying by computer simulation the set of states in which
the system spends a considerable fraction of the time. The results show that all the possible persistent regimes in the global
interaction model can also be observed in this spatial version. We also find that the mesoscopic properties of the interaction
networks that the spatial distribution induces in the model have a significant impact on the diffusion of strategies, and can
lead to new persistent regimes different from those found in previous research. In particular, community structure in the
intratype interaction networks may cause that communities reach different persistent regimes as a consequence of the
hindering diffusion effect of fluctuating agents at their borders.