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. This work extends the multiagent bargaining model by [1] including the spatial dimension in the game. Each agent is endowed with memory and plays the best reply against the opponent's most frequent demand. The results show that all the possible persistent regimes of the global interaction game can also be obtained with this spatial version. Our preliminary analysis also suggests that the topological distribution of the agents can generate new persistent regimes within groups of agents with the same tag.