Lattice Dynamics of Inequity

We discuss a model of inequity based on iteration of the Nash multi-agent bargaining game on a lattice. Agent's choices are based on a logit function and gradual decay of memories of past profits. Numerical simulations demonstrate the stability of various dynamical regimes, such as disorder, fairness or inequity, according to parameters and initial conditions. When playing the game on a lattice i.e. using neighbouring agent interactions instead of random interaction among the whole agent population, one observes spatial domains and specific patterns in addition to the temporal convergence toward attractors observed when interactions involve any pair of agents. A result specific to the network topology is the co-existence of domains with different regimes, allowing the emergence of the inequity condition even in the absence of tags.