A dynamic allocation scheme for a multi-agent Nash equilibrium

A multi-agent game, in which each one of the N agents allocates its fixed resource against others to achieve dominance, results in a Nash equilibrium in a static game under perfect information. When an agent has knowledge only of his own allocations and allocations of the others against itself, then the only way to achieve a Nash equilibrium is to dynamically update its own allocations in time. This paper provides a formal scheme which is guaranteed to converge to a Nash equilibrium under the aforementioned information structure. This result has applications in the theory of balance of power in an international political systems, as well as in the analysis of piece-wise linear multi-model dynamical system.