Hybrid coevolutionary programming for Nash equilibrium search in games with local optima

The conventional local optimization path and coevolutionary processes are studied when "local Nash equilibrium (NE) traps" exist. Conventional NE search algorithms in games with local optima can misidentify NE by following a local optimization path. We prove that any iterative NE search algorithms based on local optimization cannot differentiate real NE and "local NE traps". Coevolutionary programming, a parallel and global search algorithm, is applied to overcome this problem. In order to enhance the poor convergence of simple coevolutionary programming, hybrid coevolutionary programming is suggested. The conventional NE algorithms, simple coevolutionary programming, and hybrid coevolutionary algorithms are tested through a simple numerical example and transmission-constrained electricity market examples.