Monitoring cooperative equilibria in a stochastic differential game

The authors study a class of equilibria for stochastic differential games which are based on monitoring an implicit cooperative solution. The equilibrium is reached by implementing a random triggering scheme which changes the mode of play when there is an indication that at least one player may be departing from the cooperative solution. These equilibria make use of a particular kind of memory strategy and exploit the nonuniqueness of the solution to an associated Hamilton-Jacobi-Bellman (HJB) equation. In particular, it is shown that these equilibria, which satisfy a continuous-time dynamic programming equation, can be designed in such a way that they generate payoffs which dominate those obtained via the classical feedback Nash equilibrium for the original stochastic diffusion game