Best response dynamic in a multitask environment

We formulate best response dynamic in a multitasking environment; while agents engage in two separate games concurrently, an agent can switch action only in one of them upon receipt of a revision opportunity. The choice of the game in which to revise action makes the multitasking dynamic significantly behave differently from the separate dynamics so the transition of action distribution in each game might look inconsistent with incentives if the endogenous choice of the focusing game is ignored. Despite of such complexity in the transitory phase of the dynamic, we verify that, in a wide class of games, global stability of equilibria can be predictable from that in the separate dynamics.