We formulate the best response dynamic in a multitasking environment; while agents engage in multiple games concurrently, an agent can switch her action in only one of the games upon receipt of a revision opportunity. The choice of the game in which to revise an action makes the multitasking dynamic behave differently from standard evolutionary dynamics. The timing of revisions in a game becomes endogenous, which causes the transition of the action distribution in each game to depend on those in other games. Despite such complexity, we verify the global stability of the Nash equilibrium set in potential and contractive games as well as the local stability of a regular evolutionary stable state. We also show that the equilibrium to which the multitasking dynamic converges may depend on the task choice rules.
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