Why is the Cournot equilibrium stable? (i.e., Why dont firms have any incentive to change their output

Question:

Why is the Cournot equilibrium stable? (i.e., Why don’t firms have any incentive to change their output levels once in equilibrium?) Even if they can’t collude, why don’t firms set their outputs at the joint profit-maximizing levels (i.e., the levels they would have chosen had they colluded)?