While most takeover models assume atomistic stockholders, we analyze a single-raider model with finitely many stockholders. Because the raider can always make some stockholders pivotal, he can overcome the free-rider problem identified by Grossman and Hart (1980) and others in atomistic-stockholder models and profitably take over even without exclusion. One might expect that it would be harder for the raider to make stockholders of more widely held firms pivotal and that exclusion would thus become necessary; however, the infinite-stockholder game cannot yield this conclusion. We also consider the limit of the finite-stockholder game and give conditions under which exclusion is unnecessary. Finally, we show that exclusion leads to the possibility of inefficient takeovers.
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