Rationalizable and Coalition Proof Shareholder Tendering Strategies in Corporate Takeovers

Abstract

This paper determines the set of rational responses by shareholders to unconditional takeover offers at prices between the pre-acquisition and post-acquisition price of the firm. Two cases are considered. In the first case, coordination across shareholders is not presumed. In this case, the game is analyzed using the Rationalizability criteria (Bernheim, 1984). It is demonstrated that the Rationalizable strategy vectors include all pure strategy vectors. In the second case, the set of strategies consistent with coordination through preplay communication, the Coalition Proof Nash Equilibria (Bernheim, Peleg, and Whinston, 1987) are analyzed. It is shown that, given even a minimal degree of divisibility of shareholdings, the raider's per share profit is bounded from below by a positive constant independent of the number of shareholders. These results imply that preplay coordination between shareholders eliminates the “free-rider” problem.