Review of Quantitative Finance and Accounting, 11 (1998): 269–291
© 1998 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.
Rationalizable and Coalition Proof Shareholder
Tendering Strategies in Corporate Takeovers
THOMAS H. NOE
A. B. Freeman School of Business, Tulane University, New Orleans, LA 70118 and Research Department,
Federal Reserve Bank of Atlanta, Atlanta, GA 30303
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 Rational-
izability 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 commu-
nication, 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.
Key words: coalition proof, takeovers, free-rider problem
JEL Classiﬁcation: G34, C72, C71
The question of how shareholders will respond to an uncondional tender offer made by a
raider at a price between the pre-acquisition and post-acquisition value of the ﬁrm’s shares
has received a great deal of attention in the ﬁnancial economics literature.
problem is this: because the post-acquisition value of the ﬁrm is higher than be preac-
quisition value, each shareholder of the target ﬁrm wants the takeover to succeed. At the
same time, because the raider is offering bid price below post-acquisition value, no
shareholder wants to tender his own shares. However, if no shareholder tenders, then the
takeover attempt must fail and all shareholders are thus made worse off.
Early work on corporate takeovers (see, e.g., Grossman and Hart (1980) and Bradley
(1980)) addressing this question was based on the assumption that shareholders, in de-
termining their tendering strategy, ignore the effect of their own decisions on the outcome
of the offer. Under this assumption, it is never in the interest of shareholders to tender their
shares when the offer price is below the post-acquisition share price and they expect the
offer to succeed.
For this reason, it was argued that the “free rider” problem effectively
prevents raiders from proﬁtably acquiring target ﬁrms.
All shareholders conjecturing that their share tendering decision will have no effect on
the outcome of the takeover offer, i.e., that they are non-pivotal, is not a Nash equilibrium
conjecture, at least in ﬁnite shareholder models. In a Nash equilibrium, shareholder
conjectures regarding whether they are pivotal must reﬂect the actual probability that they
@ats-ss8/data11/kluwer/journals/requ/v11n3art3 COMPOSED: 09/14/98 4:35 pm. PG.POS. 1 SESSION: 96