For Whom is MAI? A theoretical Perspective on Multilateral Agreements on Investments

increasing with °; (iii) consider β = 0:5, then ¢E > 0 if and only if ° < °_u;
(iv) consider β = β_l, then ¢E < 0 if and only if ° > °_l.

Proof: See Appendix 2.

Result i) in Lemma 2 states that an equilibrium with partial MAI is feasible
only for intermediate values of °. When ° is sufficiently small, ¢E is surely
negative, because β* < β;. The adverse selection effect of MAI prevails in
this case. Conversely, when ° is sufficiently high, then β* > 1=2 and ¢E is
necessarily positive. The discipline effect prevails. For intermediate values of °
the two effects may offset each other, and an indifference solution for countries
may emerge, together with a partial MAI equilibrium. We also see from result ii)
that the size of MAI at which expected MNEs in and outside MAI are equalized
is decreasing with °. This means that the size z of a partial MAI is necessarily
decreasing with °. Finally, results iii) and iv) are crucial in checking for pure
strategy equilibria.

A different question is that of the characterization and uniqueness of partial
MAI equilibria. We see from (7) that, given β* ; there is only one value of z in
(0,1). It is proven also that there exists only one value of p that sustains an
equilibrium with z 2 (0; 1).

Lemma 3 i) There exists a unique value ofp 2 (0; 1) that sustains a partition
of countries z 2 (0; 1); ii) p rises monotonically with z in (0; 1); iii) limp =0
z!0

and limp =1;iv)p>z.

z!1

Proof: See Appendix 3

We remark on result iv) in Lemma 3. The fact that p> z in any partial
MAI equilibrium means that by joining MAI, countries are able to attract more
FDIs. The mere fact that a country belongs to MAI reduces its bargaining
power, rent extraction, and income. To induce some countries to be in MAI,
there must be higher expected FDI inflows for the countries in MAI, in order
to compensate for the loss in bargaining power. As will be clear in the next
section, this has important welfare implications.

Lemmas 1 to 3 are sufficient to give a full characterization of the equilib-
rium, when all countries can potentially enter MAI. In the next Proposition, we
characterize which types of equilibria emerge with respect to the strictness of
MAI (°):

Proposition 4 Consider °<β_l. Then: i) if °<°_l the only equilibrium is
“no MAI”; ii) if °>°_u the only equilibrium is “full MAI”; iii) if °_l <°<°_u
the equilibrium may either be “no MAI”, “partial MAI”, or “full MAI”.

Proof: See Appendix 4.

We can consider now all cases where °>β_l . Clearly, all countries with
β_h <°will not enter MAI, since they will not be able to extract any rent from

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