the mixed strategy equilibrium and the individuals’ expected payoffs converge to the
equilibrium for T < c∕2. Since individuals are not symmetric in this continuation
game and there is no particular reason to focus on one or the other equilibrium,11
the analysis of the individuals’ incentives to become informed will distinguish which
equilibrium is selected in case exactly one individual learned his cost of provision
and T > c∕2.
Given that the pure strategy equilibrium is selected (Lemma 3b(i)), ex ante ex-
pected payoffs are
|
E (πi) |
- {: |
- Ph ( 2c + t) — c |
if T< if T> |
C 2 C 2 |
(4) |
|
e <Λj) |
- ! : |
- pLcL - pH ( |
T+t ) |
if T < c |
(5) |
In case the mixed strategy equilibrium is selected (Lemma 3b(ii)), ex ante expected
payoffs equal
|
: : - Ph (C + T) if |
T< C | |
|
E (πi) - |
J - ⅜+T- τ < : — pH e 2+ с c if |
C < T < C - ClnPh (6) |
|
[ : — c if |
T ≥ C - clnрн | |
|
: : - PlCl - Ph (cf |
+ T) if T < C | |
|
c-2T | ||
|
e (⅞) - |
< : - Cl - ɪ e 2cl (ch + c - 2cl) if C <T< C - cln рн (G | |
|
I : |
if T ≥ c - clnpH | |
For T < c∕2, jL concedes immediately; therefore, the expected payoff of the unin-
formed individual i increases with the probability that j has a low contribution cost.
Note that in this case E (πi) > E (πj∙), i.e. the individual who does not know his cost
of provision has a higher expected payoff than the informed individual. For a large
T, however, the uninformed individual may concede immediately and gets a lower
expected payoff.
11In particular, the two equilibria cannot be Pareto-ranked.
13