1. War GameTwo opposed armies are poised to seize an island.•Each army can either "attack" or "not-attack".•Also, Army 1 is either "weak" or "strong" with probability p and (1 - p), respectively. Army 2 is always "weak".•Army's 1 type is known only to its general.•An army can capture the island either by attacking when its opponent does not or by attacking when its rival does if it is strong and its rival is weak. If two armies of equal strength both attack, neither captures the island.•The payoffs are as follows•The island is worth M if captured.•An army has a "cost" of fighting, which is equal to s > 0 if it is strong and w > 0 if it is weak (where s Strong
1\2
Attack
Not-Attack
Attack
M-s,-w
0,M
Not-Attack
M,0
0,0
with probability 1 — p.
When p
=
= 1/2, which is a pure strategy Bayesian equilibrium (there could be other equilibria that are not listed as one of the options):
Strategies listed in format: (1's type - 1's strategy; 2's strategy)
a) (Weak - Not-Attack, Strong - Attack; Attack);
b) (Weak - Not-Attack, Strong - Attack; Not-Attack);
Oc) (Weak - Attack, Strong - Attack; Attack);
d) It does not exist.