Information Technology Reference
In-Depth Information
Fig. 16.3
Hider's beliefs in conditional probability that search is occurring (numerical estimates)
(
K
=
1to6,
L
=
18)
Table 16.1
Conjectured and estimated game values and suppor
ting data
K=1
K=2
K=3
K=4
K=5
K=6
σ
K
0.5000 0.6180 0.6914 0.7413 0.7773 0.8046
1
−
σ
K
2.0000 2.6180 3.2406 3.8651 4.4905 5.1165
Estimated
T
18
,
K
2.0000 2.6180 3.2420 3.8715 4.5057 5.1496
1
Conjecture 2
In any silent discrete search-ambush game for finite
K
where
L
p
j
p
j
−
1
=
=
∞
,
∃
x
such that for all hider probabilities
p
j
where
j
>
x
,
z
for some
constant
z
which is a function of
K
.Further,
∃
y
such that all searcher strategies
that involve search in periods
i
>
y
are wait-then-exhaustive.
Naturally, substantial work remains to be done regarding investigation of these
conjectures. A reasonable starting step - and one that ought to be achievable using
mathematics no deeper than that used in obtaining the above results - would be
to analytically solve the case where
K
. This would either substantially
strengthen or undermine the patterns identified above, and in particular determining
a value for the
K
=
3,
L
=
∞
3 case may enable more precise speculation for the value under
general
K
than Conjecture 1 offers (or even lend weight again to the possibility that
Conjecture 1 holds as an equality).
=
Search WWH ::
Custom Search