Information Technology Reference
In-Depth Information
where
F
i
(
t
)=
p
(
t
)
−
v
i
(
t
)
. The mean asset value
v
i
(
t
)
and the number of asset units
u
i
(
t
)
are updated by
v
i
(
t
+1)=
v
i
(
t
)
u
i
(
t
)+
p
(
t
)
a
i
(
t
)
u
i
(
t
)+
a
i
(
t
)
(9)
and
u
i
(
t
+1)=
u
i
(
t
)+
a
i
(
t
)
,
(10)
respectively. That is, the payoff function (3) in MG is replaced by (8) in AG. Without
loss of generality, we assume that
v
i
(
t
)
,u
i
(
t
)
>
0
for any
t
T
.
The basic idea behind the payoff function is that each agent wants to decrease his
acquisition cost in order to make his appraisal gain. Figure 2(a) shows the relationship
between the price and the mean asset values of
N
=3
agents, where the price is
represented by the solid, heavy line. Notice that if the population size
N
is small, the
price change becomes drastic.
The most important feature of the AG is to appreciate the past gains and losses.
Even though an agent has bought a high-priced asset during the asset-inflated term (see
Figure 1), the mean asset value of the agent reflects the fact and an appropriate action
compared with the current price is recommended.
∈
2.3
Extended Asset Value Game
Here we consider the drawbacks of AG, and present an extended AG, denoted by ExAG,
to improve them. Though the AG captures a good feature of an agent's behavior, the
payoff function indirectly appreciates desirable strategies. If the adopted strategy is not
desirable, the agent has to wait until the desirable one gains the highest score. So, there
is a time lag between the rapid change of a price and the adjustment of an agent's
behavior.
More precisely, the movement of price is followed by the asset values (see arrows
in Figure 2(a)). This behavior can be explained by the following reasons. If the price
rapidly rises, it exceeds almost all the mean asset values. Then,
F
i
(
t
)=
p
(
t
)
−
v
i
(
t
)
becomes plus and the
a
i
(
t
)=
1
(i.e., sell) action is recommended. So, some agents
change from trend-followers to contrarians in a few steps. During the steps, such agents
remain trend-followers, that is, buy assets at the high price. Thus, their mean asset
values follow the movement of price.
trim = 10mm 80mm 20mm 5mm, clip, width=3cm
Our solution is to provide another option of the agent. That is, the agent who has
much higher/lower asset value than the current price can directly act as the payoff func-
tion, called a
direct action
. However, if so, every agent may take the same action when
the price go beyond every asset value. To avoid such an extreme situation, we give the
direct action with some probability.
Let
K
=
K
+
(
F
i
≥
−
0)
,K
−
(
F
i
<
0)
be the
F
i
's threshold over which the agent
may take the direct action, and let
λ
be some constant. Each agent takes the same action
as the payoff function (without using his strategy) with probability
p
=
1
−
exp
{−
λ
(
|
F
i
|−
K
)
}
(
K
≤|
F
i
|
)
(11)
0
(
|
F
i
|
<K
)
,
