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to be repeated, no random variable to be sampled, no issue about measurability
(the system that designers are going to build is often unique in some respects).
However, we need a method to calculate the value of probability as well as
to explain the semantic of the number. Since probability is acquired from the
requirement eliciting process involving the stakeholder, we propose using the
game-theoretic method in which we treat probability as a price. It seems to be
easier for stakeholder to reason on price (or cost) rather than probability.
The game-theoretic approach, discussed by Shafer et al. [27] in Computational
Finance, begins with a game of three players,
i.e.
Forecaster, Skeptic, and Re-
ality. Forecaster offers prices for tickets (uncertain payoffs), and Skeptic decides
a number of tickets to buy (even a fractional or negative number). Reality then
announces real prices for tickets. In this sense, probability of an event
E
is the
initial stake needed to get 1 if
E
happens, 0 if
E
does not happen. In other
words, the mathematics of probability is done by finding betting strategies.
In this paper, we do not deal with stock market but the design of evolving
software,
i.e.
we extend it for software design. We then need to change rules of the
game. Our proposed game has three players:
Stakeholder
,
Designer
,and
Reality
.
For the sake of brevity we will use “he” for Stakeholder, “she” for Designer and
“it” for Reality. The sketch of this game is denoted in protocol 1.
Protocol 1
Game has
n
round, each round plays on a software
C
i
FOR i = 1 to n
Stakeholder announces
p
i
Designer announces her decision
d
i
: believe, don't believe
If Designer believes
K
i
=
K
i−
1
+
M
i
×
(
r
i
−
p
i
)
Designer does not believe
K
i
=
K
i−
1
+
M
i
×
(
p
i
−
r
i
)
Reality announces
r
i
The game is about Stakeholder's desire of having a software
C
.HeasksDe-
signer to implement
C
, which has a cost of
M
$. However, she does not have
enough money to do this. So she has to borrow money from either Stakeholder
or National Bank with the return of interest (ROI)
p
or
r
, respectively.
Stakeholder starts the game by announcing
p
which is his belief about the
minimum ROI for investing
M
$on
C
. In other words, he claims that
r
would
be greater than
p
.If
M
equals 1,
p
is the minimum amount of money one can
receive for 1$ of investment. Stakeholder shows his belief on
p
by a commitment
that he is willing to buy
C
for price (1 +
p
)
M
if Designer does not believe him
and borrow money from someone else.
If Designer believes Stakeholder, she will borrow
M
from Stakeholder. Later
on, she can sell
C
to him for
M
(1 +
r
) and return
M
(1 +
p
) to him. So, the final
amount of money Designer can earn from playing the game is
M
(
r
−
p
).
