MODUL PERKULIAHAN
PENGAMBILAN
KEPUTUSAN
MANAJERIAL
Pengambilan Keputusan dengan
Lawan Berhadapan.
( GAME THEORI / ZERO GAME )
‘15
Fakultas
Program Studi
Fakultas Ekonomi dan
Bianis
Manajemen
1
Tatap Muka
Kode MK
05
Disusun Oleh
Hartri Putrato,SE.MM.
Abstract
Kompetensi
Mata Kuliah ini membahas tentang
proses Manajer dalam menprediksi
pengambilan Keputusan pada situasi di
masa depan dan penggunaan model
“Tulang Ikan ( Fish-Born ).
Mahasiswa diharapkan memiliki
wawasan yang luas dan mampu
menjelaskan dan menggunakan modelmodel Tulang Ikan..
Pengambilan Keputusan Manajerial
Hartri Putranto,SE.MM
Pusat Bahan Ajar dan eLearning
http://www.mercubuana.ac.id
.
the sum of gains and losses by the players are sometimes more or less than what they
began with.
Solution
For 2-player finite zero-sum games, the different game theoretic solution concepts of Nash
equilibrium, minimax, and maximin all give the same solution. In the solution, players play a
mixed strategy.
Example
A
B
C
1 30, -30 -10, 10 20, -20
2 10, -10 20, -20 -20, 20
A zero–sum game
A game's payoff matrix is a convenient representation. Consider for example the two-player
zero–sum game pictured at right.
The order of play proceeds as follows: The first player (red) chooses in secret one of the two
actions 1 or 2; the second player (blue), unaware of the first player's choice, chooses in
secret one of the three actions A, B or C. Then, the choices are revealed and each player's
points total is affected according to the payoff for those choices.
Example: Red chooses action 2 and Blue chooses action B. When the payoff is allocated,
Red gains 20 points and Blue loses 20 points.
Now, in this example game both players know the payoff matrix and attempt to maximize the
number of their points. What should they do?
Red could reason as follows: "With action 2, I could lose up to 20 points and can win only
20, while with action 1 I can lose only 10 but can win up to 30, so action 1 looks a lot better."
With similar reasoning, Blue would choose action C. If both players take these actions, Red
will win 20 points. But what happens if Blue anticipates Red's reasoning and choice of action
1, and goes for action B, so as to win 10 points? Or if Red in turn anticipates this devious
trick and goes for action 2, so as to win 20 points after all?
‘13
2
Pengambilan Keputusan Manajerial
Hartri Putranto,SE.MM
Pusat Bahan Ajar dan eLearning
http://www.mercubuana.ac.id
Émile Borel and John von Neumann had the fundamental and surprising insight that
probability provides a way out of this conundrum. Instead of deciding on a definite action to If
the game matrix does not have all positive elements, simply add a constant to every element
that is large enough to make them all positive. That will increase the value of the game by
that constant, and will have no effect on the equilibrium mixed strategies for the equilibrium.
The equilibrium mixed strategy for the minimizing player can be found by solving the dual of
the given linear program. Or, it can be found by using the above procedure to solve a
modified payoff matrix which is the transpose and negation of
(adding a constant so it's
positive), then solving the resulting game.
If all the solutions to the linear program are found, they will constitute all the Nash equilibria
for the game. Conversely, any linear program can be converted into a two-player, zero-sum
game by using a change of variables that puts it in the form of the above equations. So such
games are equivalent to linear programs, in general
Non-zero–sum
Economics
Many economic situations are not zero-sum, since valuable goods and services can be
created, destroyed, or badly allocated in a number of ways, and any of these will create a
net gain or loss of utility to numerous stakeholders. Specifically, all trade is by definition
positive sum, because when two parties agree to an exchange each party must consider the
goods it is receiving to be more valuable than the goods it is delivering. In fact, all economic
exchanges must benefit both parties to the point that each party can overcome its
transaction costs, or the transaction would simply not take place.
There is some semantic confusion in addressing exchanges under coercion. If we assume
that "Trade X", in which Adam trades Good A to Brian for Good B, does not benefit Adam
sufficiently, Adam will ignore Trade X (and trade his Good A for something else in a different
positive-sum transaction, or keep it). However, if Brian uses force to ensure that Adam will
exchange Good A for Good B, then this says nothing about the original Trade X. Trade X
was not, and still is not, positive-sum (in fact, this non-occurring transaction may be zerosum, if Brian's net gain of utility coincidentally offsets Adam's net loss of utility). What has in
fact happened is that a new trade has been proposed, "Trade Y", where Adam exchanges
Good A for two things: Good B and escaping the punishment imposed by Brian for refusing
the trade. Trade Y is positive-sum, because if Adam wanted to refuse the trade, he
theoretically has that option (although it is likely now a much worse option), but he has
determined that his position is better served in at least temporarily putting up with the
‘13
3
Pengambilan Keputusan Manajerial
Hartri Putranto,SE.MM
Pusat Bahan Ajar dan eLearning
http://www.mercubuana.ac.id