IFÁ:
THE KEY TO ITS' UNDERSTANDING
Fáşinà Fáladé
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5.Orişà
Bibliograpical references
1.Ifá 2.Orunmila 3.African Spirtuality 4. Yorùbá
8:43
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Von Neumann's War
Nm
Mor
Creation of Game Theory
e
Croatian of Game
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SOLID ANGLE
SUBMERGED
SURFACE PATROL TRACK
TARGET Visual detection of wake on Ocean surface by observer in aircraft From Philip Mose (1948) Mathematical Problems in Operations Research,
the American M e tical Society, Vol. 54. pp. 602-21. With permission from the
Locating a passive target is one thing. What happens if measure is met with countermeasure-if A's choice of search tactic depends on B's choice ofesion or defense tactic, and vice versa? "Problems of this sort, are discussed by von Neumann and Morgenstern in their Theory of games, says Morse
sad known the von Neumanns since the late 1920s, when he was completing his doctorate at Princeton. He particularly liked Mariette ancaman's first wife, and both she and Desmond Kuper, the physis or whom she had left von Neumann in 1937, would be amongst the
loses ecrits in 1946 when he became director of the Brooks cuboratory on Long Island. He also liked von Neumann, whom
whom he
Mover al archivo X
PROBABILITY OF CONTACT OF SURFACED SUBMARINE WHEN BARRIER 15 ATX
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in
POSITION OF BARRIER, Barrier patrol verstis diving submarine. Fx) = probability of contact at x and submarine is surfaced. Credit: From Philip Morse (1994
lems in Operations Research". Bulletin of the American Mathematical SocPP. 602-21. With permission from the American Mathematics
VOL 54, pp. 602-21. With permis
carded as smarter than Oppenheimer and more versatile has being advised on the use of minimax theory in the
om in late 1942, before the Theory of Games Pod Johnny von Neumann was round, genial, helpful, and in everything. Nooneleven knew could as quickly grasp the halting explanations, point out the crux of the difficulty, and to solve it. He would really listen, while simultaneously thinkin the implications of what he was heari have come out
max theory in the search
Whether in sections or all at
total distance, the rest of point along the channel, the in surveillance (Figure 12.2).
in sections or all at once, the submarine can only travel submerged istance, the rest of the time it is visible. The plane must choose a ng the channel, the width of which varies, at which it will traverse
out the crux of the difficulty, and suggest way
helpful, and interested Stap the essence of one's
Px) is the pro
thinking through
distance imm the
the probability of detection if the plane patrols at a point at mm the channel entrs, given that the submarine is visible at that
Biber the nobility
8:43
273
22
Von Neumann, Morgenstern, and the Creation of Go,
Creation of Game Theory
Von Neumann's War
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SOLID ANGLE
OBSERVER
SUBMARINE
TRACK
SUBMERGED A
ON SURFACE
PATROL TRACK
OF PLANE
TARGET Figure 12.1. Visual detection of wake on ocean surface by observer in aircraft Credit From Philip Morse (1948), "Mathematical Problems in Operations Research". Bulletin of the American Mathematical Society, Vol. 54, pp. 602-21. With permission from the American Mathematical Society,
P()
Locating a passive target is one thing. What happens if measure is met with countermeasure - if A's choice of search tactic depends on B's choice of evasion or defense tactic, and vice versa? "Problems of this sort, are discussed by von Neumann and Morgenstern in their Theory of games, says
© Mover al archivo X
+ PROBABILITY OF CONTACT OF SURFACED SUBMARINE WHEN BARRIER IS AT X
P(x)
Morse.!?
Morse had known the von Neumanns since the late 1920s, when he was completing his doctorate at Princeton. He particularly liked Ma von Neumann's first wife, and both she and Desmond Kuper, the physi for whom she had left von Neumann in 1937, would be amongst of Morse's recruits in 1946 when he became director of the Broo nuclear laboratory on Long Island. He also liked von Neumann regarded as smarter than Oppenheimer and more versat
Figure 12.2. Barrier patrol versus divi barrier is at x and submarine matical Problems in Operations Rese ety, Vol. 54, pp. 602-21. With permissi
POSITION OF BARRIER, * - Barrier patrol versus diving submarine. P(x) = probability of contact if at x and submarine is surfaced. Credit: From Philip Morse (1948). "Mathe
ms in Operations Research". Bulletin of the American Mathematical Soci
602-21. With permission from the American Mathematical Society,
Morse was thus being advised on the use of minimax the problem, in Washington in late 1942, before the Theory appeared: "Johnny von Neumann was round, genial, help! in everything. No one leven knew could as quickly grasp the ess halting explanations, point out the crux of the difficulty, and to solve it. He would really listen, while simultaneously the implications of what he was hearing have him come out with
mond Kuper, the physicist 937, would be amongst the first ame director of the Brookhaven
liked von Neumann, whom he enheimer and more versatile than Einstein.
use of minimax theory in the search
before the Theory of Games even s round, genial, helpful, and interested
y grasp the essence of one's
ifficulty, and suggest ways taneously thinking through
Whether in sections or all a total distance, a: the res point along the channel, in surveillance (Figure 12.2).
P(x) is the probability of distance from
sections or all at once, the submarine can only travel submerged ance, a: the rest of the time it is visible. The plane must choose a
the channel, the width of which varies, at which it will traverse
" is the probability of detection if the plane patrols at a point at m the channel entry, given that the submarine is visible at that
Labor the probability
8:42
of Game The
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commander normally decides to implement one of his teative strategesh Briey can select Strategy 1. 2. 3. shown in the diagram by vertical reseve
e pure strategies by von Neumann With von Neumann's more stronges ey is free to select any intermediate position between his strategies and s o
2 and 3 or 3 and 41 Rather than assuring the main pure wages. can obtain an expectation of the maximin of mixed strategies ure 1 . Mand Strategies for the Avancer-up Situation. Chat Repented by per
on from Haywood, O. G. "Military Decision and Game Theory Journal of the Pations Research Society of America, Vol. 2, No. 4, 1954. Copyright 1954. the Institute
perations Research and the Management Sciences, 7240 Parkway Drive, Suite 300 Hanover, Maryland 21076
ONGEA WTERAWAL
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gure 43. Then the extensive formschematically in e 49 is suggested Notice that the first move
game is a move by Nation, which domes the unit so be monopolist. Then, depending on what Nature
the monopolist chooses her first period price-uantity The entrant observes this price quantity choice but not
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competition in the the antwol dans le the sonop 's curly actions
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* A mation of the city degmonapolis wory where the entrants of the monopolist's costs
gure 43. Then the extensive formschematically in e 49 is suggested Notice that the first move
game is a move by Nation, which domes the unit so be monopolist. Then, depending on what Nature
the monopolist chooses her first period price-uantity The entrant observes this price quantity choice but not
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choose to enter then the polistagan chooses quay pal for the we e d But if the entrant
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Equilibrio de Nash
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Contenido relacionado
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, the players use the
Eficiencia de Pareto
However there is a dosed loop Pareto optimum which give 1.4 with the
and the required control
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Game Theoretic Growth
155
Player 2
154
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Pareto optimum
Player 1 -
3.1
2.3
Nash Equilibrium that is also a Pareto optimum
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Player 2
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2,0
1.5
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Player 1
3.2
2.2
Player 2
2.3
Player 1 —
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Pareto optimum
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272Player 1 -
1 -13 0.1
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Fig. 9.2. (a) Transitions from Xi (b) Transitions from X, (c) Transitions from
X, (d) Transitions from X, .
NO
IX
Player 2
0
3
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2.4
Pareto optimum -Nash Equilibrium
Player 1
FIG.9.3. Backward recursion from t = 3 tot 1.
FIO. 9.1.
the cumulative profits from t=1, assuming that at t = 2, the players use the Nash controls obtained in Fig. 9.2. The closed loop Nash trajectory is
x(0) = Xg, x()=, . x(2)= X and the required Nash controls are given by the sequence 01, 11, giving total profits (2, 4). I.e.
w(1)-0, uf(2)=1, u (1)=1, uz (2)=1 However there exists a closed-loop Pareto optimum which gives total profits (3, 4), with the trajectory:
x(1)=xo, x(1)=X10, x(2)=X23 and the required controls given by the sequence 01.01, i.e.
up (1)-0, u (2)=1
(1)=0, u(2)=1.
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Fr. 9.2. (a) Transition from (b) Transions from X
X id) Transition from
Player 2
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2.4
Pareto optimum
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4
15
Fig. 9.3. Backward recursion from
3 to
1.
Pro 9.1
the cut e profits from I, assuming that at 2. the players use the Nash controls obtained in Fig. 9.2. The dosed loop Nash trajectory is
=> [=*..*(2) * and the required Nash controls are given by the sequence 1, 11, giving total profits . le.
(1)-0 (2)-1, w(1)-1. (2)=1 However there exists a closed-loop Pareto optimum which gives total profits (3.4), with the trajectory:
x(1) Xox(1) X10 (2) - X23 and the required controls given by the sequence 01.01.1.c.
(1)-0, (2)=1 (1)=0, (2)=1.
