UNDERSTANDING DECISION/ GAME THEORY FOR BETTER RISK ASSESSMENT.

4/11/2015
ISBN CODE: 230001567 | Kaustav.lahiri
FORTUNE
INSTITUTE
OF
APPLIED
SCIENCES.
UNDERSTANDINGDECISION/GAME
THEORY FOR BETTERRISK ASSESSMENT.

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DECISION THEORY AND RELATED
APPLETS.
Decision Theory:
Comes from the theory of choicein economics, psychology, philosophy, mathematics, computer
science, and statistics is concerned with identifying the values, uncertainties and other issues
relevant in a given decision, its rationality, and the resulting optimal decision. It is closely
related to the field of game theory; decision theory is concerned with the choices of individual
agents whereas game theory is concerned with interactions of agents whose decisions affect
each other.
Normative and Descriptive Decision Theory:
Normative or prescriptive decision theory is concerned with identifying the best decision to
take (in practice, there are situations in which "best" is not necessarily the maximal, optimum
may also include values in addition to maximum, but within a specific or approximate range),
assuming an ideal decision maker who is fully informed, able to compute with perfect accuracy,
and fully rational. The practical application of this prescriptive approach (how people ought
to make decisions) is called decision analysis, and aimed at finding tools, methodologies and
software to help people make better decisions. The most systematic and comprehensive
software tools developed in this way are called decision support systems.
In contrast, positive or descriptive decision theory is concerned with describing observed
behaviors under the assumption that the decision-making agents are behaving under some
consistent rules. These rules may, for instance, have a procedural framework (e.g. Amos
Tversky's elimination by aspects model) or an axiomatic framework, reconciling the Von
Neumann-Morgenstern axioms with behavioural violations of the expected utility hypothesis,
or they may explicitly give a functional form for time-inconsistent utility functions (e.g.
Laibson's quasi-hyperbolic discounting).
The new prescriptions or predictions about behaviour that positive decision theory produces
allow for further tests of the kind of decision-making that occurs in practice. There is a thriving
dialogue with experimental economics, which uses laboratory and field experiments to evaluate
and inform theory. In recent decades, there has also been increasing interest in what is

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sometimes called 'behavioral decision theory' and this has contributed to a re-evaluation of
what rational decision-making requires.
What Kind of Decision’s is required to develop the
theory?
CHOICE UNDER CERTAINTY:
This area represents the heart of decision theory. The procedure now referred to as expected
value was known from the 17th century. Blaise Pascal invoked it in his famous wager (see
below), which is contained in his Pensées, published in 1670. The idea of expected value is that,
when faced with a number of actions, each of which could give rise to more than one possible
outcome with different probabilities, the rational procedure is to identify all possible outcomes,
determine their values (positive or negative) and the probabilities that will result from each
course of action, and multiply the two to give an expected value. The action to be chosen
should be the one that gives rise to the highest total expected value. In 1738, Daniel Bernoulli
published an influential paper entitled Exposition of a New Theory on the Measurement of Risk,
in which he uses the St. Petersburg paradox to show that expected value theory must
benormatively wrong. He also gives an example in which a Dutch merchant is trying to decide
whether to insure a cargo being sent from Amsterdam to St Petersburg in winter, when it is
known that there is a 5% chance that the ship and cargo will be lost. In his solution, he defines
a utility function and computes expected utility rather than expected financial value (see[2] for a
review).
In the 20th century, interest was reignited by Abraham Wald's 1939 paper[3] pointing out that
the two central procedures of sampling–distribution–based statistical-theory,
namely hypothesis testing and parameter estimation, are special cases of the general decision
problem. Wald's paper renewed and synthesized many concepts of statistical theory,
including loss functions, risk functions, admissible decision rules, antecedent
distributions, Bayesian procedures, and minimax procedures. The phrase "decision theory"
itself was used in 1950 by E. L. Lehmann.[4]
The revival of subjective probability theory, from the work of Frank Ramsey, Bruno de
Finetti, Leonard Savage and others, extended the scope of expected utility theory to situations
where subjective probabilities can be used. At this time, von Neumann's theory of expected
utility proved that expected utility maximization followed from basic postulates about rational
behavior.

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Daniel Kahneman
The work of Maurice Allais and Daniel Ellsberg showed that human behavior has systematic and
sometimes important departures from expected-utility maximization. The prospect
theory of Daniel Kahneman and Amos Tversky renewed the empirical study of economic
behavior with less emphasis on rationality presuppositions. Kahneman and Tversky found three
regularities — in actual human decision-making, "losses loom larger than gains"; persons focus
more on changes in their utility–states than they focus on absolute utilities; and the estimation
of subjective probabilities is severely biased by anchoring.
Castagnoli and LiCalzi (1996), Bordley and LiCalzi (2000) recently showed that maximizing
expected utility is mathematically equivalent to maximizing the probability that the uncertain
consequences of a decision are preferable to an uncertain benchmark (e.g., the probability that
a mutual fund strategy outperforms the S&P 500 or that a firm outperforms the uncertain
future performance of a major competitor.). This reinterpretation relates to psychological work
suggesting that individuals have fuzzy aspiration levels (Lopes & Oden). Hence it shifts the focus
from utility to the individual's uncertain reference point. Pascal's Wager is a classic example of a
choice under uncertainty.
INTERTEMPORAL CHOICE:
Intertemporal choice is concerned with the kind of choice where different actions lead to
outcomes that are realised at different points in time. If someone received a windfall of several
thousand dollars, they could spend it on an expensive holiday, giving them immediate pleasure,
or they could invest it in a pension scheme, giving them an income at some time in the future.
What is the optimal thing to do? The answer depends partly on factors such as the
expected rates of interest and inflation, the person's life expectancy, and their confidence in
the pensions industry. However even with all those factors taken into account, human behavior
again deviates greatly from the predictions of prescriptive decision theory, leading to

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alternative models in which, for example, objective interest rates are replaced by subjective
discount rates.
INTERACTION OF DECISION MAKERS:
Some decisions are difficult because of the need to take into account how other people in the
situation will respond to the decision that is taken. The analysis of such social decisions is more
often treated under the label of game theory, rather than decision theory, though it involves
the same mathematical methods. From the standpoint of game theory most of the problems
treated in decision theory are one-player games (or the one player is viewed as playing against
an impersonal background situation). In the emerging socio-cognitive engineering, the research
is especially focused on the different types of distributed decision-making in human
organizations, in normal and abnormal/emergency/crisis situations.
COMPLEX DECISION MAKING PROCESS:
Other areas of decision theory are concerned with decisions that are difficult simply because of
their complexity, or the complexity of the organization that has to make them. Individuals
making decisions may be limited in resources or are boundedly rational. In such cases the issue
is not the deviation between real and optimal behaviour, but the difficulty of determining the
optimal behaviour in the first place. The Club of Rome, for example, developed a model of
economic growth and resource usage that helps politicians make real-life decisions in complex
situations. Decisions are also affected by whether options are framed together or separately.
This is known as the distinction bias.
HEURISTICS:
One method of decision-making is heuristic. The heuristic approach makes decisions based on
routine thinking. While this is quicker than step-by-step processing, heuristic decision-making
opens the risk of inaccuracy. Mistakes that otherwise would have been avoided in step-by-step
processing can be made. One common and incorrect thought process that results from heuristic
thinking is the gambler's fallacy. The gambler's fallacy makes the mistake of believing that a
random event is affected by previous random events. For example, there is a fifty percent
chance of a coin landing on heads. Gambler's fallacy suggests that if the coin lands on tails, the
next time it flips, it will land on heads, as if it's “the coin's turn” to land on heads. This is simply
not true. Such a fallacy is easily disproved in a step-by-step process of thinking. In another
example, when choosing between options involving extremes, decision-makers may have a

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heuristic that moderate alternatives are preferable to extreme ones. The Compromise Effect
operates under a mindset driven by the belief that the most moderate option, amid extremes,
carries the most benefits from each extreme.
GAME THEORY AND PATTERNS:
Game theory is the study of strategic decision making. Specifically, it is "the study
of mathematical models of conflict and cooperation between intelligent rational decision-
makers."[1] An alternative term suggested "as a more descriptive name for the discipline"
is interactive decision theory.[2] Game theory is mainly used in economics, political science, and
psychology, as well as logic, computer science, and biology. The subject first addressed zero-
sum games, such that one person's gains exactly equal net losses of the other participant or
participants. Today, however, game theory applies to a wide range of behavioral relations, and
has developed into an umbrella term for the logical side of decision science, including both
humans and non-humans (e.g. computers, animals).
Modern game theory began with the idea regarding the existence of mixed-strategy equilibrium
in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original
proof used Brouwer fixed-point theorem on continuous mappings into compact convex sets,
which became a standard method in game theory and mathematical economics. His paper was
followed by the 1944 book Theory of Games and Economic Behavior, co-written with Oskar
Morgenstern, which considered cooperative games of several players. The second edition of
this book provided an axiomatic theory of expected utility, which allowed mathematical
statisticians and economists to treat decision-making under uncertainty.
This theory was developed extensively in the 1950s by many scholars. Game theory was later
explicitly applied to biology in the 1970s, although similar developments go back at least as far
as the 1930s. Game theory has been widely recognized as an important tool in many fields.
With the Nobel Memorial Prize in Economic Sciences going to game theorist Jean Tirole in 2014,
eleven game-theorists have now won the economics Nobel Prize. John Maynard Smith was
awarded the Crafoord Prize for his application of game theory to biology.
REPRESENTATION OF GAMES AND INDUSTRY
MODELLING:

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The games studied in game theory are well-defined mathematical objects. To be fully defined, a
game must specify the following elements: the players of the game, the information available
to each player at each decision point, and the payoffs for each outcome. (Rasmusen refers to
these four "essential elements" by the acronym "PAPI".) A game theorist typically uses these
elements, along with a solution concept of their choosing, to deduce a set of
equilibrium strategies for each player such that, when these strategies are employed, no player
can profit by unilaterally deviating from their strategy. These equilibrium strategies determine
the equilibrium, to the game—a stable state in which either one outcome occurs or a set of
outcomes occurs with known probability.
Most cooperative games are presented in the characteristic function form, while the extensive
and the normal forms are used to define non cooperative games.
EXTENSIVE FORMS:
The extensive form can be used to formalize games with a time sequencing of moves. Games
here are played on trees (as pictured to the left). Here each vertex (or node) represents a point
of choice for a player. The player is specified by a number listed by the vertex. The lines out of
the vertex represent a possible action for that player. The payoffs are specified at the bottom of
the tree. The extensive form can be viewed as a multi-player generalization of a decision tree.
The game pictured consists of two players. The way this particular game is structured (i.e., with
sequential decision making and perfect information),Player 1 "moves" first by choosing
either F or U (letters are assigned arbitrarily for mathematical purposes). Next in the
sequence, Player 2, who has now seen Player 1's move, chooses to play either A or R.
Once Player 2 has made his/ her choice, the game is considered finished and each player gets
their respective payoff. Suppose that Player 1 chooses U and then Player 2 chooses A: Player
1 then gets a payoff of "eight" (which in real-world terms can be interpreted in many ways, the
simplest of which is in terms of money but could be extrapolated to include things such as eight
days of vacation or eight countries conquered or even eight more opportunities to play the
same game against other players) and Player 2 gets a payoff of "two".
The extensive form can also capture simultaneous-move games and games with imperfect
information. To represent it, either a dotted line connects different vertices to represent them
as being part of the same information set (i.e. the players do not know at which point they are),
or a closed line is drawn around them.

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NORMAL FORM:
The normal (or strategic form) game is usually represented by a matrix which shows the
players, strategies, and payoffs (see the example to the right). More generally it can be
represented by any function that associates a payoff for each player with every possible
combination of actions. In the accompanying example there are two players; one chooses the
row and the other chooses the column. Each player has two strategies, which are specified by
the number of rows and the number of columns. The payoffs are provided in the interior. The
first number is the payoff received by the row player (Player 1 in our example); the second is
the payoff for the column player (Player 2 in our example). Suppose that Player 1 plays Up and
that Player 2 plays Left. Then Player 1 gets a payoff of 4, and Player 2 gets 3.
When a game is presented in normal form, it is presumed that each player acts simultaneously
or, at least, without knowing the actions of the other. If players have some information about
the choices of other players, the game is usually presented in extensive form.
Every extensive-form game has an equivalent normal-form game, however the transformation
to normal form may result in an exponential blowup in the size of the representation, making it
computationally impractical.
Player 2
chooses Left
Player 2
chooses Right
Player 1
chooses Up
4, 3 –1, –1
Player 1
chooses Down
0, 0 3, 4

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CHARASTERISTIC FUNCTION FORM:
In games that possess removable utility separate rewards are not given; rather, the
characteristic function decides the payoff of each unity. The idea is that the unity that is
'empty', so to speak, does not receive a reward at all.
The origin of this form is to be found in John von Neumann and Oskar Morgenstern's book;
when looking at these instances, they guessed that when a union appears, it works against
the fraction as if two individuals were playing a normal game. The balanced payoff of C
is a basic function. Although there are differing examples that help determine coalitional
amounts from normal games, not all appear that in their function form can be derived from
such.
Formally, a characteristic function is seen as: (N,v), where N represents the group of people
and is a normal utility.
Such characteristic functions have expanded to describe games where there is no removable
utility.
CHARACTERISTIC FUNCTION FORM:
In games that possess removable utility separate rewards are not given; rather, the
characteristic function decides the payoff of each unity. The idea is that the unity that is
'empty', so to speak, does not receive a reward at all.
The origin of this form is to be found in John von Neumann and Oskar Morgenstern's book;
when looking at these instances, they guessed that when a union appears, it works against
the fraction as if two individuals were playing a normal game. The balanced payoff of C
is a basic function. Although there are differing examples that help determine coalitional
amounts from normal games, not all appear that in their function form can be derived from
such.
Formally, a characteristic function is seen as: (N,v), where N represents the group of people
and is a normal utility.
Such characteristic functions have expanded to describe games where there is no removable
utility.

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DESCRIPTION AND MODELLING:
The primary use of game theory is to describe and model how human populations behave.
Some scholars believe that by finding the equilibria of games they can predict how actual
human populations will behave when confronted with situations analogous to the game being
studied. This particular view of game theory has been criticized. First, it argued that the
assumptions made by game theorists are often violated when applied to real world situations.
Game theorists usually assume players act rationally, but in practice, human behavior often
deviates from this model. Game theorists respond by comparing their assumptions to those
used in physics. Thus while their assumptions do not always hold, they can treat game theory as
a reasonable scientific ideal akin to the models used by physicists. However, empirical work has
shown that in some classic games, such as the centipede game, guess 2/3 of the average game,
and the dictator game, people regularly do not play Nash equilibria. There is an ongoing debate
regarding the importance of these experiments and whether the analysis of the experiments
fully captures all aspects of the relevant situation.[8]
Some game theorists, following the work of John Maynard Smith and George R. Price, have
turned to evolutionary game theory in order to resolve these issues. These models presume
either no rationality or bounded rationality on the part of players. Despite the name,
evolutionary game theory does not necessarily presume natural selection in the biological
sense. Evolutionary game theory includes both biological as well as cultural evolution and also
models of individual learning (for example, fictitious play dynamics).
PERSPECTIVE OR NORMATIVE ANALYSIS MODELLING:
Some scholars, like Leonard Savage, see game theory not as a predictive tool for the behavior of
human beings, but as a suggestion for how people ought to behave. Since a strategy,
corresponding to a Nash equilibrium of a game constitutes one's best response to the actions of
the other players – provided they are in (the same) Nash equilibrium – playing a strategy that is

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part of a Nash equilibrium seems appropriate. This normative use of game theory has also
come under criticism.
TYPES OF GAMES:
COOPERATIVE VS NON COOPERATIVE:
A game is cooperative if the players are able to form binding commitments. For instance, the
legal systemrequires them to adhere to their promises. In non cooperative games, this is not
possible.
Often it is assumed that communication among players is allowed in cooperative games, but
not in non-cooperative ones. However, this classification on two binary criteria has been
questioned, and sometimes rejected.[41]
Of the two types of games, non cooperative games are able to model situations to the finest
details, producing accurate results. Cooperative games focus on the game at large.
Considerable efforts have been made to link the two approaches. The so-called Nash-
programme (Nash program is the research agenda for investigating on the one hand axiomatic
bargaining solutions and on the other hand the equilibrium outcomes of strategic bargaining
procedures) has already established many of the cooperative solutions as noncooperative
equilibria.
Hybrid games contain cooperative and non-cooperative elements. For instance, coalitions of
players are formed in a cooperative game, but these play in a non-cooperative fashion.
SYMMETRIC VS ASSYMETRIC:
A symmetric game is a game where the payoffs for playing a particular strategy depend only on
the other strategies employed, not on who is playing them. If the identities of the players can
be changed without changing the payoff to the strategies, then a game is symmetric. Many of
the commonly studied 2×2 games are symmetric. The standard representations of chicken,
the prisoner's dilemma, and the stag hunt are all symmetric games. Some[who?] scholars would
consider certain asymmetric games as examples of these games as well. However, the most
common payoffs for each of these games are symmetric.
Most commonly studied asymmetric games are games where there are not identical strategy
sets for both players. For instance, the ultimatum game and similarly the dictator game have

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different strategies for each player. It is possible, however, for a game to have identical
strategies for both players, yet be asymmetric. For example, the game pictured to the right is
asymmetric despite having identical strategy sets for both players.
ZERO SUM/ NON ZERO GAME:
Zero-sum games are a special case of constant-sum games, in which choices by players can
neither increase nor decrease the available resources. In zero-sum games the total benefit to all
players in the game, for every combination of strategies, always adds to zero (more informally,
a player benefits only at the equal expense of others). Poker exemplifies a zero-sum game
(ignoring the possibility of the house's cut), because one wins exactly the amount one's
opponents lose. Other zero-sum games include matching pennies and most classicalboard
games including Go and chess.
Many games studied by game theorists (including the infamous prisoner's dilemma) are non-
zero-sum games, because the outcome has net results greater or less than zero. Informally, in
non-zero-sum games, a gain by one player does not necessarily correspond with a loss by
another.
Constant-sum games correspond to activities like theft and gambling, but not to the
fundamental economic situation in which there are potential gains from trade. It is possible to
transform any game into a (possibly asymmetric) zero-sum game by adding a dummy player
(often called "the board") whose losses compensate the players' net winnings.
E
F
E 1, 2 0, 0
F 0, 0 1, 2
An asymmetric game

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SIMULTANEOUS VS SEQUENTIAL:
Simultaneous games are games where both players move simultaneously, or if they do not
move simultaneously, the later players are unaware of the earlier players' actions (making them
effectively simultaneous). Sequential games (or dynamic games) are games where later players
have some knowledge about earlier actions. This need not be perfect information about every
action of earlier players; it might be very little knowledge. For instance, a player may know that
an earlier player did not perform one particular action, while he does not know which of the
other available actions the first player actually performed.
The difference between simultaneous and sequential games is captured in the different
representations discussed above. Often, normal form is used to represent simultaneous games,
while extensive form is used to represent sequential ones. The transformation of extensive to
normal form is one way, meaning that multiple extensive form games correspond to the same
normal form. Consequently, notions of equilibrium for simultaneous games are insufficient for
reasoning about sequential games; see sub game perfection.
In short, the differences between sequential and simultaneous games are as follows:
Sequential Simultaneous
Normally denoted by Decision trees Payoff matrices
A
B
A –1, 1 3, –3
B 0, 0 –2, 2
A zero-sum game

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Prior knowledge
of opponent's move?
Yes No
Time axis? Yes No
Also known as
Extensive-form game
Extensive game
Strategy game
Strategic game
PERFECT INFORMATION VS IMPERCFECT INFORMATION:
An important subset of sequential games consists of games of perfect information. A game is
one of perfect information if all players know the moves previously made by all other players.
Thus, only sequential games can be games of perfect information because players in
simultaneous games do not know the actions of the other players. Most games studied in game
theory are imperfect-information games. Interesting examples of perfect-information games
include the ultimatum game and centipede game. Recreational games of perfect information
games include chess, goand mancala. Many card games are games of imperfect information,
such as poker or contract bridge.
Perfect information is often confused with complete information, which is a similar concept.
Complete information requires that every player know the strategies and payoffs available to
the other players but not necessarily the actions taken. Games of incomplete information can
be reduced, however, to games of imperfect information by introducing "moves by nature".

UNDERSTANDING DECISION/ GAME THEORY FOR BETTER RISK ASSESSMENT.

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