KC 1.1 Introduction to game theory
Suppose the game where a bill raises the limit on individual contribution to federal U.S.
candidates from $1000 till $5000 but prohibits contributions from all other sources. A
billionaire offers $1 Billion dollars to the party that had delivered the most votes to getting it
passed if the bill was defeated. If the bill passes, the billionaire donates nothing to anyone.
The outcome of this: the bill would sail through congress and thus cost the Billionaire
nothing.
KC 2.1-2.6 Hofstede.
Definition of culture by Hofstede:
Culture is “the collective programming of the mind distinguishing the members of one group
or category of people from others”.
6 Dimensions of national culture:
1. Power Distance Index (PDI)
Power distance has been defined as the extent to which the less powerful members of
organizations and institutions (like the family) accept and expect that power is distributed
unequally. This represents inequality (more versus less), but defined from below, not above.
It suggests that a society’s level of inequality is endorsed by the followers as much as by the
leaders.
The position of people in a society relative to each other is measured by the PDI on a scale
from 0 to 100. The higher, the larger the power distance. The scores can be assumed to be
stable over time because people learn values of power distance from their parents in their
childhood.
2. Uncertainty Avoidance Index (UAI)
Uncertainty Avoidance is not the same as risk avoidance; it deals with a society’s tolerance
for ambiguity. It indicates to what extent a culture programs its members to feel either
uncomfortable or comfortable in unstructured situations. Unstructured situations are
novel, unknown, surprising and different from usual. Uncertainty avoiding cultures try to
minimize the possibility of such situations by strict behavioral codes, laws and rules,
disapproval of deviant opinions, and a belief in absolute Truth; ‘there can only be one Truth
and we have it’.
3. Individualism vs. Collectivism (IDV)
Individualism on the one side versus its opposite, collectivism, as a societal, not an
individual characteristic, is the degree to which people in a society are integrated into
groups. On the individualist side we find cultures in which the ties between individuals are
loose: everyone is expected to look after him/herself and his/her immediate family. On the
collectivist side we find cultures in which people from birth onwards are integrated into
strong, cohesive in-groups. Often extended families that continue protecting them in
,exchange for unquestioning loyalty and oppose other in-groups.
It is measured relative to other societies. It is expressed in an IDV score from 0 to 100. The
larger the score, the more individual the country. The scores can be assumed to be stable
over time. The individualism goes up over time, but in every country, so the scores stay the
same.
4. Masculinity vs. Femininity (MAS)
Masculinity = manlike, femininity = womenlike. Masculinity versus its opposite, Femininity,
again as a societal, not as an individual characteristic, refers to the distribution of values
between the genders which is another fundamental issue for any society, to which a range
of solutions can be found. The woman in feminine countries have the same modest, caring
values as the men; in the masculine countries they are somewhat assertive and
competitive, but not as much as the men, so that these countries show a gap between
men’s values and women’s values.
5. Short-term Orientation vs. Long-term Orientation (LTO)
The long-term pole corresponds to Bond’s Confucian Work Dynamism. Values found at this
pole were perseverance, thrift, ordering relationships by status, and having a sense of
shame; values at the opposite, short term pole were reciprocating social obligations,
respect for tradition, protecting one’s face and personal steadiness and stability.
6. Indulgence vs. Restraint (IND)
Indulgence stands for a society that allows relatively free gratification of basic natural
human desires related to enjoying life and having fun. Restraint stands for a society that
controls gratification of needs and regulates it by means of strict social norms.
Lecture 1.1: Sequential Move Games
Different forms of games:
Simultaneous Move Games. Decisions are made simultaneously.
Sequential Move Games, decisions are made sequentially. Players move in turns.
A sequential move game is shown in a Game Tree.
A game tree consists of Initial nodes, Branches, Final nodes, Players decision nodes, actions
and Payoffs (see the picture).
, Assumptions in sequential move games:
Players are rational, they maximize their own payoff. They don’t care about the
payoff of the other person neither do they care about the amount of their payoff
compared to the payoff of the other player.
Common knowledge of the game.
Everyone knows that everyone is rational. So does Everyone know that everyone
knows that everyone is rational.
A sequential move game is solved by reasoning backwards.
Rule of Strategy 1: Look forward and reason backward.
Outcome of the game is Nash Equilibrium. That describes a stable situation.
If no player wants do deviate to another strategy given that the rest of the players are
playing the equilibrium strategy. So, no player wants to change strategy while being aware
of the opponent’s strategy.
Subgame perfect Nash Equilibrium is defined by the players’ choices in all decision nodes of
the game tree, for example: (E A3 T2, A1).
The Equilibrium path is the same as the equilibrium outcome and is the path you get when
you connect the initial note with the end note.
Choices OFF the equilibrium path are the choices of the equilibrium that do not lie on the
equilibrium path.
You write the subgame perfect Nash Equilibrium, Equilibrium outcome and the choices off
the Equilibrium path like this: P1 first, then P2 etc. Then go from the top to the bottom, left
first, then right.
The Equilibrium behavior in sequential move games depends on things that never happen
(the choices Off the Equilibrium path). The things that do happen, happen exactly because of
things that do not happen!
Experiment 1: The Thrust Game
Player A starts the game with 100 units. Player A could send a number of units between 0 ≤ x
≤100 to player B. The amount of units’ player A sends to B was either multiplied by 2 or 4.
Player B then could return a number of units between 0 ≤ y ≤ m times x to player A.
The theory of this experiment would predict the following outcome:
Player B maximizes his payoff by not transferring any units back to player A. Player A
anticipates this move, maximizing his own payoff, by not transferring any units to B in the
first place.
Suppose the game where a bill raises the limit on individual contribution to federal U.S.
candidates from $1000 till $5000 but prohibits contributions from all other sources. A
billionaire offers $1 Billion dollars to the party that had delivered the most votes to getting it
passed if the bill was defeated. If the bill passes, the billionaire donates nothing to anyone.
The outcome of this: the bill would sail through congress and thus cost the Billionaire
nothing.
KC 2.1-2.6 Hofstede.
Definition of culture by Hofstede:
Culture is “the collective programming of the mind distinguishing the members of one group
or category of people from others”.
6 Dimensions of national culture:
1. Power Distance Index (PDI)
Power distance has been defined as the extent to which the less powerful members of
organizations and institutions (like the family) accept and expect that power is distributed
unequally. This represents inequality (more versus less), but defined from below, not above.
It suggests that a society’s level of inequality is endorsed by the followers as much as by the
leaders.
The position of people in a society relative to each other is measured by the PDI on a scale
from 0 to 100. The higher, the larger the power distance. The scores can be assumed to be
stable over time because people learn values of power distance from their parents in their
childhood.
2. Uncertainty Avoidance Index (UAI)
Uncertainty Avoidance is not the same as risk avoidance; it deals with a society’s tolerance
for ambiguity. It indicates to what extent a culture programs its members to feel either
uncomfortable or comfortable in unstructured situations. Unstructured situations are
novel, unknown, surprising and different from usual. Uncertainty avoiding cultures try to
minimize the possibility of such situations by strict behavioral codes, laws and rules,
disapproval of deviant opinions, and a belief in absolute Truth; ‘there can only be one Truth
and we have it’.
3. Individualism vs. Collectivism (IDV)
Individualism on the one side versus its opposite, collectivism, as a societal, not an
individual characteristic, is the degree to which people in a society are integrated into
groups. On the individualist side we find cultures in which the ties between individuals are
loose: everyone is expected to look after him/herself and his/her immediate family. On the
collectivist side we find cultures in which people from birth onwards are integrated into
strong, cohesive in-groups. Often extended families that continue protecting them in
,exchange for unquestioning loyalty and oppose other in-groups.
It is measured relative to other societies. It is expressed in an IDV score from 0 to 100. The
larger the score, the more individual the country. The scores can be assumed to be stable
over time. The individualism goes up over time, but in every country, so the scores stay the
same.
4. Masculinity vs. Femininity (MAS)
Masculinity = manlike, femininity = womenlike. Masculinity versus its opposite, Femininity,
again as a societal, not as an individual characteristic, refers to the distribution of values
between the genders which is another fundamental issue for any society, to which a range
of solutions can be found. The woman in feminine countries have the same modest, caring
values as the men; in the masculine countries they are somewhat assertive and
competitive, but not as much as the men, so that these countries show a gap between
men’s values and women’s values.
5. Short-term Orientation vs. Long-term Orientation (LTO)
The long-term pole corresponds to Bond’s Confucian Work Dynamism. Values found at this
pole were perseverance, thrift, ordering relationships by status, and having a sense of
shame; values at the opposite, short term pole were reciprocating social obligations,
respect for tradition, protecting one’s face and personal steadiness and stability.
6. Indulgence vs. Restraint (IND)
Indulgence stands for a society that allows relatively free gratification of basic natural
human desires related to enjoying life and having fun. Restraint stands for a society that
controls gratification of needs and regulates it by means of strict social norms.
Lecture 1.1: Sequential Move Games
Different forms of games:
Simultaneous Move Games. Decisions are made simultaneously.
Sequential Move Games, decisions are made sequentially. Players move in turns.
A sequential move game is shown in a Game Tree.
A game tree consists of Initial nodes, Branches, Final nodes, Players decision nodes, actions
and Payoffs (see the picture).
, Assumptions in sequential move games:
Players are rational, they maximize their own payoff. They don’t care about the
payoff of the other person neither do they care about the amount of their payoff
compared to the payoff of the other player.
Common knowledge of the game.
Everyone knows that everyone is rational. So does Everyone know that everyone
knows that everyone is rational.
A sequential move game is solved by reasoning backwards.
Rule of Strategy 1: Look forward and reason backward.
Outcome of the game is Nash Equilibrium. That describes a stable situation.
If no player wants do deviate to another strategy given that the rest of the players are
playing the equilibrium strategy. So, no player wants to change strategy while being aware
of the opponent’s strategy.
Subgame perfect Nash Equilibrium is defined by the players’ choices in all decision nodes of
the game tree, for example: (E A3 T2, A1).
The Equilibrium path is the same as the equilibrium outcome and is the path you get when
you connect the initial note with the end note.
Choices OFF the equilibrium path are the choices of the equilibrium that do not lie on the
equilibrium path.
You write the subgame perfect Nash Equilibrium, Equilibrium outcome and the choices off
the Equilibrium path like this: P1 first, then P2 etc. Then go from the top to the bottom, left
first, then right.
The Equilibrium behavior in sequential move games depends on things that never happen
(the choices Off the Equilibrium path). The things that do happen, happen exactly because of
things that do not happen!
Experiment 1: The Thrust Game
Player A starts the game with 100 units. Player A could send a number of units between 0 ≤ x
≤100 to player B. The amount of units’ player A sends to B was either multiplied by 2 or 4.
Player B then could return a number of units between 0 ≤ y ≤ m times x to player A.
The theory of this experiment would predict the following outcome:
Player B maximizes his payoff by not transferring any units back to player A. Player A
anticipates this move, maximizing his own payoff, by not transferring any units to B in the
first place.
