Dominique van Schagen
Filosofie literatuur
Peterson: Decisions under Ignorance
In decision theory, ignorance is a technical term with a very precise meaning. It refers to cases
in which the decision maker:
- Knows what their alternatives are and what outcomes they may result in but
- Is unable to assign any probabilities to the states corresponding to the outcomes
Also called decision under uncertainty.
If our desires and beliefs about the world are revealed by our choices, and partial beliefs can
be represented by a probability function, we are always able to assign probabilities to states
we know very little about.
Maximin and Leximin
Maximin principle focuses on the worst possible outcome of each alternative. One should
maximize the minimal value obtainable with each act.
Does not require that we compare outcomes on an interval scale.
Problem: it tells you to be indifferent between 2 acts if the minimums are the same. E.g. one
act will give you €1 or €2 and the other will give you €1 or €100, this algorithm tells you you
should be indifferent when you clearly shouldn’t.
Solution: lexical maximin à if worst outcomes are equal, choose the second worst. If you have
the same problem, choose the third, etc.
Game theory I: Basic Concepts and Zero-sum Games
A branch of decision theory in which the probability of the states depends on what you decide
to do.
Game theory II: Nonzero-sum and Cooperative Games
Nash equilibrium: “an equilibrium point is [a set of strategies] such that each
player’s…strategy maximizes his pay-off if the strategies of the others are held fixed. Thus,
each player’s strategy is optimal against those of the others.”
à most nonzero-sum games have more than one Nash equilibrium.
Pareto efficient state: a state is Pareto efficient if and only if no one’s utility level can be
increased unless the utility level for someone else is decreased. All Pareto efficient states
should be avoided.
Difference finite and infinite games: In finite games, the players know when the last round is
and they know that the other player knows this, too. In infinite games, no matter if it’s really
infinite or not, they do not know in advance that the next round will be the last one.
à Infinite games are likely to reach a tit-for-tat strategy.
Trembling hand hypothesis: the opponent made a mistake, without having any intention of
not trying to cooperate.
Filosofie literatuur
Peterson: Decisions under Ignorance
In decision theory, ignorance is a technical term with a very precise meaning. It refers to cases
in which the decision maker:
- Knows what their alternatives are and what outcomes they may result in but
- Is unable to assign any probabilities to the states corresponding to the outcomes
Also called decision under uncertainty.
If our desires and beliefs about the world are revealed by our choices, and partial beliefs can
be represented by a probability function, we are always able to assign probabilities to states
we know very little about.
Maximin and Leximin
Maximin principle focuses on the worst possible outcome of each alternative. One should
maximize the minimal value obtainable with each act.
Does not require that we compare outcomes on an interval scale.
Problem: it tells you to be indifferent between 2 acts if the minimums are the same. E.g. one
act will give you €1 or €2 and the other will give you €1 or €100, this algorithm tells you you
should be indifferent when you clearly shouldn’t.
Solution: lexical maximin à if worst outcomes are equal, choose the second worst. If you have
the same problem, choose the third, etc.
Game theory I: Basic Concepts and Zero-sum Games
A branch of decision theory in which the probability of the states depends on what you decide
to do.
Game theory II: Nonzero-sum and Cooperative Games
Nash equilibrium: “an equilibrium point is [a set of strategies] such that each
player’s…strategy maximizes his pay-off if the strategies of the others are held fixed. Thus,
each player’s strategy is optimal against those of the others.”
à most nonzero-sum games have more than one Nash equilibrium.
Pareto efficient state: a state is Pareto efficient if and only if no one’s utility level can be
increased unless the utility level for someone else is decreased. All Pareto efficient states
should be avoided.
Difference finite and infinite games: In finite games, the players know when the last round is
and they know that the other player knows this, too. In infinite games, no matter if it’s really
infinite or not, they do not know in advance that the next round will be the last one.
à Infinite games are likely to reach a tit-for-tat strategy.
Trembling hand hypothesis: the opponent made a mistake, without having any intention of
not trying to cooperate.
