An Introduction to Decision Theory

Axiom: An axiom is a fundamental premise of an argument for which no further justification is given. Example: According to the asymmetry axiom, no rational agent strictly prefers x to y and y to x.

Bargaining problem: The bargaining problem is a cooperative game with infinitely many Nash equilibria, which serves as a model for a type of situation that arises in many areas of society: A pair of players are offered to split some amount of money between the two of them. Each player has to write down his or her demand and place it in a sealed envelope. If the amounts they demand sum to more than the total amount available the players will get nothing; otherwise each player will get the amount he or she demanded. The players are allowed to communicate and form whatever binding agreements they wish. A general solution to this problem was offered by Nash, who based his proposal on a small set of intuitively plausible axioms.

Bayes’ theorem: Bayes’ theorem is an undisputed mathematical result about the correct way to calculate conditional probabilities. It holds that the probability of B given A equals the probability of B times the probability of A given B, divided by the following two terms: the probability of B times the probability of A given B and the probability of not-B times the probability of A given not-B. Put in symbols:

Bayesianism: The term ‘Bayesianism’ has many different meanings in decision theory, statistics and the philosophy of those disciplines. Most Bayesian accounts of decision theory and statistics can be conceived of as claims about the correct way to apply Bayes’ theorem in various real-life contexts. In decision theory, Bayesianism is particularly closely associated with the view that probabilities are subjective and that rational decision makers seek to maximize subjective expected utility.

Cardinal scale: Cardinal scales are used when we measure objects numerically and differences or ratios between measurement points are preserved across all possible transformations of the scale. Example: Time, mass, money and temperature can be measured on cardinal scales. Cardinal scales can be divided into two categories, namely interval scales and ratio scales.