Question

One version of the rational action model of decision making is expected utility theory. Examine the major tenets of this theory. How are payoffs and probability handled by proponents of this theory? Explain?

Answer 1

Propounded by Daniel Bernoulli who used it solve the St. Petersburg Paradox.Expected utility refers to the utility of an entity or aggregate economy over a future period of time, given unknowable circumstances. It is used to evaluate decision-making under uncertainty.

In other words,The expected utility theory deals with the analysis of situations where individuals must make a decision without knowing which outcomes may result from that decision, this is, decision making under uncertainty.

*The major tenets of theory are in the form of axioms which are four in number.

Completeness assumes that an individual has well defined preferences and can always decide between any two alternatives.

This means that the individual prefers A to B, B to A or is indifferent between A and B. This represents weak ordering hypothesis.

Transitivity assumes that, as an individual decides according to the completeness axiom, the individual also decides consistently. i. e if he prefers A more than B and B more than C, so when he will be given choice between A & C , he will always prefer A more than C

Independence of irrelevant alternatives pertains to well-defined preferences as well. It assumes that two gambles mixed with an irrelevant third one will maintain the same order of preference as when the two are presented independently of the third one. The independence axiom is the most controversial axiom.

• Axiom (Independence of irrelevant alternatives): Let A, B, and C be three lotteries with {\displaystyle A\succeq B}, and let {\displaystyle t} be the probability that a third choice is present: {\displaystyle t\in [0,1]};
  if {\displaystyle tA+(1-t)C\succeq tB+(1-t)C,} then the third choice, C, is irrelevant, and the order of preference for A before B holds, independently of the presence of C.

Continuity assumes that when there are three lotteries (A, B and C) and the individual prefers A to B and B to C, then there should be a possible combination of A and C in which the individual is then indifferent between this mix and the lottery B.

• Axiom (Continuity): Let A, B and C be lotteries with {\displaystyle A\succeq B\succeq C}; then there exists a probability p such that B is equally good as {\displaystyle pA+(1-p)C}.

If all these axioms are satisfied, then the individual is said to be rational and the preferences can be represented by a utility function, i.e. one can assign numbers (utilities) to each outcome of the lottery such that choosing the best lottery according to the preference {\displaystyle \succeq } amounts to choosing the lottery with the highest expected utility.

The Probabilty is used to calculate Expected Payoffs:

Probability is used to calculate expected values (or payoffs) for uncertain outcomes. • Suppose that an outcome, g y p y , e. g. a money payoff is uncertain. There are n possible values, X 1, X 2,...,X N. Moreover, we know the probability of obtaining each value. • The expected value (or expected payoff) of the uncertain outcome is then given b y: P(X 1)X 1+P(X 2)X 2+...P(X N)X N.