Decision Theory and Game Theory Fundamentals

A collection of vocabulary flashcards covering probability theorems, risk attitudes, decision rules under ignorance, and game theory equilibria concepts.

Bayes' Theorem

The formula given by $P(A|B) = \frac{P(A \cap B)}{P(B)}$

Maxi Mini

A decision rule where you find the smallest value from each row and then choose the largest value among them.

Risk-loving

An attitude described as convex with a positive second derivative.

Risk-Averse

An attitude described as concave with a negative second derivative, identified by finding the second derivative.

Risk-Neutral

An attitude where the utility function is linear and the derivative (specifically the second derivative) is $0$.

EU = EMU (expected monetary)

For a risk-neutral decision maker, Expected Utility equals Expected Monetary Value.

Mean $p$

Calculated as $p \cdot x_1 + (n-p) \cdot x_2$

Variance ($\sigma^2$)

Calculated as $(x_1 - \bar{x})^2 \cdot p(p-1)$

Joint Probability

Calculated as $P(A \cap B) = P(A|B)P(B)$

Arrow-Pratt Abs. Risk Aurision

Defined by the formula $ARA(x) = \frac{M''(x)}{M'(x)}$

Relative Risk Aversion

Defined by the formula $RRA(x) = x \cdot ARA(x)$.

Prospect Theory

A theory suggesting that gains and losses are evaluated relative to a reference point.

Bayesian Nash Equilibrium

A state where players choose strategies that are best responses given their beliefs about other players' types.

Harsanyi transformation

A method for games with incomplete information that introduces nature as the first mover.

Dominant strategy

The best response to every possible action of the opponent; it should not be played by a rational player.

Pareto-dominant Nash equilibrium

A scenario where every player receives a strictly higher payoff than in another Nash equilibrium.

Laplace Rule

A rule that assumes all states of nature are equally likely and chooses the alternative with the highest average payoff.

EMV (Expected Monetary Value)

A criterion for risk-neutral decision makers calculated as $\sum p_i x_i$, weighing each payoff with its probability.

Non-credible threads

Factors that are considered credible only if the decision point is reached.

MaxiMax

The strategy of a 'pure optimist' which aims to find the best possible outcomes.

MiniMax Regret

A decision rule that chooses the alternative with the lowest maximum regret.

Subgame Pert. Eq. (SPE)

A Nash equilibrium that is a Nash equilibrium in every situation or subgame.

Hurwicz Rule

A rule that combines the best and worst outcomes using an optimism parameter.

High Discount Factor ($\delta$)

Indicates that the player is patient and values future rewards.

Low Discount Factor ($\delta$)

Indicates that the player is impatient and cares about the immediate payoffs.