Quantitative and Analytical Reasoning: Statistics, Game Theory and Graphs
This domain tests the quantitative literacy the rest of the exam presumes: reading data summaries critically, solving small games, and interpreting graphs of economic relationships.
Descriptive statistics and inference
Mean, median and mode differ in sensitivity to outliers; report the median for skewed distributions such as income. Variance is the average squared deviation, standard deviation its square root, and the standard error of a mean is s/√n - the basis of confidence intervals and t-tests. A p-value is the probability of data at least this extreme if the null hypothesis is true; it is not the probability that the null is true. Type I error rejects a true null; Type II error fails to reject a false one; power is 1 minus the Type II rate. In regression, a coefficient is the conditional mean change in y per unit of x, and it is credible only if omitted variables, selection and simultaneity are addressed. Correlation is not causation.
Game theory
A Nash equilibrium is a profile where no player gains by unilateral deviation; a dominant strategy is best against every opponent action. The prisoner's dilemma has a unique inefficient Nash equilibrium, escapable through repetition, contracts, or reputation. Backward induction identifies subgame-perfect equilibria in sequential games. Mixed-strategy equilibria exist where pure ones do not.
Graphs
Read slopes as marginal relationships and areas as totals: consumer surplus above price and below demand, deadweight loss as the triangle between demand and marginal cost over suppressed output. Elasticity is not the slope; on a linear demand curve elasticity varies with the price–quantity ratio.
Worked example
Matching pennies: Row chooses Up or Down, Column chooses Left or Right. Row's payoffs are (Up,Left)=1, (Up,Right)=−1, (Down,Left)=−1, (Down,Right)=1; Column's are the negatives. No pure equilibrium exists. Let Row play Up with probability p. Column's payoff from Left is −p + (1−p) = 1−2p; from Right it is p − (1−p) = 2p−1. Indifference requires 1−2p = 2p−1, so p = ½, and by symmetry Column also mixes ½–½. Expected payoff is zero: the value of a fairly randomised zero-sum game.
Traps
Do not read the p-value as the probability of the hypothesis. Do not confuse statistical with substantive significance. Do not call an outcome a Nash equilibrium because it is optimal jointly. Do not equate the slope of a demand curve with elasticity. Do not read a correlation from a scatter plot as a causal effect without an identification argument.