52 Prisoner’s Dilemma
Two accomplices are interrogated separately. Each may Co-operate (stay silent) or Defect (betray). Mutual co-operation yields 2 years each; mutual defection 5 years each; unilateral betrayal frees the defector and jails the co-operator for 10 years. Because defection strictly dominates, rational agents defect, landing at 5 + 5 instead of 2 + 2. The dilemma exposes a chasm between individual rationality and collective welfare and underpins research on repeated play, reputation, and mechanisms—ranging from treaty verification to microbial cooperation—that can sustain co-operative equilibria.
53 Parrondo’s Paradox
Game A: toss a biased coin, lose on average. Game B: toss one of two coins whose bias depends on your current capital modulo some number; B also loses on average. Astonishingly, alternating A and B (or mixing them stochastically) produces a winning expectation. The secret is non-linearity: Game B’s state-dependent bias lets the fluctuations introduced by Game A steer the system into the favourable sub-state more often. Parrondo’s insight applies to Brownian ratchets, financial hedging, and evolutionary strategies where two disadvantages combine into an advantage.
54 Newcomb’s Problem
Two boxes: Box A contains $1 000; Box B contains either $1 000 000 or $0. A predictor with near-perfect accuracy has already placed $1 000 000 in B iff she predicted you will take only B. You now choose between B alone or A + B. Dominance reasoning says pick both: either way you add $1 000. Evidential reasoning says one-box: your choice correlates with what is already inside B, and one-boxing nets $1 000 000 in 99.9 % of matched cases. The stalemate forces decision theorists to distinguish causal from evidential expected utility and has spawned variants such as timeless or functional decision theory.
55 Allais Paradox
Choose between (A1) $1 000 000 for sure, and (B1) 89 % chance $1 000 000, 10 % chance $5 000 000, 1 % nothing. Most prefer A1 (certainty effect). Now choose between (A2) 11 % chance $1 000 000, 89 % nothing, and (B2) 10 % chance $5 000 000, 90 % nothing—here most prefer B2. Yet expected-utility theory with a single concave utility curve cannot accommodate both switches. The Allais paradox revealed non-linear probability weighting and led to prospect theory, where outcomes are framed relative to a reference point and small probabilities are overweighted.
56 Ellsberg Paradox
An urn holds 30 red balls and 60 balls that are either black or yellow in unknown proportions. Bet 1 pays $100 if red is drawn; Bet 2 pays $100 if black. Most people pick Bet 1 (known 1⁄3 probability) over Bet 2 (ambiguous). Offered Bet 3 (red or yellow) versus Bet 4 (black or yellow), they switch, again avoiding the ambiguous colour. The pattern violates expected-utility independence and exposes human ambiguity aversion. The result stimulated models like max-min expected utility and smooth ambiguity to capture preferences under unknown probabilities.
57 Braess’s Paradox
Adding a new road to a traffic network can increase overall congestion. Drivers selfishly reroute to what is now (individually) the shortest path, but the collective shift overloads critical links, lengthening everyone’s travel time. Removing the road later restores smoother flow. Braess’s paradox generalises to data networks and power grids, warning engineers that more capacity does not guarantee better performance without accounting for strategic agent behaviour.
58 Friendship Paradox
On average, your friends have more friends than you do. Graph-theoretic proof: high-degree nodes appear in more friendship pairs and thus are over-represented in acquaintances’ friend counts. The paradox warps perception: popular people dominate social sampling, leading individuals to underestimate their own centrality or overestimate risky behaviours (“everyone else is partying”). Understanding the bias guides network epidemiology and peer-comparison interventions.
59 Samaritan’s Dilemma
A donor wishes to aid a recipient in need, but the prospect of aid may encourage the recipient’s dependency or under-investment (moral hazard). The donor would like to pre-commit to helping only genuine hardship cases, yet ex post compassion induces aid even for avoidable predicaments. Anticipating this, recipients reduce effort. The dilemma motivates conditional aid schemes (work requirements, insurance deductibles) and highlights the tension between altruism and incentive compatibility.
60 Tullock Paradox
Political economists predict that rent-seeking groups will spend up to the full value of a monopoly privilege to secure it. Empirically, lobbying expenditures are often far smaller than the available rents. Explanations include coordination costs among potential rent seekers, diminishing marginal returns to lobbying, and informational uncertainty about success probabilities. The paradox thus nuances public-choice theory: while rent-seeking is real, the efficiency losses may be bounded by strategic frictions.
Leave a Reply