Game-Theoretic Models & Paradoxes

← Back to Domain-Specific Families

Abstractions about strategic interaction formalized as games, covering decision paradoxes and thought experiments (Allais, Ellsberg, St. Petersburg, Monty Hall), canonical named games (Chicken, Centipede, Ultimatum, Prisoner's Dilemma variants), and equilibrium refinements (Nash, subgame perfect, trembling-hand, Bayesian).

37 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Allais Paradox — An engineered pair of lottery choices whose majority preference pattern (A over B, D over C) violates the independence axiom of expected-utility theory, isolating the certainty effect as the culprit.
• Bayesian Nash Equilibrium — The solution concept for games of incomplete information: recast not knowing an opponent's payoffs as Nature drawing each player's private type from a common prior, then solve for a fixed point of type-conditional strategy functions where every type's action is a best response in expectation and the supporting beliefs are Bayes-consistent.
• Beauty Contest Game — Have players simultaneously pick a number to land closest to p times the group average, so that iterated best-response contracts the target toward zero — turning the infinite tower of 'what others expect others to expect' into a single measurable reasoning-depth scalar read off the choices.
• Bellman Equation — The recursive optimality condition V(s) = max over a of [R(s,a) + γ·E V(s')] that reframes a sequential decision problem as a fixed point in value space, collapsing a combinatorial search over policy sequences into a solvable |S|-dimensional problem.
• Berge–Zhukovskii Equilibrium — A normal-form game profile at which, holding any one player's own strategy fixed, no joint change by all the other players can raise that player's payoff—the mutual-support counterpart to Nash's own-deviation stability.
• Border's theorem — Border's theorem gives necessary and sufficient inequalities for whether interim allocation rules can be implemented by an auction.
• Centipede Game — A sequential finite-horizon game in which each player can take the larger share or pass to grow the pot, where backward induction prescribes taking on the first move — isolating common knowledge of rationality as the load-bearing assumption cooperation depends on.
• Chicken Game — A two-player payoff structure (DC > CC > CD > DD) where each side prefers the other to yield and mutual non-yielding is catastrophic but off-path, so the strategic question is not what to play but which asymmetric equilibrium gets selected — resolved by whoever can most credibly and irreversibly commit first.
• Cognitive Hierarchy Theory — Predict strategic play by mixing reasoning-depth types whose positive levels best respond to beliefs over all strictly lower levels.
• Decoy Effect — Add a third option that is worse than one existing choice on every dimension but not strictly worse than the other, and preferences shift toward the option that dominates the decoy — even though the decoy itself is never chosen.
• Determinacy — Classify a specified perfect-information win-or-lose game by whether one player has a strategy that defeats every possible counterplay.
• Dollar Auction — Mechanize the escalation trap with one rule change — the second-highest bidder also pays and gets nothing — so that backward induction makes each additional bid locally rational and rational players escalate past the prize's value.
• Edgeworth's limit theorem — Edgeworth's limit theorem is an economic theorem, named after Francis Ysidro Edgeworth, stating that the core of an economy shrinks to the set of Walrasian equilibria as the number of agents increases to infinity.
• Ellsberg Paradox — Show that people prefer betting on a known-composition urn over an ambiguous one of equal expected value on both colors at once — a pattern no single subjective probability can rationalize — proving ambiguity is a separately priced dimension of uncertainty distinct from risk.
• Folk Theorem (Repeated Games) — Show that in a sufficiently long, patiently discounted repeated game, almost any mutually acceptable outcome can be held as an equilibrium by credible intertemporal punishment — so repetition both explains cooperation and destroys predictive determinacy.
• Formula Game — Evaluate a closed quantified Boolean formula as a perfect-information contest in which Existential and Universal assign their variables in prefix order and truth is equivalent to Existential having a winning strategy.
• Glicksberg's theorem — A continuous zero-sum game result guaranteeing equality of maximin and minimax expected payoff over Borel mixed strategies on compact Hausdorff strategy spaces under the stated semicontinuity condition.
• Global Games — Pick a single prediction out of a coordination game's many self-fulfilling equilibria by giving each player a private noisy signal of a common fundamental and deleting dominated strategies inward until one threshold cutoff survives.
• Grim Trigger — A repeated-game strategy that cooperates every period until the opponent defects once, then switches to permanent defection forever — the severity-maximal, zero-forgiveness deterrent that sustains cooperation whenever the discount factor is high enough.
• Guess ⅔ of the Average — A single-shot game where each player picks a number closest to two-thirds of the group's mean — its Nash equilibrium of zero is never reached, and because each level of iterated best-response leaves a distinct numerical signature, the modal guess reads off a population's depth of strategic reasoning.
• Iterated Prisoner's Dilemma — The prisoner's-dilemma stage game (payoffs T > R > P > S) played over many observed rounds, where a high enough continuation probability lets the threat of future punishment deter present defection — turning the one-shot game's unavoidable mutual defection into sustainable cooperation.
• Kinetic Exchange Models of Markets — Model a market distribution through stochastic pairwise transfers of a declared conserved money or wealth stock.
• Kuhn's theorem — In game theory, Kuhn's theorem is a foundational result in the analysis of extensive-form games, first formalized by American mathematician Harold W.
• Matching pennies — Force randomization with the smallest strictly-competitive game — a matcher wins on agreement, a mismatcher on difference — where the best-response cycle admits no pure equilibrium and each player must mix to leave the opponent indifferent.
• Median Voter Theorem — Under majority rule with single-peaked preferences on one policy dimension, binary competition converges to the median voter's ideal point, because that position is the unique Condorcet winner — any platform away from it is beaten by one moving closer.
• Minority Game — Model any anti-coordination setting as an odd population repeatedly choosing between two actions where only the minority side wins, reading collective volatility off one control parameter — strategy diversity relative to population — that fixes a sharp crowded-versus-dilute phase transition.
• Mixed Strategy Equilibrium — Solve a game with no stable deterministic play by having each player randomize over their actions in exactly the proportions that leave every opponent indifferent, so no one can profitably deviate.
• Monty Hall problem — A worked three-door puzzle in which switching wins ⅔ of the time because the host's reveal was constrained by what he knew — drilling the move of updating on the protocol that produced an observation, not on its bare surface.
• Perfect Information — In an extensive-form game, every decision maker can identify the exact history at each turn, so every decision information set is a singleton.
• Pirate game — A toy sequential-bargaining model showing how backward induction in a propose-vote-or-eliminate mechanism lets the most senior proposer capture nearly the whole prize, because each voter's price is their continuation payoff and downstream subgames impoverish enough players to buy a cheap minimum coalition.
• Quantum Game Theory — A strategic-interaction framework in which admissible strategies are quantum operations or measurements on specified quantum systems, with measurement-induced outcome probabilities and payoffs compared against a protocol-matched classical strategy set.
• St. Petersburg Paradox — A gamble whose expected monetary value is infinite yet which real deciders will pay only a few coins to enter, exposing that a value function linear in money mishandles fat-tailed payoffs and must be replaced by a concave or bounded utility.
• Subgame Perfect Equilibrium — Refine the Nash equilibria of a sequential game by keeping only strategy profiles that prescribe a best response in every subgame, discarding outcomes propped up by threats a player would never actually carry out.
• Traveler's Dilemma — Isolate recursion depth as the variable governing whether an iterated-dominance equilibrium predicts behavior — using the same weak-dominance move as the Prisoner's Dilemma chained 98 times, so the $2 prediction evaporates while behavior tracks an incentive gradient the concept is blind to.
• Trembling-Hand Perfect Equilibrium — Filter the Nash equilibria by giving every action a vanishing positive probability of being played by mistake and keeping only those that survive as the tremble shrinks to zero, discarding equilibria propped up by threats that never have to be carried out.
• Ultimatum Game — A two-player, one-shot bargaining test in which a proposer splits a fixed stake and a responder may accept or reject for nothing, isolating costly punishment of unfairness by pitting the selfish equilibrium against the offers and rejections people actually make.
• Volunteer's Dilemma — A game where a shared good is produced if any single member pays a private cost to provide it, so each prefers someone else volunteer — and, counterintuitively, larger groups grow no more (often less) likely to produce it.