Strategic Interaction & Game Theory

Abstractions about strategic interaction formalized as games — named payoff structures like the stag hunt, chicken, and prisoner's dilemma alongside solution concepts such as Nash refinements, dominance, mixed strategies, and repeated-game equilibria — that predict how rational agents coordinate, compete, or fail to.

23 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.

• Assurance Game — The stag-hunt game in which each player strictly prefers to cooperate if and only if the others do, producing two self-enforcing equilibria — a payoff-dominant cooperative one and a risk-dominant defection one — so the binding constraint is mutual confidence, not incentives.
• Battle of the Sexes — A 2×2 game in which both players prefer coordinating on some common outcome to failing, but each prefers a different one — so the conflict is not whether to cooperate but which of two cooperative agreements is reached, a distributional fight the payoff matrix cannot settle.
• 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.
• 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.
• Dominant Strategy — An action that yields a payoff at least as high as any alternative regardless of what opponents choose, so the player needs no model of the others — a belief-free best response that makes the strategic problem collapse to a row-by-row dominance check on the payoff matrix.
• Dominated Strategy — Rule out an action that yields a lower payoff than some alternative for every possible profile of opponents' actions — a belief-free test requiring no model of the opponent, licensing iterated elimination and the dominant-strategy robustness that mechanism design targets.
• 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.
• 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.
• Hawk–Dove Game — Model an anti-coordination contest with mutually destructive escalation as a 2x2 game whose entire equilibrium is fixed by the cost-to-prize ratio V/C — predicting a structural, tunable rate of costly conflict among fully rational players who would all prefer peace.
• 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.
• 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.
• 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.
• Stag Hunt — Model a cooperation problem in which the joint payoff-dominant choice and a certain safe choice are both equilibria, so the barrier to cooperating is not temptation but coordination under uncertainty about the partner — fixed by assurance, not enforcement.
• 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.
• 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.