Strategic Games & Equilibrium Concepts

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Abstractions about strategic interaction in classic games, covering canonical coordination and conflict games (stag hunt, battle of the sexes, hawk-dove game), solution concepts like dominant and dominated strategies, and design or auction mechanisms including game balance, kingmaker scenarios, and the Vickrey auction.

13 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.
• 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.
• Game — A bounded activity in which participants act under constitutive rules within an artificial challenge or play structure that gives states, actions, and outcomes game-internal significance.
• Game balance — Game balance is the deliberate tuning of rules, resources, risks, rewards, and player options so a game produces its intended distribution of viable strategies, difficulty, and competitive outcomes.
• 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.
• Kingmaker Scenario — A multiplayer endgame where a nonwinning participant can choose or decisively alter which rival wins.
• Max-dominated strategy — A game-theoretic strategy that is never a best response to any admissible strategy profile of the other players, even though no single alternative need yield a strictly higher payoff against every profile.
• Public Goods Game — Model voluntary contributions to a shared account whose private and group returns pull in different directions.
• 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.
• Vickrey Auction — A sealed-bid auction where the highest bidder wins but pays the second-highest bid, decoupling what you win from what you pay so that bidding your true valuation is the dominant strategy — no rival-modeling needed — and the item reaches whoever values it most.
• Zugzwang — A turn-based game condition in which the obligation to move worsens a player's position because every legal move is worse than a pass or an alternate-turn counterfactual.