Equilibrium & Mechanism Design

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Abstractions about strategic equilibrium, cooperation, rationalizability, risk dominance, learning dynamics, regret, computation, and distributed mechanism design.

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.

• Contingent cooperator — An agent willing to contribute to a collective good when enough others are observed or expected to cooperate, but not unconditionally.
• Distributed algorithmic mechanism design — The design of incentive-compatible mechanisms whose communication and computation are performed across strategic networked agents rather than by one trusted center.
• Game form — A specification of players’ action sets and an outcome function, leaving each player’s preferences or utilities over outcomes unspecified.
• Mean-field game theory — A framework for strategic control in very large populations where each negligible agent responds to the aggregate state distribution generated by all agents.
• Mertens-stable equilibrium — A robust set-valued refinement of Nash equilibrium requiring strategically coherent equilibrium components to persist under admissible perturbations and satisfy invariance and rationality properties.
• Nash equilibrium computation — The computational problem of finding an exact or approximate Nash equilibrium from a represented game and reporting a strategy profile with bounded unilateral deviation gain.
• Non-cooperative game theory — The study of strategic interaction modeled through individual players’ actions and incentives without externally enforced binding coalition agreements.
• Quantal response equilibrium — A game-theoretic fixed point in which each player's action probabilities respond smoothly and positively to expected payoffs while beliefs are consistent with those same probabilistic choices.
• Rationalizable strategy — A game strategy that is a best response to some belief about opponents' strategies consistent with common knowledge of rationality, equivalently surviving iterated elimination of never-best responses.
• Risk dominance — An equilibrium-selection criterion favoring the coordination equilibrium with the larger basin of attraction under uncertainty about others’ actions.
• Stochastically stable equilibrium — An equilibrium state retaining positive limiting stationary probability as perturbation noise in an evolutionary or learning process vanishes.
• Swap regret — The cumulative improvement available in hindsight from consistently replacing every occurrence of each chosen action with a possibly different alternative action.
• Theorycraft — The mathematical and empirical analysis of game rules, statistics and hidden mechanics to compare builds, tactics or strategies and estimate optimal play.