Mechanism Basics

Game Theory · Axiom Academy

LESSON Mechanism Design Basics Understanding the fundamental components and concepts of mechanism design theory Outcome Space (X): The set of all possible final outcomes or allocations Message Space (M): The set of messages or strategies available to each agent Outcome Function (g): A function that maps messages to outcomes: g: M → X 2 Type Space and Private Information Type Space (Θᵢ): The set of all possible types for agent i Type (θᵢ): Agent i's actual private information, drawn from Θᵢ Type Profile (θ): The combination of all agents' types: θ = (θ₁, θ₂, ..., θₙ) Players: The agents participating in the mechanism Strategies: Each agent chooses a message mᵢ ∈ Mᵢ based on their type θᵢ Payoffs: Determined by the outcome g(m) and agent's type θᵢ Social Choice Function (f): Maps type profiles to desired outcomes: f: Θ → X Implementation in Dominant Strategies: Truth-telling is optimal regardless of others' strategies Bayesian Implementation: Truth-telling is optimal given beliefs about others' types Nash Implementation: Equilibrium strategies achieve desired outcomes Start with a goal: Define the social choice function f(θ) you want to achieve Design the mechanism: Choose message spaces M and outcome function g Analyze strategic behavior: Determine how rational agents will play the induced game Verify implementation: Check if equilibrium outcomes match your desired social choice function

This is the written version of the interactive lesson above. See the full Game Theory course.