• What is a mechanism?

    • A specification of a message space for each individual and an outcome function that maps vectors of messages into social decisions and transfers.
    • Bidding language
    • Winner determination rule
    • Payment rule

  • Whay is a mechanism design?

    • Sub-field of microeconomics and game theory
    • Goal: finding mechanisms compatible with individual incentives that result in:
      • Efficient decisions (maximizing total utility)
      • The voluntary participation of the individuals, and
      • balanced transfers (taxes and subsidies that net to zero across individuals).”

  • Of what components is a mechanism comprised?

    • Bidding language - what type of auction is used? Which instruments are used?
    • Winner determination rule - player with highest bid in Vickrey Auction
    • Payment rule - winner pays the second highest bid in Vickrey Auction

  • What is a mechanism‘s main goal?

    • Main goal of a mechanism is finding the best solution for the optimization problem

  • Describe the Mechanism Design Problem

    • The mechanism design problem is to implement an optimal system-wide solution
    • to a decentralized optimization problem
    • with self-interested agents
    • with private information about their preferences for different outcomes

  • How are the participants described?

    • Participant can be assigned to a agent type - by preferences, attributes, etc.
    • We can have a mechanism with two agent types - voting in the final stage of elections
    • Or we can have a mechanism where each agent has own type - english auction

  • What is a social choice function?

    • The outcome we want to achieve, dependent on the types of the agents
    • Example: population (set of different agents) want to chose a president

  • Properties a social choice function can implement.

    • Pareto Optimality: No alternative outcome is strongly preferred by at least one agent, and weakly preferred by all other agents
    • Allocation Efficiency: The outcome maximizes the total utility
    • Budget Balancing: The outcomes have balanced transfers across agents.
    • Individual Rationality: Are agents willing to participate? Does it make sense for them? → Is utility of “participate” not less then “not participate”

  • Social Choise Function, Mechanism and Mechanism Implementation

    • Mechanism defines the strategy space available to each agent and outcome rule
    • Mechanism Implementation: The Mechanism‘s outcome should achieve the Social Choice Function
    • → we have set of strategies of all agents, and outcome rule that requires the strategies of all agents and calculates outcome allocation. We want a mechanism that give us g(s(o)) = f(o)

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  • Direct and Indirect Mechanisms

    • Indirect mechanism: actor report his strategy (i want to invest in FTSI ETF), his risk aversity is unknown
    • Direct mechanism: actor report his type (i vote for Macron)

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  • What is a Revelation Principle?

    • Any indirect mechanism can be transformed into a direct-revelation mechanism using the revelation principle
    • You can chose your mix of risk and profit expectations, and market creates best portfolio for it
    • → Strategy can be constructed by the mechanism using the preferences of agent
    • → Only direct mechanisms are needed

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  • What does Strategy Proofness mean?

    • How do we prevent agents from lying?

    • A direct-revelation mechanism 𝑀 is strategy-proof if truth-revelation is a (at least weak) dominant-strategy equilibrium.

    • → Mechanism is strategy proofing, when the best strategy is to tell the truth (like in the Vickrey auction)

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  • What is Incentive Compatibility?

    • A mechanism is called incentive-compatible if every participant can achieve the best outcome to themselves just by acting according to their true preferences.

  • What is the difference between Incentive Compatibility and Strategy Proofness?

    • Strategy Proofing Mechanism that produces an outcome mathcing the social choise function is called Incentive Compatibile
    • Strategy Proofness is thargeted on one agent, Incentive Compatibile means Strategy Proofness for the group.

  • Explain how Vickrey-Clarke-Groves (VCG) Mechanisms works

    • Each agent should tell his valuation, sealed-bid (valuations of other agents are unknown)

    • Highest bid wins

    • Winner pays an amount that equal to his contribution to the autction result (sum of utilities of other agenrs is winner would not play in auction)

    • Example:

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      • A would pay the sum, that other players would get or lose in abscence of A. C would win both items (+6), and B will get nothing (-2). 6-2=4
      • B would pay the sum, that other players would get or lose in abscence of B. C would win both items, and A will get nothing (-5). 6-5=1