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# Insurance Example
📗 Consider two insurance contracts, the insurer (players) pays \(\pi\) and in case of an accident (probability \(p\)) the insurance company (mechanism designer) pays the loss minus \(x - d = 1000 - d\).
➩ Contract 1 (low premium high deductible): \(\pi = 10, d = 500\).
➩ Contract 2 (high premium low deductible): \(\pi = 100, d = 100\).
📗 Suppose there are two types of players safe with \(p = 0.1\) and risky with \(p = 0.5\).
➩ Safe players prefers Contract 1: \(-10 - 0.1 \left(500\right) > -100 - 0.1 \left(100\right)\).
➩ Risky players prefers Contract 2: \(-10 - 0.5 \left(500\right) < -100 - 0.1 \left(100\right)\).
# Mechanism Design
📗 The mechanism design problem is about finding the set of contracts (designing a game) such that:
(1) The mechanism designer optimizes:
(i) Social welfare: sum of players' payoffs.
(ii) Revenue maximization: total transfer from the players to the designer.
(2) The players:
(i) Choose to participate in the mechanism (game).
(ii) Choose the contract (action) designed for them.
📗 The mechanism designer only observes the selected contract (action), not the types of the players.
# Revelation Principle
📗 Revelation principle reduces any mechanism to a direct mechanism (games where the action set is the same as the type set, i.e. players report their types instead of choosing an action, and the mechanism designer chooses the actions for the players):
(i) Choose to participate in the mechanism (game): Individual Rationality (IR).
(ii) Choose to report their type truthfully (not pretend to be another type): Incentive Compatibility (IC).
Last Updated: November 25, 2025 at 1:46 AM