22. Implementation Theory

Can a desired social choice rule be "implemented" as the outcome of Nash equilibrium — see the mandatory screening test, Maskin monotonicity, with your own eyes.

• Maskin Monotonicity — This scene tests whether a desired rule can arise as a game's equilibrium. Two people choose among three options. The test is called Maskin monotonicity. Suppose some option wins in one situation. In another situation, that option has fallen for nobody. If the rule then picks something else, it fails. No game can ever implement such a rule. A dictator rule passes the test. The pick-the-bottom rule gets a red violation. For example, your class votes on what to play. This week ⚽ soccer wins. Next week nobody has soured on soccer. If the result suddenly flips to 📚 reading, the rule is fishy. Such a rule cannot come from any fair game.