Amy and Becky are playing a game. Six cards – numbered 1 through 6 – are placed face down on the table. The cards are shuffled, and each one takes a card at random. The person with the higher number wins. Amy looks at her card and finds it is #2. Becky looks at hers and asks if Amy wants to trade her card. What should Amy’s response be? Note both players are rational.
If Becky had a 6, she wouldn’t ask for a trade, as #6 is guaranteed to win. If she had #5, the only card she benefits from is #6, something Amy would never trade. That eliminates #5 and #6 from the game. By extending the logic, 4 and 3 are also eliminated. That leaves #1 something Becky is happy to offer, but Amy will never accept.
So Amy’s answer to the call is a NO.
These types of games are known as the Iterated Elimination of Strictly Dominated Strategies (IESDS).
