Read a descriptive note bellow
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Teaching undergraduate students basic concepts of game theory might not be as intuitive as many economics instructors might hope. Having students experiencing these concepts and developing them by themselves is a much more effective and lasting approach. This interactive game provides the instructor with the perfect tool for doing so. The main concept to be explored with this game is backward induction. The game also helps in teaching the concepts of best response and the strategic advantage of being the first or the second mover. In this game each player can remove 1 to 3 buttons in each play, starting with 17 buttons. The player to remove the last button wins. The optimal winning strategy is to always leave the opponent with a multiple of 4 buttons. Students quickly notice that a player facing 4 buttons cannot win. In another round, they realize that in fact a player facing 8 buttons cannot win, since for any possible play, the opponent can lead her to the 4-button scenario. This will help teaching the concept of best response. With enough repetitions they realize that it is possible to extend this reasoning to the start of the game and know the winner even before the game starts. This is precisely the concept of backward induction that the instructor wants to teach with this game. This game also illustrates that the first mover has a strategic advantage. Clicking the Rules button you will find detailed rules of the game and a generic derivation of the optimal strategy and game solution. With the Configuration button you can change the game parameters to suit her needs. For example, by changing the starting number of buttons to 16 the second mover will have the strategic advantage. My suggestion is to project the game in the front of the class and call two students to play. Let them play in a system in which winner stays and a new challenger comes. Let the winner and/or the challenger announce if their strategy depends at all on being the first or second mover. Since being the first mover is the winning position of the game, this will reveal the students’ current understanding of the game. Once you notice a student figured the game out, you can have her announcing her strategy to the class. |
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