Goal. Surface the idea of a strategy and of reasoning about what others will do, and use the result to motivate the difference between normal form and extensive form games.
The deck. There is a write-on deck at /decks/games/main.pdf: blank axes for each round's distribution, the ladder of iterated reasoning, and space to work out what a strategy is in each form of the game. Project it and annotate it live.
Play the 2/3 of the average game. Use Menti to collect each student's number, then reveal the distribution and the winning value (2/3 of the mean). Play a second round and ask students to explain how and why their number changed.
Discuss the Games chapter.
Discussion Point: After showing the definition for an extensive form game and a normal form game, ask what type of game the 2/3 of the average game is.
Discussion Point: After the definition of a strategy, ask what a strategy would look like for the 2/3 of the average game.
Discussion Point: After the definition of a strategy in an extensive form game, ask how we could modify the 2/3 game to be an extensive form game and what a strategy would look like.
Everything the class produces is theirs to fill in. These are the values I need to have ready for the rest of the boxes.
The ladder. If everyone picks uniformly at random the average is \(50\), so I should pick \(2/3 \times 50 \approx 33\). If everyone reasons that far the average is \(33\), so I pick \(22\). Iterating drives the number to \(0\), which is the unique Nash equilibrium: everybody choosing \(0\). A real class usually stops after one or two steps and lands somewhere in the twenties or thirties, which is the interesting gap to point at.
Which kind of game. In a normal form game everyone chooses simultaneously, with no information about what the others have done. In an extensive form game players move in sequence and can see what has happened. Ours is a normal form game, because we all submit a number at the same time and nobody sees anyone else's first.
Strategies. In the game we played, a strategy is just a single number in \(\{0, 1, \ldots, 100\}\). In the sequential version, a strategy has to say which number to pick for every number that could have been announced before you, so it is a function from what you have heard to what you play. That gap is the point of the page.
This activity feeds into the Nash equilibrium material. Use Question 1 (the in-class activity) on the Nash Equilibrium page to show students how the ideas here become a full-mark exam answer.
General email templates to send before and after this class. Fill in the bracketed placeholders before sending.
Hi all,
A reminder that our next Game Theory class covers Games.
All of the course materials, including the relevant chapter, are available
at https://vknight.org/gt/. It is worth skimming the chapter beforehand.
See you in class,
Vince
Dear all,
Thanks for your work in today's class on Games.
A recording is available here [RECORDING LINK] and on Learning Central.
All class resources are available at https://vknight.org/gt/.
Thanks,
Vince