I'm doing a self-study of Game Theory Evolving by Gintis, and am stuck on problem 4.16 "Poker with Bluffing".
The first question asks "Show that Ollie has 64 pure strategies and Stan has 8 pure strategies.". But no matter how I try to approach this, I can't get more then 4 strategies for Stan!
Here is the game tree for the game in question:
The question marks (?) in the figure mean that the payoff depends on who has the higher card.
Here is the game description:
- Two players, each with a deck of three cards: H (high), M(medium) or L (low).
- Each puts \$1 in the pot, chooses random card
- Ollie (P1) either stays or raises
- Stan (P2) simultaneously also stays or raises
- If both raise/stay - highest card wins the pot (tie - they take their money back)
- If Ollie raises, Stan stays Ollie gets the \$3 pot.
- If Stan raises and Ollie stays - Ollie gets another chance:
-> Drop - Stand wins the \$3 pot
-> Call - add \$1 to the pot.
Why does Stand have 8 pure strategies?