Posts
The Magic Dribble Book
The Magic Dribble Book Entry Two. Master Mind
Posts
18. Imperfect information: information sets and sub-game perfection
18. Imperfect information: information sets and sub-game perfection We consider games that have both simultaneous and sequential components, combining ideas from before and after the midterm. We represent what a player does not know within a game using an information set: a collection of nodes among which the player cannot distinguish. This lets us define games of imperfect information; and also lets us formally define subgames. We then extend our definition of a strategy to imperfect information games, and use this to construct the normal form (the payoff matrix) of such games. A key idea here is that it is information, not time per se, that matters. We show that not all Nash equilibria of such games are equally plausible: some are inconsistent with backward induction; some involve non-Nash behavior in some (unreached) subgames. To deal with this, we introduce a more refined equilibrium notion, called sub-game perfection. Whenever you find yourself in a tree, play nash equilibriu
17. Backward induction: ultimatums and bargaining
17. Backward induction: ultimatums and bargaining. Ben Polak We develop a simple model of bargaining, starting from an ultimatum game (one person makes the other a take it or leave it offer), and building up to alternating offer bargaining (where players can make counter-offers). On the way, we introduce discounting: a dollar tomorrow is worth less than a dollar today. We learn that, if players are equally patient, if offers can be in rapid succession, and if each side knows how much the game is worth to the other side, then the first offer is for an equal split of the pie and this offer is accepted. But this result depends on those assumptions; for example, bargaining power may depend on wealth. A proper exchange. One of a win win outcome. Wealth is much more than one could ever imagine. It's all the little things one has to experience with one another.