This lecture (from May 1 2013, second hour) introduces several interpretations of probability….the language of uncertainty in game theory. We develop the idea of probability as measuring personal beliefs about uncertain events, then show how to “operationalize” – ie measure – those beliefs using simple betting situations. The idea is that a belief should be more than just a report – but a willingness to back up your report by making small scale bets on the events that are uncertain.
Following on from week 2’s short clip on PDIP and the 6 questions we introduce a simple sequential 2 player 2 move game – first in an abstract form using “cards” in class with both money and chocolate bar payoffs, then by telling a story about an attempt to deter entry of a competitor by investment in large capacity . Both stories have similar strategic structure…revealled in their game trees. Ina separate, subsequent clip for week 2 we introduce the idea of rolback reasoning – backward induction – to analyze this game. Note that the reasoning processes given by students in the classroom game is/was a great example of intelligent intuition based on rollback reasoning. The next clip for this week on rollback reasoning uses this intuition in a more structured way using the 2×2 game tree. It’s a fairly straightforward way of reasoning…but absent from so many political and institutional managers/players in all walks of life . Hopefully not you!!
This clip is an edited version of the last half an hour of lecture 3 in econ 223 Thurs Feb 21 2013
In Game Theory: A “strategy” for a player in a game is a “complete specification of what that player will do in all the circumstances they find themselves in”. Easy to say, sometimes not so easy to do – ie identify in a complex game or describe in words.
In some games “lists” are a convenient method of identifying strategies, as explained in this simple 2 person game example. It works well here – so try it in the 3 person “Garden Contributions sequential game” from Dixit , Skeath and Riley pp 61. You’ll quickly understand why the shorthand “list” way of describing a strategy is much superior to say trying to write down all of the logically possible strategies via a combination (conjunction) of “if….then…” statements. But in more complex games writing down discrete lists can be both tedious and confusing.