3-10-2012 Lecture 2:1I. Solving Game TreesA. Strategies vs. actionsB. Equilibrium vs. outcomeII. Counting strategiesIII. Scope of Game TheoryA. Assumptions of A GameB. Basic Assumption of Game TheoryThere will be 6 HW assignments this quarter, given and due in class on Tuesdays. They will be graded by the TA's on effort, thus making them low stakes. 5/6 of your best scores will be counted towards your grade. These HW assignments are not expected to be done in one setting."What's your raising fund strategy?"- Strategies: Complex- Game Theory: multiple parts (ex. if ____ RF then ____)- Actions: Simple- ordinary language (ex. won't RF)Equilibrium Path(what happens) RF Not(5, 0) (0, 5) Off the Equilibrium PathRF Not RF Not (but part of RE)Inc wins Inc wins Chal wins Inc wins(5, -2) (5, 0) (0, 5) (7, 0) To solve: compare payoffs of who controls the nodeInc: 2 Strategies- Each has 1 action- RF- NChal: 4 Strategies- Each has 2 actions (because 2 nodes)- what to do if Inc RF- what to do if Inc NIncChal ChalChal's Equilibrium StrategyN if Inc RF , RF if Inc NOff the Equilibrium PathEquilibrium Path (counterfactual usually)(what we expect to play) explains why other player makes her choice*important in understanding / analysis Actions: each branch at a nodeStrategies: multiple actionsEquilibrium: multiple strategiesRollback Equilibrium: A set of strategies, one for each player, in which each player takes herbest action at each node given the choices of the others'tells us to look at strategic equivalents - Result of analysis; Answer for the HW problems- summarizes what we think is going on in the game & why- Inc: RF- Chal: N if Inc RF RF if Inc NRollback: aka Backward InductionOutcome: what happens? what have we observed?=Equilibrium Path- the last part of our analysis (after actions are highlighted; the set of highlighted paths from the top of the graph to the bottom)Suppose player has n nodesLet xi be the # of branches at node iPlayer's total # of strategies = xi x x2 x ... xnL M R L R L R L RStrategies:1: L, M, R (3)2: L L L R R R 2 x 2 x 2 = 8Play around with Game Trees and count the strategies for practice.We are currently discussing matters in the beginning of Chapter 3 in the book. While Chapter 1and 2 could be skimmed, Chapter 3 is very dense and should be read with a notebook and pencil.Alternative:- scorched earth- different stakes (ex. already have funds)- yes / no choices (how much?)- asymmetric information (bluffing)12