STRATEGY An Introduction to Game Theory

One strategy does not dominate another if they yield the same payoff against some strategy of the other players.

For example, to check if one of player 1’s strategies dominates another, just scan across the two rows of the payoff matrix, column by column. You do not have to compare the payoffs of player 1 across columns. If the payoff in one row is greater than the payoff in another, and this is true for all columns, then the former strategy dominates the latter. If a strategy is not dominated by another pure strategy, you then must determine whether it is dominated by a mixed strategy.

The definition of a strategy (a complete contingent plan) requires a specification of player l’s choice at his second information set even in the situation in which he plans to select O at his first information set. Furthermore, we really will need to keep track of behavior at all information sets—even those that would be unreached if players follow their strategies—to fully analyze any game. That is, stating that player l’s plan is “O” does not provide enough information for us to conduct a thorough analysis.

1. Representing Games (1) elements of games : players, strategy set, information set, payoffs, preference P.7 (2) two forms to present a game : the extensive form, the normal form (3) strategy space, strategy profile P.23 (4) classic normal-form games: Matching Pennies, Prisoners’ Dilemma(solution to PD: repeated interactions, contracts, other external forces), Battle of Sexes, Hawk-Dove/Chicken, Coordination(solution: communication), Pareto Coordination, Pigs. P.31 2. Analyzing Behavior in Static Setting (1) strict/weak dominance. P.46 (2) best response. (3) relationship between dominance and best response IEDS (iterated elimination of dominated strategy) and UD (undominated strategies) P.60 Rationalization Strategies and BR (best response). P.60 UD=BR when there are only two players or in the situation of uncorrelated conjectures when there are more than two players .不相关推测 P.54 P.309 (4) if a game is dominant solvable with strict IEDS, then that outcome is the unique NE. if a game is dominant solvable with weak IEDS, then the outcome may not be unique NE. (5) weakly congruous: every strategy is best response. Example: NE一致性 p.81 best response complete: every best response is inside. Example: the entire strategy space both weakly congruous and best response complete are congruous. Example: the set of rationalizable strategies (6) mixed-strategy NE indifference principle U1(σ1, σ2)=U1(a, σ2)=U1(b, σ2) p.105 every finite game has at least one NE (pure or mixed) (7) applications location game and partnership game. P.67 Cournot duopoly model p.95 Bertrand duopoly model P.97 tariff setting by two countries P.98 for strictly competitive games, the NE is both players play security strategy. P.112 aside: sound strategy. Lecture4 class game: picking the right number: the one whose number is the closest to 2/3 times the group average is the winner in that group. Lecture2 (8) three kinds of strategic tensions first: the clash between individual and group interests. Example: prisoners’ dilemma. P.47 second: Strategic uncertainty. Example: coordination problem, stag hunt game. P.62 third: inefficient coordination. Example: QWERTY. P.89 aside: behavioral game theory. P.90 3. Analyzing Behavior in Dynamic Setting (1) sequential rationality and backward induction P.139 subgame perfect NE (SPE): it specifies a NE in every subgame of original game. P.142 Zermelo’s Theorem: evey finite perfect information game has a backward induction solution. Moreover, if no two payoffs are the same for any player, then there is a unique backward induction solution. Lecture5 (2) applications of SPE class game: picking chalks. Lecture5 Stackelberg competition(cournot duopoly model in sequential situation). Lecture5 advertising and competition. P.150 a model of limit capacity p.154 ultimatum games: power to the proposer. P.180 two-period, alternating-offer games: power to the patient. P.182 infinite-period, alternating-offer game. Discounting .P.186 game of duel. Lecture6 best price guarantee. Lecture6 (3) repeated games and reputation. P.210 In a repeated game, repeatedly playing a NE in every period is always a SPE; to support cooperation(that is not a NE of the stage game), there must be credible punishments and reward in the future. Prisoners’ dilemma and renegotiation. Lecture7 all religions promised after-life: making life an infinite game. Lecture8 when the discount factor goes to one, any individual rational payoff vector can be supported in SPE in an infinitely repeated game. P.222 goodwill and trading of a reputation. P.230 4. Information (1) asymmetric information, move of nature(chance node), type. P.238 (2) Bayesian NE(BNE): two method. P.256 (3) application of BNE private value, second price auctions. Lecute9 private value, first price auctions. Lecture9 common value, first price auctions. Lecture10 common value, second price auctions, Lecture10 a principal-agent game. P.249 lemon market p.262 the Cournot model with incomplete information. Lecture10 the Bertrand model with incomplete information. Lecture10 purification of mixed strategies. Lecture10 Adverse selection. Lecture10 (3) perfect Bayesian equilibrium(PBE): separating strategy and pooling strategy. P.277 (4) application of PBE jobs and school p.282 reputation and incomplete information p.285 homework5，Ex.2 5. Summary static dynamic Complete information NE SPE Incomplete information BNE PBE