哈佛大学博弈论 section1.ppt

GOV 2005: Game Theory Agenda What is game theory? Exercise: convergence to equilibrium Key terms and definitions Formal theory: what Leo has to say about it How do you do it (using formal theory) Application: Alliance Formation Final thoughts What Defines Game Theory? Mathematically precise List of players Complete description of allowable moves Description of information Specification of how actions cause outcomes Specification of players’ preferences Exercise: Moving to Equilibrium Three or Four Important Concepts Dominant Strategy One best strategy no matter what your opponent does Weakly dominant versus strongly (strictly dominant) strategies Mixed Strategy Moves are chosen randomly from the set of pure strategies Every simultaneous move game has a Nash equilibrium in mixed strategies Key Terms and Definitions Normal form and extensive form Nodes (initial, terminal) Information sets Strategy: complete contingent plan One for every information set Equilibrium: a stability concept Welfare Pareto optimality: no free lunch Formal Theory: What’s it good for? We have absolutely certain or scientific knowledge only of those subjects of which we are the causes… The construction must be conscious construction; it is impossible to know a scientific truth without knowing at the same time that we have made it. The world of our constructs is therefore the desired island that is exempt from the flux of blind and aimless causation. Applying Formal Theory Goal (research question) Story (model) Formalization (abstraction) Analysis (manipulation) Solution (definition of equilibrium) Translation (external and internal validity) Example: Alliance Formation Goal: Gain insight into dynamics of power and motivation What motivates countries to form alliances? Story: Setting: 3 countries fighting a war Each has power (military capability), which is positively associated with probability of winning Each is rational and has its own interests at heart Formalization States are i