1. 2008/01/30Lecture 11 Game Theory

2. 2008/01/30Lecture 12 What is Game Theory? Game theory is a field of Mathematics, analyzing strategically inter-dependent situations in which the outcome of your actions depends also on the actions of others.  Are mathematical models helpful?  Is strategic thinking really important?

3. 2008/01/30Lecture 13 Are mathematical models helpful? Physical phenomena Follow natural laws. We cannot ask objects for the reason behind the event.  Mathematical models are necessary. Economic phenomena Each person acts anyway she wants. She can explain why she took a specific action.  No mathematical model is needed (?)

4. 2008/01/30Lecture 14 Two alternative approaches Institutional knowledge: Look into the “facts” in detail.  Superficial knowledge alone cannot explain economic movement. Economic Theory: Look for the “laws” behind facts. Q: What’s the fundamental economic law? A: Each person acts for her own interest.

5. 2008/01/30Lecture 15 Advantages of math models Mathematical model can be served as a Guideline for fact-finding. Device of checking consistency between different explanations. Common language shared by researchers. Two approaches are both important: not substitute, but complement.

6. 2008/01/30Lecture 16 Is strategic thinking relevant? In price theory, the market outcome is derived by the intersection of the demand curve and the supply curve. (demand-supply analysis) There is no strategic inter-dependence in its framework. Q: What’s the underlying assumption? A: Each economic agent is a “price-taker.”

7. 2008/01/30Lecture 17 The birth of Game Theory Q: Are most of problems in Economics indeed mere applications of “constrained optimization”? A: NO! von Neumann and Morgenstern (1944) “We need essentially new mathematical theory to solve variety of problems in social sciences.”

8. 2008/01/30Lecture 18 Strategic Thinking: Example Example: Nintendo vs. Sony Nintendo’s action depends on how Nintendo predicts the Sony’s action. Nintendo’s action depends on how Nintendo predicts how Sony predicts the Nintendo’s action. Nintendo’s action depends on how Nintendo predicts how Sony predicts how Nintendo predicts the Sony’s action. and so on…

9. 2008/01/30Lecture 19 Revolution by Game Theory Game theory can solve the problem of strategic inter-dependence by pinning down how to predict other players’ action. Therefore, game theory Provides us tools for analyzing important economic phenomena beyond market economy (with perfect competition). Enables us to compare different resource allocation mechanisms.

10. 2008/01/30Lecture 110 New Areas Pioneered by GT How does economy function if market is immature or not existing?  Economic History, Development Economics How do governments behave?  Political Economics What’s going on inside private companies?  Organizational Economics How to compare different types of market economy?  Comparative Institutional Analysis

11. 2008/01/30Lecture 111 Discovery by vN=M Any social problem can be formalized as a “game,” consisting of three elements: Players: i=1,2,…,N i’s Strategy: i’s Payoff: Q: What’s the solution of games?  They failed to establish a general solution concept…

12. 2008/01/30Lecture 112 Nash Equilibrium John Nash: “A Beautiful Mind” (movie) The solution of games must satisfy the following criterion. Nash equilibrium (mathematical definition)

13. 2008/01/30Lecture 113 Interpretations of NE. No one can benefit if she unilaterally changes her action from the original Nash equilibrium.  NE describes a stable situation. Everyone correctly predicts other players’ actions and takes best- response against them.  NE serves as a rational prediction.

14. 2008/01/30Lecture 114 Rationality Question Q: Does NE heavily depend on rationality of players? A: Not necessarily so. Example: NE in Evolutionary Biology Strategy = “phenotype” : a character of each animal determined by its gene Payoff = “fitness” : a number of the offspring NE is a stable situation reached not by rationality but by evolutionary dynamics.

15. 2008/01/30Lecture 115 Existence Question Q: Does NE always exist? A: Yes (in almost every cases). Theorem (Nash, 1950) “There exists at least one Nash equilibrium in any finite games in which the numbers of players and strategies are both finite.”