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Chapter 3: An Introduction to Game Theory

Study

Summary

This chapter introduces basic concepts and game theoretic models that allow us to estimate how decision makers are likely to interact strategically. The focus is on noncooperative games because they capture the essence of the strategic situations that characterize international relations.

The chapter introduces the concept of the Nash equilibrium and demonstrates it first in the context of normal form games. Specifically, we analyze the prisoner's dilemma game and explain the strategic situation underlying it. The mixed-strategy Nash equilibrium is briefly mentioned.

Next, we move to introducing extensive form games. The chapter shows how to solve such games using backward induction and introduces the concept of the subgame perfect Nash equilibrium. The chapter explains the meaning of complete and perfect information games and shows the importance of counterfactual reasoning (off the equilibrium paths) in the context of extensive form games. The chapter demonstrates these points using the running example of the Iranian nuclear program.

Finally, the chapter shows how to solve games with uncertainty (incomplete information games) and demonstrates it in the context of U.S.-Iranian dispute over Iran's nuclear program. The chapter shows how beliefs about the type of the opponent affect the strategy that a player chooses. In this context, the chapter explains the concepts of cheap talk and costly signaling. The chapter demonstrates how to solve such games for the threshold probability, which makes the player with the incomplete information indifferent between his two strategies.

Review Questions

1. What is the main difference between cooperative and noncooperative games?
   



2. What is a Nash equilibrium?
   



3. What does it mean to act strategically (in the context if game theory)?
   



4. How many pure strategy Nash equilibria are there is the prisoner's dilemma game? What are they? Why other strategies are not Nash equilibria?
   



5. What is a mixed-strategy Nash equilibrium?
   



6. What is a subgame perfect Nash equilibrium? What is the difference between a subgame perfect Nash equilibrium and a simple Nash equilibrium?
   



7. What is cheap talk? What is a costly signal?
   



8. How do we solve games with incomplete information?