Game Theory Basics - Department of Mathematics

Chapter 2Games as trees and in strategic formThis chapter introduces the main concepts of non-cooperative game theory: game treesand games in strategic form and the ways to analyse them.We occasionally refer to concepts discussed in chapter 1, such as “game states”, toclarify the connection, but chapter 1 is not a requirement to study this chapter.2.1 Learning objectivesAfter studying this chapter, you should be able to:• interpret game trees and games in strategic form;• explain the concepts of move in a game tree, strategy (and how it differs from move),strategy profile, backward induction, symmetric games, dominance and weak dominance,dominance solvable, Nash equilibrium, reduced strategies and reduced strategicform, subgame perfect Nash equilibrium, and commitment games;• apply these concepts to specific games.2.2 Further readingThe presented concepts are standard in game theory. They can be found, for example, inthe following book:• Osborne, Martin J., and Ariel Rubinstein A Course in Game Theory. (MIT Press,1994) [ISBN 0262650401].Osborne and Rubinstein treat game theory as it is used in economics. Rubinstein isalso a pioneer of bargaining theory. He invented the alternating-offers model treated inchapter 5. On the other hand, the book uses some non-standard descriptions. For example,Osborne and Rubinstein define games of perfect information via “histories” and not gametrees; we prefer the latter because they are less abstract. Hence, keep in mind that the27