In this chapter, we will study the most well-known games in the literature, with the colourful names Prisoner’s Dilemma, Stag Hunt, and Chicken. I will also introduce you to the two most fundamental methods in game theory: normal form games, which we use when players move simultaneously, and extensive form games, when players move sequentially. You have already seen examples of simultaneous and sequential games in the previous chapter: the Cournot, Augustin, and Bertrand models are games with simultaneous moves, while the Stackelberg model is a game with sequential moves. In these games, the strategic variable is continuous, whereas in game theory we often consider a limited number of choices, for example, high or low price. We begin with simultaneous moves and look at the world’s most famous game: Prisoner’s Dilemma. We describe the Nash equilibrium in this game, and then move on to games with multiple equilibria, where the theory therefore does not give clear answers on what the outcome will be. Next, we study games with sequential moves, and how we use backward induction (that is, starting with the choice of the player who moves last) to find the equilibrium.

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Game Theory

  • Kjetil Bjorvatn

摘要

In this chapter, we will study the most well-known games in the literature, with the colourful names Prisoner’s Dilemma, Stag Hunt, and Chicken. I will also introduce you to the two most fundamental methods in game theory: normal form games, which we use when players move simultaneously, and extensive form games, when players move sequentially. You have already seen examples of simultaneous and sequential games in the previous chapter: the Cournot, Augustin, and Bertrand models are games with simultaneous moves, while the Stackelberg model is a game with sequential moves. In these games, the strategic variable is continuous, whereas in game theory we often consider a limited number of choices, for example, high or low price. We begin with simultaneous moves and look at the world’s most famous game: Prisoner’s Dilemma. We describe the Nash equilibrium in this game, and then move on to games with multiple equilibria, where the theory therefore does not give clear answers on what the outcome will be. Next, we study games with sequential moves, and how we use backward induction (that is, starting with the choice of the player who moves last) to find the equilibrium.