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Unformatted text preview: C H A P T E R 24 Strategic Thinking and Game Theory This chapter is a fresh start, so to speak. It does not directly build on any of the previous material in the text but instead constructs a new set of tools that allow us to think more clearly about the idea of strategic thinking when it matters. We have had little need for these tools up until now because so far, almost every- thing we have done relied on the assumption that individuals are small relative to their economic environment and thus in no need of strategic thinking. (There have been some exceptions to this in our chapter on adverse selection as well as in our chapter on monopoly where we have muddled through without the formal tools we are now introducing.) The new tool kit is known as game theory . Simply put, models will now take the form of games that incorporate real world incen- tives and thus allow us to focus on strategy. In part A of the chapter, we introduce complete information games, whereas in part B we focus on incomplete informa- tion games. Chapter Highlights The main points of the chapter are: 1. A game is defined by the set of players, actions (including the sequence in which actions are taken) and payoffs. When all actions are taken at the same time, the game is called a simultaneous move game , and when some players move ahead of other players, the game is called a sequential move game . 2. It is common for us to use a payoff matrix to represent a simultaneous move game and a game tree to represent a sequential move game (but it is possible to represent either type of game in either form.) 3. A strategy is a complete plan of action for the game not just the set of actions that is actually taken. In sequential move games, this implies that at least some players will have strategies that consist of actions which are not taken but which would be taken if the game evolved in a way that is different than the actual evolution of the game. Such plans for actions can play an Strategic Thinking and Game Theory 582 important role in determining how players interact in practice because knowing what other players would do if I changed by actions is important for me to think strategically about what I should do. 4. A Nash equilibrium is a strategy for each player such that every players strat- egy is a best response to the other players strategies. A subgame-perfect Nash equilibrium is a Nash equilibrium (in a sequential move game) that in- volves no non-credible threats. In sequential move games, every subgame- perfect Nash equilibrium is a Nash equilibrium but not every Nash equilib- rium is subgame perfect. 5. A dominant strategy is a strategy that is a best response to all strategies that other players might play. Most games do not have dominant strategies, but the Prisoners Dilemma is an important game that does. It is important in part because it is the starkest example of a game in which strategic thinking leads to sub-optimal outcomes.leads to sub-optimal outcomes....
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- Fall '08