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VI.GAME THEORY Brazil and Italy had played through two overtimes to a 0-to-0 tie in the final game of the 1994 World Cup. For the first time, the world championship of soccer (“football” to everyone in the world except Americans) was being decided by a penalty kick shoot-out. One by one, each team sent five players to take shots at the goal from a few yards in front of the net. The score was Brazil 3 and Italy 2 as Baggio, the European player of the year, stepped up to take the fifth, and possibly final, kick for Italy. Taffarel, Brazil’s goalie, knew that once the ball left Baggio’s foot, it would be too late to react. He had to make up his mind to throw his body one way or the other just as Baggio kicked the ball. Which way should Taffarel go? It all depended on what he thought Baggio was going to do. Which way should Baggio kick the ball? It all depended on what he thought Taffarel was going to do. (I’d really like to give an example from the match between Galatasaray- Arsenal but unfortunately Arsenal players hit the post) The situation just described is a “game” in two senses of the word. One, it is a sport. Two, it is a strategic situation: Each decision maker has to take into account what he or she thinks the other is going to do. Economists call any strategic situation -including, for example, oligopoly- a game. The notion of Nash equilibrium is part of a larger set of tools for analyzing strategic behaviour –in economics, politics, card games, and other arenas of conflict –known as non-cooperative game theory. This theory is labeled “non-cooperative” because each decision maker acts solely in his or her own self-interest. Despite the label, the theory is relevant to the analysis of cooperation. Even “selfish” economic agents will cooperate if doing so is in their self-interest. For example, a self-enforcing agreement among firms to cooperate in restricting industry output is non-cooperative in the technical sense of the word –each firm adheres to the agreement solely because it is in the firm’s self-interest to do so. In this chapter, we develop a useful way to represent strategic situations graphically, and we use this representation to analyze oligopoly further. In particular, we use game theory to investigate the behaviour of oligopoly when there is a threat of entry. We will also see how game theory provides important insights into behaviour in a variety of other strategic situations. It is often convenient to think of players’ behaviour in a game in terms of strategies. A strategy tell you what the player will do each time s/he has to make a decision. So, if you know the player’s strategy, you can predict his behaviour in all possible scenarios with respect to the other players’ behaviour. When you list or describe the strategies available to each player and attach payoffs to all possible combinations of strategies by the players, the resulting ‘summary’ of the game is called a normal form or strategic form representation. In games of complete information all players know the rules of the game. In incomplete information games at least one player only has probabilistic information about some elements of the game (e.g. the other players’ precise characteristics). An example of the latter category is a game involving an insurer -who only has probabilistic information about the carelessness of an individual who insures his car against theft- and the insured individual who knows how careless he is. A firm is also likely to know more about its own costs than about its competitors’ costs.
Approximate Word count = 2370
Approximate Pages = 9.5
(250 words per page double spaced)
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