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2x2-games - Games Introduction Most of classical...

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Games - Introduction Most of classical microtheory is static. We assume that either a consumer’s choices don’t affect the prices she faces or else that she doesn’t realize that she affects them. Similarly, a firm makes decisions about production as a response to prices and demand assuming it’s production does not affect these market parameters. ECG 700 Static Games 1/ 24 Games - Introduction For many situations, these decisions interact. Dell’s prices depend on Apple’s prices which depend on Dell’s prices. The size of the USA’s army depends on the size of Russia’s army which depends on the size of the USA’s army. If you and I are bidding on an item on Ebay, my bid will depend on what I think you will bid, but your bid will depend on what you think I will bid. ECG 700 Static Games 2/ 24
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Games - Introduction A game is any situation with strategic interaction. Roulette is not a game. My choices I make do not affect your strategy in any rational way. Poker is a game. My strategy should be a function of your strategy and vice versa. Chess is a game. Blackjack is not a game. ECG 700 Static Games 3/ 24 Games - Introduction We will look at simple games and hope to gain economic insight from them. There are several elements to a game: Players (most important, how many are there?) Strategies. (often a strategy is just what action a player choses, but it can be much more complicated than this.) Payoffs. Timing. Do agents move at the same time or does one go first? Information. If I am selling you a car, I probably know more about the car than you do. How does this affect how we bargain? ECG 700 Static Games 4/ 24
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Static Games Definition An n -player, static game of complete information consists of an n -tuple of strategy sets and an n -tuple of payoff functions, denoted by G = { S 1 , . . . , S n : u 1 , . . . , u n } . S i , the strategy set of player i , is the set of all permissible moves for player i . We write s i S i for one of player i ’s strategies. u i , the payoff function of player i , is the utility, profit, etc. for player i , and depends on the strategies chosen by all the players: u i ( s 1 , . . . , s n ) .
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