statgames - GAME THEORY First Dose: Simultaneous Moves...

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1 G AME T HEORY First Dose: Simultaneous Moves Games 1 Game Theory is ideal for analyzing Multi-Person Decision Problems . We will use it to study strategic interactions among firms. A. What is a game? A game is a situation where the players or participants' payoffs depend both on own actions as well as on rival's actions. Hence, players' optimal behavior depends on opponents' behavior. That is what we call strategic interdependence . My optimal behavior depends on what you do in the game. When players move simultaneously, they would like to form a belief (prediction) about what the opponent will do. Example of strategic interdependence: The profitability of Airbus’ Super Jumbo depends on Boeing’s decision to introduce a Super Jumbo as well. If Boeing enters the market, both firms will probably lose money, as usually happens with aircrafts models that have a close substitute (eg DC10 vs L1011). Four elements are needed to describe a game. 1. players 2. rules: when each player moves, what actions are possible, what is known to each player at the moment they move… 3. outcomes 4. payoffs as a function of the outcomes. B. How to Represent a Game We will represent games using a matrix or a tree. A matrix representation is good enough for static (simultaneous move) games. For dynamic games, when moves are taken one after the other, we will see that trees capture additional details about the game that are essential for us to consider. Matrix Representation 1. Matching pennies: each player selects one side of a coin, if the coins match player 1 wins (gets one dollar from player 2), if they do not, payer 2 wins (she gets one dollar from player 1). The following matrix represents the relevant information about the game. 1 We will cover only games in which players know their opponents preferences (namely their payoffs). These are called games of complete information. Information about your opponent’s profits might be incomplete. For instance, a firm may not know how efficient the rival is. When buying a house you may have incomplete information about the seller’s reservation price. Games of incomplete information bring additional challenges, which we should not worry in this course, but in principle they are analyzed in roughly the same way as games of complete information.
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2 Player 2 Head Tail Head 1 ,-1 -1 , 1 Player 1 Tail -1 , 1 1 , -1 The matrix represents the players, their possible actions, the outcomes and payoffs. On the left of each cell (closer to Payer 1) we report the Player 1’s payoffs, in this case 1$ after HH and TT, and –1$ after HT or TH. On the right of each cell we report Player 2’s payoffs. Remember this convention to avoid mixing up the payoff of the players.
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This note was uploaded on 07/28/2010 for the course ECON 101 taught by Professor Hansen during the Fall '07 term at Wisconsin.

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statgames - GAME THEORY First Dose: Simultaneous Moves...

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