Transcription of Game Theory: Normal Form Games
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Game Theory: Normal Form Games
Game Theory: Normal form GamesMichael LevetJune 23, 20161 IntroductionGame Theory is a mathematical field that studies how rational agents make decisions in both competitiveand cooperative situations. It has widespread applications in economics, political science, psychology, biology,computer science, and data science. Some of the applications include radio spectrum auctions, voting, andorgan donations. These notes introduce the basic strategic form game, also known as the Normal form ModelIn this section, we formally define the Normal form game. Let s begin with some intuition. A Normal formgame has a set of players. Each player has a set of strategies. These players each select a strategy and playtheir selections simultaneously. In this manner, no player is responding to another s selection. Furthermore,we think of the players strategies as setting the rules of the game. Finally, the selection of strategies resultsin payoff or utility for each player.
The mixed extension of a normal form game considers the same set of players and utility functions. However, each player i’s strategy set in 0is ( S i), where ( S i) is the set of all probability distributions over i’s strategy set S iin . We then consider …
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