MIT16_410F10_lec24

MIT16_410F10_lec24 - 16.410/413 Principles of Autonomy and...

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Unformatted text preview: 16.410/413 Principles of Autonomy and Decision Making Lecture 24: Sequential Games Emilio Frazzoli Aeronautics and Astronautics Massachusetts Institute of Technology December 6, 2010 E. Frazzoli (MIT) L24: Sequential Games December 6, 2010 1 / 21 Outline 1 Game Theory Overview Games in normal form: Nash equilibria, pure and mixed strategies Games in extensive form 2 Sequential Games E. Frazzoli (MIT) L24: Sequential Games December 6, 2010 2 / 21 Game Theory Games Multiple “players” independently choose actions, based on the available information, to pursue individual goals. Created by John Von Neumann in the late 1920s. Applications Economics Political Science/Diplomacy/Military Strategy Biology Computer Science/Artificial Intelligence Computer games Resource allocation in networks (internet, cell phones,...) Robust control (disturbance rejection) Air traffic collision avoidance UAV Pursuit-evasion E. Frazzoli (MIT) L24: Sequential Games December 6, 2010 3 / 21 Types of Games Zero-sum games All the gains/losses of a player are exactly balanced by the gains/losses of all other players (possibly modulo a constant). Zero-sum: a game of chess, tic-tac-toe, rock/paper/scissors, poker (with no house cut), risk, dividing a cake, presidential election, dogfights (?). Non-zero sum: contract negotiation, trade agreements, chicken and hawk/dove game, prisoners dilemma, MMORPGs, dogfights (?). Cooperative vs. non-Cooperative Games A game is cooperative if groups of players may enforce binding agreements. (E.g., through a third party, such as a legal system.) A game is non-cooperative if no such binding agreements exist. Cooperation may occur, but is self-serving. E. Frazzoli (MIT) L24: Sequential Games December 6, 2010 4 / 21 Types of Games, cont’d. Symmetric games The game is invariant to relabeling on the players. E. Frazzoli (MIT) L24: Sequential Games December 6, 2010 5 / 21 Types of Games, cont’d. Symmetric games The game is invariant to relabeling on the players. Sequential/simultaneous games In a sequential game, the players act at well-defined turns, and have some information on what the other(s) did at previous turns. In a simultaneous game, all players act at the same time, or equivalently, have no information on the actions of the others in the same turn. E. Frazzoli (MIT) L24: Sequential Games December 6, 2010 5 / 21 Types of Games, cont’d. Symmetric games The game is invariant to relabeling on the players. Sequential/simultaneous games In a sequential game, the players act at well-defined turns, and have some information on what the other(s) did at previous turns. In a simultaneous game, all players act at the same time, or equivalently, have no information on the actions of the others in the same turn....
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This note was uploaded on 12/26/2011 for the course SCIENCE 16.410 taught by Professor Prof.brianwilliams during the Fall '10 term at MIT.

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MIT16_410F10_lec24 - 16.410/413 Principles of Autonomy and...

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