TAILIEUCHUNG - Game Thoery Instructor

In this course on game theory, we will be studying a range of mathematical models of con°ict and cooperation between two or more agents. The course will attempt an overview of a broad range of models that are studied in game theory, and that have found application in, for example, economics and evolutionary biology. In this Introduction, we outline the content of this course, often giving examples. | Stat 155 Yuval Peres Fall 2004 Game theory Contents 1 Introduction 2 2 Combinatorial games 7 Some definitions . 7 The game of nim and Bouton s solution. 10 The sum of combinatorial games. 14 Staircase nim and other examples. 18 The game of Green Hackenbush. 20 Wythoff s nim . 21 3 Two-person zero-sum games 23 Some examples. 23 The technique of domination . 25 The use of symmetry . 27 von Neumann s minimax theorem. 28 Resistor networks and troll games. 31 Hide-and-seek games. 33 General hide-and-seek games . 34 The bomber and submarine game. 37 A further example. 38 4 General sum games 39 Some examples. 39 Nash equilibrium . 40 General sum games with k 2 players. 44 The proof of Nash s theorem . 45 Some more fixed point theorems. 47 Sperner s lemma. 49 Proof of Brouwer s fixed point theorem . 51 Some further examples. 51 Potential games. 52 1 Game theory 2 5 Coalitions and Shapley value 55 The Shapley value and the glove market. 55 Probabilistic interpretation of Shapley value. 57 Two more examples . 59 6 Mechanism design 61 1 Introduction In this course on game theory we will be studying a range of mathematical models of con ict and cooperation between two or more agents. The course will attempt an overview of a broad range of models that are studied in game theory and that have found application in for example economics and evolutionary biology. In this Introduction we outline the content of this course often giving examples. One class of games that we begin studying are combinatorial games. An example of a combinatorial game is that of hex which is played on an hexagonal grid shaped as a rhombus think of a large rhombus-shaped region that is tiled by a grid of small hexagons. Two players R and G alternately color in hexagons of their choice either red or green the red player aiming to produce a red crossing from left to right in the rhombus and the .

• Sinh học
• The sum of combinatorial games
• Some examples
• General hide and seek games
• A further example
• Nash equilibrium
• Potential games
• Therapeutic Potential
• Principles and Application
• Thyroid Cancer Research
• Evaluation and Management
• Pediatric Thyroid Nodules
• Papillary Thyroid