Introduction to Game Theory Games with Continuous Strategy Sets推荐.pdf

Introduction to Game Theory: Games with Continuous Strategy Sets John C.S. Lui Department of Computer Science Engineering The Chinese University of Hong Kong John C.S. Lui (CUHK) Advanced Topics in Network Analysis 1 / 45 Outline Outline 1 Infinite Strategy Sets 2 The Cournot Duopoly Model 3 The Stackelberg Duopoly Model 4 Sequential Bargaining 5 Bank Runs 6 War of Attrition John C.S. Lui (CUHK) Advanced Topics in Network Analysis 2 / 45 Infinite Strategy Sets Introduction So far, we have considered players choose action from a discrete set. it is possible for that the pure strategy set is from subsets of the real line, or infinite dimension. For example, the pure strategy (action) sets are a subset of real number a b. A pure strategy is a choice x a b. A mixed strategy is defined by giving a function p x such that the probability that the choice lies between x and x dx is p x dx . The existence of NE for games with continuous pure-strategy sets was proved independently by Debreu, Glicksburg and Fan. Let us study some classical games with continuous strategy sets. John C.S. Lui (CUHK) Advanced Topics in Network Analysis 4 / 45 The Cournot Duopoly Model Cournot Duopoly Consider two firms competing for a market by producing some infinitely divisible product (e.g., petroleum). We allow firms to choose how much they produce, e.g., firm i decides on q , the quantity to produce, in which q 0 . i i Each unit production cost is