香港科技大学：Advanced Topics in Next Generation Wireless Networks

香港科技大学：Record Linkage for Big Data

香港科技大学：《软件开发》教学资源（PPT课件讲稿）Functions

香港科技大学：Clustering（PPT讲稿）

香港科技大学：Latent Tree Models

香港科技大学：社会影响与信息传播（PPT讲稿）SOCIAL INFLUENCE AND INFORMATION DIFFUSION

香港科技大学《基础数学》讲义之：基础代数学

then there exists AE R\ such that (Kuhn-Tucker condition) G(s') =0 and 1. Lagrange Method for Constrained Optimization FOC: D.L(,\)=0. The following classical theorem is from Takayama(1993, p.114). Theorem A-4 (Sufficieney). Let f and, i= ,..m, be quasi-concave, where Theorem A-1. (Lagrange). For f: and G\\, consider the following G=(.8 ) Let r' satisfy the Kuhn-Tucker condition and the FOC for (A.2). Then, x' problem is a global maximum point if max f() (1)Df(x') =0, and f is locally twice continuously differentiable,or

Thus, to find Nash equilibria in IN=N, A(Si)), uin, we use the conditions: for ach player i (1)he is indifferent among all strategies in St,and (2)any strategy in St is at least as good as any strategy in S Example 3.7.(Meeting in an Airport ). Mr Wang and Ms Yang are to meet in an irport. However, they do not know whether they are to meet at door a or door B. The payoffs are specified in the following

Social welfare function W: Rn-R gives social utility W(u1, u2,. un ). W is strictly increasing is socially optimal if it solves max Wu(a1), u2(a2),., un(n) st>Tis>w Proposition 1.29. If is SO, it is PO. I Proposition 1. 30. Suppose that preferences are continuous, strictly monotonic, and strictly convex. Then, for any PO allocation x* with >>0,v i, there exist ai