2. Properties Of PS. Additive(free entrance) y∈Y, and yEY, then y+y∈Y Convexity yeY, and y'EY, then ay+(1-a)y∈Y, here a∈[0,1 o Proposition: if Y is convex, so is v(q) o Proposition 2 if V(g) is convex, f(x)is quasi concave lecture 1 for Chu Kechen Honors Collegelecture 1 for Chu Kechen Honors College 2.Properties of PS. • Additive (free entrance) : • Convexity: See the fig. • Proposition1: if Y is convex, so is V(q). • Proposition2: if V(q) is convex, f(x) is quasi￾concave. y Y y Y y y Y   +  ,and , then   y Y y Y y y Y   + −   ,and , then (1 ) , here [0,1]     