Compute the nash equilibria of the following location game. there are two people who simultaneously select numbers between zero and one. suppose player 1 chooses s1 and player 2 chooses s2 . if si < sj , then player i gets a payoff of (si + sj )> 2 and player j obtains 1 − (si + sj )> 2, for i = 1, 2. if s1 = s2 , then both players get a payoff of 1> 2. make sure to explain why the nash equilibrium (if exists) is what it is.

Given: lines a and b are parallel and line c is a transversal. prove: 2 is supplementary to 8 what is the missing reason in the proof? statement reason 1. a || b, is a transv 1. given 2. ∠6 ≅ ∠2 2. ? 3. m∠6 = m∠2 3. def. of congruent 4. ∠6 is supp. to ∠8 4. def. of linear pair 5. ∠2 is supp. to ∠8 5. congruent supplements theorem corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem