Question 3: Linear public goods game (20 points) N players are endowed with X tokens. Each player secretly chooses how many of their private tokens xi to put into a public pot. The tokens in this pot are multiplied by a factor and this "public good" payoff is evenly divided among players. Each player also keeps the tokens they do not contribute. Therefore, the expected payoff for every player i is i(xi,xi)Xxi+Nj=1Nxj 1. Show that if 0<<1 then xi=0 is a strategy Nash equilibrium and explain your answer. ( 5 points) 2. Show that if 1< then xiX is a strategy Nash equilibrium and explain your answer. ( 5 points) 3. Explain why the values of (i.e., greater or lower than 1) change the type of Nash equilibrium than we can expected. (4 points) 4. Give an example of a real situation where we can expect 0<<1, originality of the examples will be taken into account. ( 3 points) 5. Give an example of a real situation where we can expect 1<, originality of the examples will be taken into account. ( 3 points).