Question 1. There are two goods: a public good x and money. The unit cost of providing the public good is $1 per unit. Let's consider a game where two agents have to voluntarily contribute to procure this public good that they both benefit from. The players are initially endowed only with money: Player 1 has $w, and Player 2 has $w2. Each of them chooses an amount, $z, and $z2 respectively, to contribute to procuring the public good. If player i contributes $z;, then she is left with $w; - z; left over and the level of the public good is x = Z1 + Z2. There utility of player i is Ui ( x , Zi ) = aix - - x 2 2 - + ( wi - zi ). The parameter a; is player i's private information and either a; = 4 or a; = 6. The other player believes that a; = 4 with probability 0.5 and a; = 6 with probability 0.5. That is, each player knows their own parameter but has a belief that the other player's parameter is 4 or 6 with equal probability. Find a Bayesian Nash equilibrium of this game. Hint: A strategy specifies a player's contribution level as a function of her parameter. Focus on finding a symmetric BNE where both players use the same strategy