Do the same exercise above, but for the Trust Game. In this two$-$person sequential game, the first mover starts with $$100,$ and he she chooses how much to transfer to the second mower. Every dollar transferred from the first mover to the second mover is tripled. The second mover

receives this tripled amount and then choose how much to transfer back to the first mover. The amount transferred back is not tripled.

Two division managers can invest time and effort in creating a better working relationship. Each invests $e_{i}0,$ and if both invest more both are better off, but it is costly for each manager to invest. In particular the payoff function for player $i$ is $U_i=(a+e_j)e_i-e_i^2.$

a$)$ Find the externalities and the strategic relationship;

b$)$ Find the best$-$response functions and draw them in a separate graph;

c$)$ Find the Nash Equilibrium;

d$)$ Find the Subgame Perfect Nach Equilibrium Does the game generate first$-$ or secondmover advantage?

e$)$ If there was a way for the players to cooperate and choose the same level of effort that generates a Pareto Optimal outcome, what would their efforts be$?$