Let us introduce the following "Trust Game", which is usually adopted to measure the

level of trust within a society. Assume Chi is an (I)nvestor who is observing the market for

investment opportunities. At some point, she identifies a promising start-up whose business

is to produce crocodile leather Bitcoins wallets. Daniel, the "(E)ntrapreneur" is confident

his company can exploit crypto-currencies market momentum to increase his company's core

value. Therefore, the Investor can decide whether to purchase stocks worth $10 (call this

strategy, trust). If the Investor decides to keep the $10 (call this strategy, end), and the

game ends with the Investor getting $10 and the Entrepreneur getting $0. Otherwise, if the

investor purchases the stocks, the market value of the start-up gets tripled. Daniel can then

decide to either shut down the start-up1 and keep all of the $30 to himself (call this strategy,

keep) or maintain the start-up in the market and pay a $15 dividend to the Chi (call this

strategy, split).

a). Draw the extensive form representation of the above sequential game. What is the

equilibrium of this game if both Chi and Daniel are purely self-interested?

b). Suppose the two players have distributional preferences as introduced in class: if xI ; xE

are the amounts of money the Investor and the Entrepreneur end up with, respectively,

then the Investor's utility is described by:

CE if TI 2 TE UI(CITE) = -IE if II