Q3. Consider the sequential trust game played between a Trustor and a Trustee, where the trustor has a personal endowment of $100 and the trustee has zero endowment. The trustor has to decide how much of their endowment to give to the trustee, where the trustor has two possible choices: either Give $0 or Give $80 to the trustee. Suppose for each $1 that the trustor gives to the trustee, the trustee receives $3 (i.e. a 300% rate of return). After the trustor’s choice, the trustee has to decide how much to give back to the trustor, while keeping the rest. The trustee has two possible choices: either Return Nothing (i.e. 0%) or Return Half (i.e. 50%), of the received amount to the trustor.

Suppose the trustor and the trustee are of the type whose behavior is dictated by one of the following norms:

Self-regarding norm behavior – The person is only interested in maximizing his or her own payos.

Reciprocal norm behavior – The person rewards actual or expected nice behavior by being nice and punishes actual or expected mean behavior by being mean, even when it is personally costly to do so.

For each of the following combinations of trustor and trustee types, determine the backward induction based equilibrium outcome choices for the trustor and trustee and their respective payos under this equilibrium outcome. Assume that in each of these cases the types of the two players (i.e trustor and trustee) is common knowledge.

(a) Both trustor and trustee are of the self-regarding norm behavior type.

(b) The trustor is of the self-regarding norm behavior type, while the trustee is of the reciprocal norm behavior type.

(c) The trustor is of the reciprocal norm behavior type, while the trustee is of the self-regarding norm behavior type.

(d) Both the trustor and the trustee are of the reciprocal norm behavior type.