Week 5:
Preparation: Chap 10: Repeated interaction and the
value of revenge.
In the case of repeated interaction, decision makers can establish cooperation in
equilibrium if they have the punishment strategies at their disposal, which they
can play in case other decision makers do not cooperate.
Trigger strategy: tells a player to cooperate as long as the other player
cooperates in all previous periods and punish the other player as much as
possible in all future periods as soon as she does not cooperate in one period.
Discount factor: a euro tomorrow is equivalent to = 1 / (1 + r) euro today.
A player discounts each period with <1; interaction in the next period
continue with probability P<1
Then = P.
So, prospect of earning 1€ in the next period: = P/ (1 + r)
It can be shown that the trigger strategy is a subgame perfect Nash equilibrium
(only) if it holds true for all players that ≥ (∏D - ∏C) /(∏D - ∏N)
∏C = player’s payoff if all players cooperate.
∏D = payoff if deviating from the cooperative outcome while all other players
stick to it.
∏N = payoff in her last preferred one-shot Nash equilibrium.
NPVC = ∏C / ( 1 - ) for cooperative periods.
NPVC = ∏D + ( ∏C) / ( 1 - )
The higher a player’s cooperative payoff, the lower and the greater the range
of discount factors V for which cooperation is feasible.
Chap 11: Relational
contracts
In a subgame perfect Nash Equilibrium, the principal pays no bonus inducing the
agent to shirk.
Both obtain 0 utility, while if the agent worked and the agent gave a
bonus, each would get a payoff.
Implicit contracts: agreements between two parties that cannot be enforced by
the court of any kind – written, verbal, tacit.
Relational contract: special case of implicit contract, if it involves agreements
enforceable because parties interact repeatedly, if they have a long-term
relationship with each other.
Relational contracts are relevant for internal actions within organizations.
The principal and agent cooperate in equilibrium if the principal is sufficiently
patient.
But the Principal-Agent model is unrealistic. It assumes that the principal can
observe whether the agent works or shirks, usually what is seeable is the output
and that the principal always benefits from the agent’s effort – and the agent’s
output might not be a good representation of its work.
Higher incentives do not always lead to higher performance but determining the
optimal incentive scheme or level of reward isn’t an easy job.
Preparation: Chap 10: Repeated interaction and the
value of revenge.
In the case of repeated interaction, decision makers can establish cooperation in
equilibrium if they have the punishment strategies at their disposal, which they
can play in case other decision makers do not cooperate.
Trigger strategy: tells a player to cooperate as long as the other player
cooperates in all previous periods and punish the other player as much as
possible in all future periods as soon as she does not cooperate in one period.
Discount factor: a euro tomorrow is equivalent to = 1 / (1 + r) euro today.
A player discounts each period with <1; interaction in the next period
continue with probability P<1
Then = P.
So, prospect of earning 1€ in the next period: = P/ (1 + r)
It can be shown that the trigger strategy is a subgame perfect Nash equilibrium
(only) if it holds true for all players that ≥ (∏D - ∏C) /(∏D - ∏N)
∏C = player’s payoff if all players cooperate.
∏D = payoff if deviating from the cooperative outcome while all other players
stick to it.
∏N = payoff in her last preferred one-shot Nash equilibrium.
NPVC = ∏C / ( 1 - ) for cooperative periods.
NPVC = ∏D + ( ∏C) / ( 1 - )
The higher a player’s cooperative payoff, the lower and the greater the range
of discount factors V for which cooperation is feasible.
Chap 11: Relational
contracts
In a subgame perfect Nash Equilibrium, the principal pays no bonus inducing the
agent to shirk.
Both obtain 0 utility, while if the agent worked and the agent gave a
bonus, each would get a payoff.
Implicit contracts: agreements between two parties that cannot be enforced by
the court of any kind – written, verbal, tacit.
Relational contract: special case of implicit contract, if it involves agreements
enforceable because parties interact repeatedly, if they have a long-term
relationship with each other.
Relational contracts are relevant for internal actions within organizations.
The principal and agent cooperate in equilibrium if the principal is sufficiently
patient.
But the Principal-Agent model is unrealistic. It assumes that the principal can
observe whether the agent works or shirks, usually what is seeable is the output
and that the principal always benefits from the agent’s effort – and the agent’s
output might not be a good representation of its work.
Higher incentives do not always lead to higher performance but determining the
optimal incentive scheme or level of reward isn’t an easy job.
