When is a threat credible, and how can repetition support cooperation?
Sequential games use backward induction; repeated games compare today’s deviation gain with future punishment.
Follow the cause and effect
At every terminal decision node, choose the actual best response.
Discard threats the issuer would not want to carry out.
In repetition, compare cooperation value with one-time deviation plus punishment.
The model you are using
Conditions for this model
Repeated example uses the previous payoffs, permanent (L,L) punishment, observable actions and 0≤δ<1.
The exam trap
A severe announced punishment is not credible if carrying it out is worse for the threatener.
Connect the reasoning to the graph
What changes
- A game tree shows order and information sets; do not collapse it into a matrix when timing matters.
What stays fixed
Repeated example uses the previous payoffs, permanent (L,L) punishment, observable actions and 0≤δ<1.
Keep these conditions throughout the comparison; change only what the case above specifies.
What to inspect
In repetition, compare cooperation value with one-time deviation plus punishment.
Compare before and after, and locate the conclusion on the graph.
5 MINUTES · TRANSFER THE IDEA
Can you explain it without the lesson?
Find the δ threshold supporting cooperation under grim trigger for your own payoff numbers.