Imagine you and a friend have robbed the Union Market. You are caught speeding out of the parking lot and are promptly apprehended by Campus Security. A scuffle ensues and you are both charged with resisting arrest. They isolate the two of you so that you may be questioned separately. Your interrogator tells you that your resisting arrest charge carries a jail sentence of 1 year, but if you agree to testify against your partner, they will drop the arrest charge. The robbery charge carries a sentence of 5 years, but you know Campus Security has no evidence because they wouldn’t offer you such a deal otherwise. If you squeal and
your partner keeps quiet, you won’t be implicated in the robbery or charged with resisting arrest, and will thus
get no jail time at all. However, this all depends on the assumption that your partner cooperates with you. If
you and your partner both defect, you will both be convicted of the robbery charge.
Draw a payoff matrix that depicts the four possible scenarios (in terms of jail time in years) given the above
parameters.
Normalize your matrix, such that there are no negative values in your chart.
Note that the terms “cooperate” and “defect”should refer to your behaviour toward your partner, not the authorities.
This is not a biology question
To construct the payoff matrix, we need to consider the possible outcomes based on the choices of both you and your partner. Since there are two possible choices for each player (cooperate or defect), we will have four potential scenarios. The given parameters indicate the jail time in years for each scenario. Let's analyze each case:
1. If both you and your partner cooperate:
- Robbery charge: 0 years
- Resisting arrest charge: 0 years
2. If you cooperate and your partner defects:
- Robbery charge: 5 years
- Resisting arrest charge: 0 years
3. If you defect and your partner cooperates:
- Robbery charge: 5 years
- Resisting arrest charge: 1 year
4. If both you and your partner defect:
- Robbery charge: 5 years
- Resisting arrest charge: 1 year
To normalize the matrix, we can subtract the minimum value from each cell, so there are no negative values. In this case, the minimum value is 0. Therefore, the normalized payoff matrix becomes:
| Cooperate | Defect
——————————————
Cooperate | 0, 0 | 0, 1
——————————————
Defect | 5, 0 | 5, 1
This matrix represents the four possible scenarios with normalized jail time in years associated with each combination of cooperation or defection between you and your partner.