This document discusses applying game theory to enforcement decision-making in collections and recoveries. It presents three "games" to analyze different scenarios: 1) The "Asset-Rich Borrower Game" shows that the creditor will always defect by enforcing collection, while the borrower will cooperate by agreeing to a payment plan, as this is the best outcome for both. 2) The "Everyone Cares about Reputation" game shows that when reputation is highly valued, both parties will cooperate by agreeing to a payment plan, as this results in the best outcomes. 3) The "Many Creditors Scrambling" game is a prisoner's dilemma, where individual defection yields the best outcome, but

1. Andrew Jackson, Head of Collections & Recoveries
Applying Game Theory to
Enforcement Decision-Making
6 October 2015

2. Introduction
Sector
Game theory is concerned with the
actions of decision-makers, who are
conscious that their actions affect each
other.
A Game needs: players, actions, payoffs,
information, strategies, equilibrium and
outcome

3. Game Theory Heroes – John von Neumann
Sector

4. Game Theory Heroes – John Nash
Sector

5. The Prisoner’s Dilemma
Sector

6. A Zero-Sum Game
Sector

7. Nash Equilibrium

8. Real world application

9. Application to Collections & Recoveries
The Asset-Rich Borrower Game
To map out this game, we need to first map out the assumptions, and score the outcomes:
• Defecting = commencing legal proceedings or obtaining relief through formal
insolvency.
• Co-operating = working with the counterparty to agree a payment plan.
 The game does not take into account any actions or inactions of other creditors.
 There are other creditors, and so formal insolvency will mean that assets will be
shared.
 There are sufficient assets in the business to pay the creditor in full, but to do so will
make it much harder for the business to survive.
 The creditor gives equal weighting to speed and size of recovery.
 The business is viable and the borrower wants his business to survive.
 Recoveries from enforcement without insolvency will be short term, enforcement with
insolvency will be medium term, and a payment plan will be long-term.
 Based on the above, the following factors are the only ones relevant for scoring (0 =
worst, 5 = best)…

10. Scoring Matrix
Defect / Defect Defect / Co-
operate
Co-operate /
Defect
Co-operate /
Co-operate
CREDITOR
Speed of
Recovery
3 5 3 1
Size of Recovery 2 5 2 5
TOTAL 5 10 5 6
BORROWER
Survival of
business
0 2 0 5
TOTAL 0 2 0 5

11. “The Asset Rich Borrower Game”
Borrower
Formal
Insolvency
= Defecting
Sell assets to
pay
= Co-operate
Creditor Enforce
= Defecting 5, 0 10, 2
Payment plan
= Co-
operating
5, 0 6, 5
 Where the borrower defects, it does not matter whether the creditor defects or
not (5 is neutral), but where there borrower co-operates it will be better for the
creditor to defect (10 beats 6). Therefore, the creditor will always defect.
 Where the creditor defects, it will be best for the borrower to co-operate (2 beats
0); and since the creditor will always defect we do not need to consider its co-
operation. Therefore, the borrower will always co-operate.
 This game highlights that the unattractiveness to both parties of the borrower’s
insolvency (i.e. his defecting). It means that the only strategy that matters is the
creditor’s defection with co-operation from the borrower.

12. Another Game
Everyone Cares about Reputation
• Defecting = commencing legal proceedings or obtaining relief through formal
insolvency.
• Co-operating = working with the counterparty to agree a payment plan.
• There are other creditors, so formal insolvency will mean that assets will be shared.
• There are not enough assets to pay the creditor in full immediately on demand.
• The creditor gives equal weighting to speed of recovery and size of recovery, but twice
as much weighting to reputation. To be too aggressive or too passive damages its
reputation the most.
• The borrower has a viable business, and so using formal procedures for debt relief will
damage its reputation the most.
• Recoveries from defecting will be short term and smaller in value, but from co-
operation will be long-term and larger in value.
• The following factors are the only important ones (i.e. costs, trust in the borrower etc.
are not included), and the scoring is correct (0 = worst, 5 = best):

13. Scoring matrix
Defect / Defect Defect / Co-
operate
Co-operate /
Defect
Co-operate / Co-
operate
CREDITOR
Speed of Recovery 3 5 3 1
Size of Recovery 2 5 2 5
Reputation 6 1 1 10
TOTAL 11 11 6 16
BORROWER
Survival of business 0 1 3 5
Reputation 1 3 1 5
TOTAL 1 4 4 10

14. “Everyone cares about reputation”
This game shows us that:
• The borrower will not defect (4 beats 1, and 10 beats 4).
• Since the borrower will not defect, the creditor will co-operate (16 beats 11).
• Accordingly, the parties co-operate where the impact on reputation is very high for
both parties. It is strictly dominant for both parties.
Borrower
Formal
Insolvency
= Defecting
Sell assets
to pay = Co-
operate
Creditor Enforce =
Defecting
11, 1 11, 4
Payment
plan = Co-
operating
6, 4 16, 10

15. And Another Game
Many creditors scrambling
• Defecting = commencing legal proceedings or formal insolvency.
• Co-operating = working with the other creditors to agree a payment plan.
• There are other creditors, so formal insolvency will mean that assets will be shared.
• There are not enough assets to pay the creditors in full.
• Recoveries from defecting will be highest if the other party co-operates, since the
defector sweeps up the assets whilst the co-operator waits.
• Recoveries from both co-operating will be higher than both defecting as the longer-
term strategy will create more overall assets for distribution.
• The following factors are the only important ones (i.e. reputation, costs, trust in the
borrower etc. are not included), and the scoring is correct (0 = worst, 5 = best)…

16. Scoring matrix
Defect /
Defect
Defect /
Co-operate
Co-operate
/ Defect
Co-operate
/ Co-
operate
CREDITOR
Amount of
recoveries
2 5 1 4
OTHER CREDITORS
Amount of
recoveries
2 1 5 4

17. “Many creditors scrambling”
This game shows us that:
• This is the traditional prisoner’s dilemma.
• It is better for each creditor, acting selfishly, to defect on a single game.
• If creditor becomes known for always defecting then the other creditor will always
defect too, and sub-optimal result of 2, 2 will always be obtained.
Other creditors
Enforce =
Defecting
Payment
plan = Co-
operate
Creditor Enforce =
Defecting 2, 2 5, 1
Payment plan
= Co-
operating
1, 5 4, 4
…if the game is played infinitely then co-operating is the best strategy, but co-
operation only works where there is TRUST.

18. Conclusion
• Game Theory gives us a rigorous way of testing our assumptions,
and our decisions relating to those assumptions.
• It also enables us to challenge the importance of different
assumptions relative to each other, and so increases our
organisational self-awareness.
• Game Theory relies on rational players, who are acting rationally,
and may therefore not be directly applicable to dealing with
debtors who are experiencing high emotional stress
• It should be the aim of a sophisticated collections team to
facilitate rational decision-making.

19. QUESTIONS