ECC3841 Chap.6 Crime and Key Players
Crime and Key Players
Crime networks can change returns through learning, partnership, norms and perceived detection. Positive peer spillovers create strategic complements and a social multiplier. Empirical clustering does not by itself establish influence because offenders may select peers or share neighborhood conditions.
A key-player policy removes the node that reduces total equilibrium activity most; it requires a reduced-network solution rather than a degree ranking.
What this chapter covers
- 01
Peer learning and criminal collaboration
- 02
Selection and shared neighborhood conditions
- 03
Strategic complements in effort
- 04
Walk-based equilibrium amplification
- 05
Friendship and competition matrices
- 06
Social multipliers
- 07
Key-player removal
- 08
Evidence and policy limitations
Worked example · free
Solve a linked pair
- +1Substitute to obtain x1=1.1+0.0625x1.
- +1Rearrange to 0.9375x1=1.1.
- +1Calculate x1=1.1733.
- +1Back-substitute x2=1.4933.
- +1Check both best replies and interpret positive feedback.
Key terms
- Social multiplier
- Amplification created when one agents response feeds through peers and returns through the network.
- Crime complementarity
- A relationship where peers higher crime effort raises an individuals best reply.
- Competition matrix
- A matrix recording which agents compete in the relevant criminal market or activity.
- Removal counterfactual
- The equilibrium recomputed after deleting a node and all incident links.
- Displacement
- Movement of activity to other people, places or offenses after intervention.
- Co-offending tie
- A relationship recording joint participation in an offense. It is an observed collaboration link, not necessarily the same as friendship, communication or influence, so its interpretation depends on how events are recorded.
- Detection spillover
- A change in one offenders perceived probability of detection caused by associates behavior or police attention. The sign can differ from a learning spillover and must be read from the payoff specification.
- Network disruption
- An intervention that removes or weakens selected relationships rather than removing a person. Its equilibrium effect depends on which feedback paths disappear and whether remaining agents create replacement links.
- Fixed-network assumption
- The short-run modeling assumption that links among remaining agents do not change after intervention. It makes the removal counterfactual tractable but can overstate durable effects when the group can rewire.
- Peer selection
- The formation of ties among people already similar in criminal propensity or environment. Selection can create behavioral correlation without causal influence and therefore threatens a naive peer-effect interpretation.
- Intensive margin
- The amount of activity chosen by someone already participating. A continuous effort game describes this margin unless a separate entry decision is modeled for the extensive margin.
- Policy counterfactual
- A comparison between baseline equilibrium activity and activity after a specified intervention. It requires the remaining agents to optimize again rather than holding their choices at baseline values.
- Network sensitivity
- The degree to which a policy ranking changes when uncertain links or interaction parameters are varied. High sensitivity warns that incomplete police data can make a seemingly precise target fragile.
- Equilibrium reduction
- The fall in total modeled activity between the baseline and a solved intervention network. It includes the removed action and every adjustment by remaining agents, making it the relevant key-player comparison rather than headcount alone.
- Rewiring response
- New relationships formed after a node or link is removed. Rewiring can restore feedback paths, shift activity toward substitutes and make a short-run fixed-network estimate larger than the durable policy effect.
Crime and Key Players FAQ
Why can crime cluster without peer influence?
People may select similar associates, face common policing and labor-market conditions or share neighborhood shocks. A causal design must separate those factors. Recompute the reduced-network equilibrium and discuss identification, rewiring and displacement before giving policy advice.
What makes a node a key player?
Its removal creates the largest decline in total equilibrium activity after all remaining agents adjust. Recompute the reduced-network equilibrium and discuss identification, rewiring and displacement before giving policy advice.
Why not subtract only the removed effort?
Under strategic interaction, the remaining agents change their choices when links and peer inputs disappear. Recompute the reduced-network equilibrium and discuss identification, rewiring and displacement before giving policy advice.
What should a policy answer include?
Show the modeled counterfactual, then discuss identification, displacement, implementation and fairness rather than presenting centrality as the whole recommendation. Recompute the reduced-network equilibrium and discuss identification, rewiring and displacement before giving policy advice.
Exam move
Write each matrix convention before starting algebra. If friendship lowers detection risk while common-market activity creates competition, keep the two matrices separate and state what a one means in each. Translate every payoff term into words, then derive best replies line by line. The sign on neighbors activity determines whether the model amplifies or offsets crime.
Verify every equilibrium by substitution and retain enough decimal precision that a close policy ranking is not reversed by rounding. For every removal candidate, redraw the reduced graph, remove incident links and solve again. Record baseline total activity, reduced total activity and the difference in a table. The key player is the largest equilibrium reduction, not automatically the highest degree or Bonacich score.
Explain which feedback paths disappear. Then question the fixed-network assumption: associates may rewire, activity may move to another offense or location, and unobserved relationships can change the ranking. Discussion questions require a separate empirical layer. Similar behavior among friends may reflect influence, selection, common policing or shared labor-market conditions.
Name those threats before praising a peer coefficient. Explain the assignment, timing or comparison that makes exposure plausibly independent. Use the source tutorials to rehearse the visible method sequence, but do not memorize a past-paper stem. Create an original three-node path, solve it, remove the center, remove an endpoint and compare. Change the complementarity coefficient and predict how the removal gap changes.
Next, create friendship and competition matrices that differ by one link and trace which payoff term changes. For policy, distinguish what the model predicts from what the evidence establishes and what an institution should do. Consider incentive changes, link disruption and legitimate opportunities alongside removal. A centrality result is a leverage diagnosis, not a complete legal recommendation.
Close every answer with a limitation about identification, missing ties, displacement or rewiring. Add a sensitivity exercise: delete one uncertain link, resolve the game and see whether the key-player ranking changes. Compare a policy that lowers every private return with one that removes a link. The first changes incentives throughout the graph; the second changes specified feedback paths.
Explain which depends less on complete network observation. Distinguish participation from effort because a continuous-action model does not automatically predict entry. When a coefficient measures exposure to criminal peers, ask whether it captures learning, norms, collaboration or detection. Different channels imply different interventions.
Practise a paragraph that starts with evidence, moves to the modeled mechanism and ends with qualified policy. On the final day, write the adjacency matrix, utilities, best replies, equilibrium check and removal comparison in a fixed sequence. That sequence exposes method for partial credit and prevents a plausible policy paragraph from hiding an unsolved game.
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