agent contain at least one opioid package times the number of opioid packages the agent will find: 100 (1/10) (1/2)
* 1 = 5 opioid packages. For the Centralized strategy, the expected capture rate
is 100 (1/1000) 100 = 10 opioid packages, because the Teamwork Modification strategy suggests that other agents
will help the one who finds a first opioid
package. Together, they will find all 100
in the 1-in- 10 chance that some agent
finds at least one opioid package.
Conclusion. The Distributed strategy enjoys a greater expected number
of opioid packages that get through for
T than the Centralized strategy.
The consequences for the smugglers are somewhat different however. With the Distributed strategy, approximately five smugglers would be
captured. With the Centralized strategy, at most one and only with probability 1/10.
Suppose L allocates its agents randomly to 100 of the 1000 importers and
each agent inspects five containers of
that importer. L instructs the agents
to modify the purely random strategy
with what L calls the “Teamwork Modification:” if an agent finds an opioid
package then another agent will help
the first one so together they will inspect all the containers of that importer. We call this combined strategy the
Random with Teamwork strategy.
Warm-up. What is the expected
number of opioid packages that L will
capture, when using the Random with
Teamwork strategy, based on each extremal strategy of T?
Solution to Warm-Up. The expectation for the Distributed strategy is the
number of agents times the probability
that an agent is inspecting a smuggler’s
containers times the probability that
the five containers inspected by the
THERE ARE TWO sources of illegal opioids: legitimately manufactured ones
that have been diverted to drug dealers, and criminally manufactured ones
that were always intended for dealers.
A special video dispenser, markings
on the pills, and a little machine vision
can go a long way toward dealing with
the legitimately manufactured ones.
This column, however, is concerned
about with the criminally manufactured opioid pills.
The setting is 10 ports of entry. For
simplicity each port has 1000 importers of whom 100 are smugglers (but
law enforcement does not know who
they are). Each importer brings in 10
containers per day (so 10,000 containers per port per day) and there are 10
packages per container. One agent can
inspect five containers per day. Law
enforcement (L) has 1000 agents altogether for all 10 ports.
The trafficker (T) wants to bring
in 100 opioid packages a day through
each port and may allocate them in
many ways among smugglers. Law
enforcement (L) wants to capture as
many opioid packages as possible.
Good strategies for each party depend
on how many days this “game” goes on.
If we consider a game of just one
day and L distributes 100 agents to
each port, then consider two extremal strategies between which T could
choose for each port:
˲ (Centralized) Give all 100 opioid
packages to one smuggler to put in
evenly among that smuggler’s 10 containers; and
˲ (Distributed) Give one opioid package to each of 100 smugglers. Each
smuggler will put the opioid package
in a random one of the 10 containers
that smuggler imports. [CONTINUED ON P. 95]
DOI: 10.1145/3332802 Dennis Shasha