Kidnapping: AMBER Alert Network & Game theory applications
The first connection of this topic to lecture material is how the presence and impact of networks can be seen with the increasing success of AMBER Alert–a broadcast emergency response system used to notify people on a statewide, regional, or local levels regarding missing children. As of April 2019, nearly 1,000 children have been rescued in result of AMBER Alert. In December 2018, the U.S. Senate unanimously passed legislation to expand this system to U.S. territories as well. The increasing success of these alerts can be attributed to an expanding national network, allowing for the engagement between those who issue out an AMBER Alert and those who respond.
On a related note, the analysis of kidnapping and child-abduction cases also requires game theory. Nobel Laureate in Economic Sciences, Reinhard Selten performed extensive research on the standard model for kidnapping cases, also known as the Selten’s game, which is a two-person sequential game involving an abducted victim and a kidnapper who demands a ransom in exchange for the victim’s release. In sensitive decision-making situations such as this, it is safe to assume that each player will critically analyze all possible alternatives along with the opposing player’s possible choices to maximize benefits for their own actions. Selten used the notion of perfect equilibrium to solve for the equilibrium of the Kidnapping game.
It’s interesting to note other outcomes and game theories not covered in class. Selten introduced the concept of “subgame perfection,” which means that a strategy represents a nash equilibrium in every subgame of the original game. The options are A) The victim is kidnapped, no ransom is paid and the victim is killed; B) The victim is kidnapped, ransom is paid and the victim is released; and C) The victim is not kidnapped. The kidnapper releasing the hostage and the victim’s family paying the ransom remains the optimal choice for the kidnapper. But, if the kidnapper knows that the victim’s family cannot meet the ransom, then the kidnapper could either lower the ransom amount and/or decide whether to execute the hostage on rational grounds.
Relevant Links:
https://www.amberalert.gov/statistics.htm
https://royalsocietypublishing.org/doi/10.1098/rsos.171484
https://www.broadcastingcable.com/news/senate-votes-to-expand-amber-alert-to-territories