Kidnapping Model: An Extension of Selten's Game

TL;DR

This paper extends Selten's kidnapping game model by incorporating asymmetric capture probabilities based on hostage outcomes, leading to a new equilibrium analysis relevant for policy and strategic decision-making.

Contribution

It introduces an asymmetric kidnapping game model where capture probabilities depend on hostage outcomes, and identifies a unique perfect equilibrium point.

Findings

New equilibrium point identified in the extended model

Capture probability asymmetry affects strategic outcomes

Enhanced understanding of kidnapping game dynamics

Abstract

Selten's game is a kidnapping model where the probability of capturing the kidnapper is independent of whether the hostage has been released or executed. Most often, in view of the elevated sensitivities involved, authorities put greater effort and resources into capturing the kidnapper if the hostage has been executed, in contrast to the case when a ransom is paid to secure the hostage's release. In this paper, we study the asymmetric game when the probability of capturing the kidnapper depends on whether the hostage has been executed or not and find a new uniquely determined perfect equilibrium point in Selten's game.