If Zippo decided to enter other markets, would a global marketing strategy or a multidomestic strategy work best?
Zippo ligthers have been around for more than 75 years. But as the number of smokers in the U.S continues to decline, Zippo has spent the last half-century scouting the world for new markets. Today, Zippo is a status symbol among chinese consumers, who prefer U.S products. To reduce the sale of made in china knockoffs, Zippo's ads show chinese consumers how to identify a real Zippo. In addition, Zippo has worked with U.S govt. officials to find a safe way to package its lighters for air travel. Both of these examples demonstrate a firm adapting to requirements of a new marketplace.
Given the additional information that you have given under your question, it is clear that Zippo should pursue a multi-domestic strategy. The reason for this is that the different markets appear to have very different needs.
A multi-domestic marketing strategy should be pursued when there are differences in the sort of strategies that will work in each market. In this case, we can see that Zippo lighters need to be marketed much differently in China (as a luxury good) than in America (emphasizing utility with respect to security procedures). This shows that lighters are things that should be marketed differently in different countries. Therefore, a multi-domestic approach would be best.