They are the unlikeliest of adversaries: On one side is Ty Warner, the billionaire founder of the decidedly low-tech Beanie Babies and Beanie Boos plush-toy empire. He’s worth nearly $4 billion. On the other is Bill Gates, the co-founder of the decidedly high-tech software behemoth Microsoft and one of the world’s richest men, with a fortune estimated these days at around $100 billion.

They are not duking it out over stuffed animals or computer code, though. Instead, they are fighting about luxury hotels, in both Manhattan and Santa Barbara.