As an alumnus of Hamilton College, John Pitaressi, a reporter for The Observer-Dispatch, is familiar with the game and posted a comment to initial message about the 1899 Carlisle-Hamilton College game although he wasn’t present at it. He has two possible reasons for why the game was scheduled:
1. Melancton Woolsey Stryker, President of Hamilton College, was very much an admirer of the Carlisle team and a big believer in football as a maker of men.
2. Hamilton Coach Edwin Sweetland, a former Cornell player, had a relationship with Pop Warner that lasted for years.
These reasons sound plausible. The financial deal that was struck surely played a part but we don’t know (as yet) what that was.
The game received considerable build up in the Syracuse newspapers (Utica is east of Syracuse, between it and Albany) because their readers could easily catch a train to attend the game and Syracusans hadn’t seen the Indians play their local college team. That didn’t happen until 1906. According to the November 5 edition of The Sunday Herald, the Indians rarely played outside of New York City and Chicago. Omitting their homes games or games played across town at Dickinson College, the previous season, in 1898, the Indians played at Ithaca and Albany in New York; New Haven, Connecticut; Cambridge, Massachusetts; Philadelphia, Pennsylvania; and Chicago, Illinois. Carlisle obviously played in many cities, including two smaller cities in New York State. In 1899, they did play two games in New York City but none, other than the Hamilton game, in smaller New York cities.
The Herald went on to say that playing the game in Utica happened because of the efforts of Congressman James S. Sherman of Utica, chairman of the House Committee on Indian Affairs. I suspect that Pitaressi is closer to the truth that was The Herald because Carlisle was playing most any team they felt like except Army and the War Department approved that in 1905. That 5,000 bought tickets to see the game probably made it worthwhile for both schools. Playing the Indians probably helped Hamilton improve its level of play, because the next year, 1900, they went 8-1-0 with wins over Williams and Colgate.