https://phys.org/news/2018-06-allies-decrease-country-power.html

The scientists developed a simple, yet sophisticated, computer game to examine relationships between countries and the resulting strategic environments."We have developed a power allocation game to study countries' strategic interactions in a complex environment," said Yuke Li from Yale University. Dr. Li and Prof. A. Stephen Morse, the Dudley Professor of distributed control and adaptive control in electrical engineering at Yale University, used the game to ask if having more allies in a networked, strategic environment will always be beneficial to a country in terms of power allocation outcomes. "The answer is, surprisingly, no. This is especially so for a country without sufficient power to mediate between the conflicts among its potential allies."

The researchers call their analysis a game on signed graphs, which is an emerging field in political science, according to Li. A graph becomes "signed" when each edge, or node, has a positive or negative sign. In Li and Morse's work, a positive node represents a friendly relationship, while a negative node translates to a non-friendly relationship.