Captain! They’re going to Disrupt our Core!

Or will they?

When dealing with cores in game theory, it is easy to know that the best payoffs for each coalition involved can be found in the core. So, does that mean everyone is happy and there’s is nothing else to be discussed? Not even close.

Even once the core is found, there is a matter of finding the best point where everyone is their happiest. There are several methods of going about this including Shapley’s point, finding the nucleous, and the topic of this article: The Gately point. Of the methods that can be used, the Gately point is the most interest to me personally. Instead of looking to provide the highest possible payout or attempting to keep the values as close to one another as possible, this method looks at the player’s temptation to disrupt. The goal of this perspective provides is the keep the gran coalition together. This is done by having the values place that ensures a low temptation to disrupt the coalition.

In the diagram shown above, the formula equates to, ‘how much everyone else will lose, over how much the player in question will lose’. If players are found to be in threat of disrupting then the values are adjusted until a point is reached in which lowering anyone would raise another player.