For more than 30 years, Professor Andrew McLennan has been working to complete our knowledge of the Nash equilibria.
The Nash equilibrium is one of the most well-known game theory solutions used by economists to understand and predict the outcomes from social interactions that are modelled as games.
Nash equilibria are the configurations of strategies players employ, which have the property that for each individual any change in strategy is unbeneficial, taking the strategies of others as given. That is, no single player can benefit from changing his or her strategy unless some other players also change their strategies.
Professor McLennan, in more recent years, has focused his research on the computational complexity of finding the Nash equilibria.
“My specific results have been to find that there are a lot of Nash equilibria; both the maximum number and the average number can be quite large, and these numbers grow exponentially with the number of strategies,” said Professor McLennan.
“This means that for practical purposes, you have to choose simple scenarios or games in which to use the Nash equilibrium concept to predict outcomes or strategies,” he said.
“For instance, in complicated games such as military battles, the notion of Nash equilibria is not very useful because there are too many people involved and too many computations to predict the outcome.
“In reality, there are very few applications simple enough that practical algorithms can be used to find the Nash equilibria. This was suspected, but I’ve confirmed and explained why this is the case—completing the picture.”
Professor McLennan’s break-through work has applications for software developers and experimental economists.
