From Nature: 

The field of quantum game theory (QGT) is still in its infancy: just tens of economists and quantum physicists have so far published a total of 200 or so papers on the topic. Its roots stretch back to a paper published in 1999 by mathematician David Meyer of the University of California, San Diego¹. In it, Meyer showed how a quantum approach always beats a classical strategy in a simple game where two players flip a coin. This is because the laws of quantum mechanics allow the coin to exist in a state that is a combination of heads-up and tails-up at the same time, so the person playing by classical rules will always be outmanoeuvred.

Meyers came up to Portland State last year and talked during one of our Quantum Games seminars.  He’s a brilliant guy, and knocked some of the research being done here for a loop.

One of the current struggles is finding which games are even worth pursuing with a Quantum strategy, since many are equally (or better) achieved in the classical game.

For me the new frontier is Quantum Neuroscience or Modeling of the mind using quantum computers and Quantum Information theory.  There are crazy links between this seemingly sci-fi field and the reality of how the human mind processes information.