where no agent has anything to gain by changing strategy [@hof98]. The question of if, and how, game players reach an equilibrium has been the subject of a great deal of work since. The dynamics of games can have different driving mechanisms. In “evolutionary game theory” [@May82], devised by John Maynard Smith in 1973, agents (living organisms) whose strategies are effective against competitors survive and reproduce more rapidly. This replicates their genes, and strategies they encode, in higher concentration in future generations. The “replicator equations” which describe this process have applications in diverse scientific settings from the evolution of language [@Mit04] to behavioural dynamics and decision making [@Pai12]. Alternatively, death and reproduction need not be involved if agents are able to learn from experience. An early example of such a learning rule is “fictitious play” [@Bro51] where players believe that their opponents are choosing strategies at random from a stationary distribution. They build a progressively clearer picture of this fictitious distribution through repeated interactions and at each round play the best response. The rule has an obvious flaw in that the real distribution is non-stationary. An alternative, derived from psychology, is reinforcement learning [@Sut98] of which an an example is 