A 2£ 2 Game without the Fictitious Play Property ⁄

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Empirically Evaluating Multiagent Learning Algorithms (2014, background): “These games are said to have the ﬁctitious play property (see, for instance Monderer and Shapley (1996); for an example of a simple 2 × 2 game without this property see Monderer and Sela (1996)).”
Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games (2019, background): “…when it converges (Robinson (1951); Miyasawa (1961); Milgrom and Roberts (1991); Monderer and Shapley (1996b,a); Berger (2005); Hofbauer and Sandholm (2002)) and when it does not (Shapley (1964); Jordan (1993); Monderer and Sela (1996); Foster and Young (1998); Krishna and Sjöström (1998)).”
A Counter-example to Karlin's Strong Conjecture for Fictitious Play (2014, unknown): “[22, 15, 30, 12, 25]).”
On the Rate of Convergence of Fictitious Play (2010, background): “This statement is perfectly consistent with the fact that FP is guaranteed to converge for both constant-sum games [26] and identical interest games, i.e., games that are best-response equivalent (in mixed strategies) to a common payoff game [22].”