a game theory example

Recording here as much as anything for my further reference an example by Viossat (2008), who credits it to Eilon Solan, who adapted it from Flesch et al (1997):

W L R T 1,1,1 0,1,1 B 1,1,0 1,0,1

E L R T 1,0,1-x 1,1,0 B 0,1,1 0,0,0

I have not verified this for myself, but allegedly (for x≥0)

• If x=0, TLW is the only Nash equilibrium; it is not quasi-strict.
• Any strategy profile in which players 2 and 3 play L and W and and player 1 plays T with probability of at least 1/(1+x) is a Nash equilibrium.

For x=0, aside from action profile TLW, player 1 gets payoff 0 for matching player 3 and 1 otherwise; similarly 2 wants not to match 1 and 3 wants not to match 2.