Ostrovski's transition-combinatorics conjecture for fictitious play

Let a bimatrix game have a unique, completely mixed Nash equilibrium, and let $\mathcal{B\!R}_A$ and $\mathcal{B\!R}_B$ denote the players' best-response correspondences. Assume the game has the stated transition combinatorics; in particular, suppose

$$\mathcal{B\!R}_A(e_j)\ne\mathcal{B\!R}_A(e_{j'})\quad\text{for all }j\ne j',\qquad \mathcal{B\!R}_B(e_i)\ne\mathcal{B\!R}_B(e_{i'})\quad\text{for all }i\ne i'.$$

Ostrovski's conjecture. Under these conditions, the Nash equilibrium does not Pareto dominate typical fictitious-play orbits. This conjecture gives a sufficient transition-combinatorial condition under which equilibrium is not expected to dominate typical fictitious-play behavior in payoff terms. The supplied text gives no resolution.