12 problems

Let ${\mathcal{W}}$ be the state space of population states, and consider the multi-population replicator dynamics induced by a potential on ${\mathcal{W}}$. A trajectory is said t…

Consider the interacting replicator system described in the paper, and let the stationary distribution be the distribution identified by Theorem. Long-term convergence conjecture.…

Let $\bm R(t)=\bm r(\tau(t))$ be the process obtained from the replicator coalescent, and let $\bm x^*$ be an evolutionarily stable strategy for the matrix $\bm A$, so that the cor…

Hölder-exponent convergence conjecture. For sufficiently strong between-group competition, the population should converge to the unique steady-state distribution having the same Hö…

Let $(g_{\boldsymbol{\lambda}})_{\boldsymbol{\lambda}}$ and $(f_{\boldsymbol{\mu}})_{\boldsymbol{\mu}}$ be the two families of dynamical systems considered in the paper. Coordinate…

Hawk–Dove steady-state convergence conjecture. Then

Let $\beta$, $\gamma$, $\alpha$, $\lambda$, and $\theta$ be the model parameters and the Hölder exponent near $x=1$, respectively. Let $\mu_t$ be the population distribution at tim…

Negative-growth-points conjecture. There are points $x\in{\mathcal A}$ at which $f(x)<0$.

Consider games sufficiently close in payoff space to game … , but the paper's proof does not extend because its rescaling lemma requires a very specific payoff structure.

Let the distributed replicator equation be the reaction-diffusion system denoted by, and let the corresponding local replicator system be denoted by. The stability notion for the d…

Let $\mu$ be a weak limit point of the quasi-stationary distributions $\mu^\varepsilon$ for the replicator process with $c>0$ sufficiently large. In the rock-paper-scissors case, l…

Let $X(t)$ denote the stochastic learning dynamics on a reducible network, and let $\Delta^{*}$ be the entire affine set of equilibria associated with the network. Assume a suitabl…