13 problems

Let $G(x)$ be the polynomial whose roots determine the equilibria of the replicator-mutator dynamics, with coefficients depending on the model parameters. The authors' conjecture.…

Consider a deterministic evolutionary game dynamic with periodic orbits, and let ISO denote the invasion-stability condition for periodic orbits; for a fixed point, ISO of order…

A deterministic evolutionary game dynamic admits periodic orbits of period $k$, with $k>2$, and the higher-period ISO condition denotes the corresponding extension of the invasion-…

Let $w$, $v$, $d$, and $\beta$ satisfy … and let $0<\bar{\epsilon}<1$. Suppose the ODE solution trajectory is increasing below $\bar{\epsilon}$ and decreasing above…

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…

Conjecture on the black equilibrium. If $G_1>0$ and $q\in(q_{green},1]$, then the black equilibrium remains unstable and no evolution of cooperation occurs.

Density monotonicity conjecture. For the general $d$-player, $n$-strategy normal evolutionary game, the density function decreases with $t_i$ and increases with $d$.

General equilibrium-count conjecture. In a multi-player multi-strategy game, these asymptotic relations hold; moreover,

Stable limit-cycle conjecture. For any fixed admissible $M$, there is an open set of parameters $(\mu,c)$ arbitrarily close to $(0,0)$ for which the replicator-mutator system has s…

Consider games with Nash equilibria and evolutionary dynamics, including multi-population dynamics. Broad elimination conjecture. For many other dynamics, including multi-populatio…

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 $\mu$ 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…