Isolation of parameter values admitting heteroclinic orbits in cyclic competition games

From papers

Let (ϵX,ϵY)(\epsilon_X,\epsilon_Y) be a pair of game parameters, and let Za,Zb,Zc,Zd,Ze,ZfZ^a,Z^b,Z^c,Z^d,Z^e,Z^f denote the equilibria appearing in the cyclic competition bimatrix game. A heteroclinic orbit from an equilibrium ZiZ^i to an equilibrium ZjZ^j is an orbit whose backward and forward limits are ZiZ^i and ZjZ^j, respectively. Isolation conjecture. The set of pairs (ϵX,ϵY)(\epsilon_X,\epsilon_Y) for which there is a heteroclinic orbit from ZbZ^b to ZaZ^a is isolated in the parameter space. The same is asked for heteroclinic orbits from ZaZ^a to ZdZ^d, from ZdZ^d to ZcZ^c, from ZcZ^c to ZeZ^e, from ZeZ^e to ZfZ^f, and from ZfZ^f to ZbZ^b. The observation motivating this question comes from parameter values such as (ϵX,ϵY)=(0.09,0.79)(\epsilon_X,\epsilon_Y)=(-0.09,-0.79), where the stable manifold of ZaZ^a and the unstable manifold of ZbZ^b appear very close; whether the corresponding parameter sets are isolated remains open.

Progress summary

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Sources & referencesView supporting material

Primary source

Cezary Olszowiec, “Complex behaviour in cyclic competition bimatrix games”, arXiv:1605.00431 (2016).

Solutions 0

No solutions have been posted yet.