cmsette / solvesimplex

Evolutionary game theory solver for R. Classifies internal and face equilibria of 1-population games with continuous replication, 2-5 competitors. User-defined payoff matrix.

solveSimplex

solveSimplex is an evolutionary game theory solver for R.

This program describes the equilibrium dynamics of single-population evolutionary game theory games of 2-5 strategies. All strategies are assumed to exist in admixture, and engage in continuous time replicator dynamics. Analysis of face and edge games allows for better understanding of equilibrium dynamics in the system and invasion pathways for individual strategies.

This code:

1. Solves for all internal and edge equilibria present (rows in Equilibria solutions table).
2. Assesses stability of equilibrium (Eq) (Source, Saddle, or Sink) using the eigenvalue technique (Friedman and Sinervo, 2016). (Saddle# indicates the number of positive eigenvalues.)
3. Identifies games and faces with strict-sense intransitivity (Int).
4. Identifies strategies with strict-sense apostasis (Apo), negative frequency-dependence, and anti-apostasis (A_Apo), positive frequency-dependence.
5. Allows for analysis of face games as independent games in order to assess possibility of hysteresis in the system.

Download the R workspace: https://github.com/cmsette/solveSimplex/blob/master/solveSimplex.Rproj

Or the code: https://github.com/cmsette/solveSimplex/tree/master/R

solvesimplex's Issues

Classify discrete time games

Implement classification for discrete time replicator games using modification of Lyapunov method w/ difference equations.

Name game types

Implement classification of 2-strategy games and faces based on CO (SD), HD, LF framework
Implement classification of 3-strategy games and faces based on RPS 1-4 & ESS/NE framework

Classification error edge case

Break in cases when soln = Inf: test funs need "if(any(Re(soln)==Inf)){return(c(Re(soln),0))} else"

Revisit output style

Change the output style to expand output list. Return eigenvalues from solving step.
Output list:
$W-matrix
$Game classification
$Full game table
$eigenvalues
$Wi (face games)
$eigenvalues

Remove expressions

Replace expressions with equivalent functions

Implement new classifications

Possibly implement alternative to Lyapunov classification method for Inconclusive cases.