# R/ILogit.R In EvolutionaryGames: Important Concepts of Evolutionary Game Theory

#### Documented in ILogit

```#' @name ILogit
#' @title ILogit dynamic
#' @description Imitative Logit dynamic as a type of evolutionary dynamics.
#' @aliases ILogit
#' @export ILogit
#' @author Jochen Staudacher \email{jochen.staudacher@@hs-kempten.de}
#' @param time Regular sequence that represents the time sequence under which
#'  simulation takes place.
#' @param state Numeric vector that represents the initial state.
#' @param parameters Numeric vector that represents parameters needed by the
#'  dynamic.
#' @return Numeric list. Each component represents the rate of change depending on
#'  the dynamic.
#' @references Weibull, J. W. (1997)
#' "Evolutionary Game Theory", MIT Press.
#' @examples
#' dynamic <- ILogit
#' A <- matrix(c(-1, 0, 0, 0, -1, 0, 0, 0, -1), 3, byrow=TRUE)
#' state <- matrix(c(0.1, 0.2, 0.7, 0.2, 0.7, 0.1, 0.9, 0.05, 0.05), 3, 3, byrow=TRUE)
#' eta <- 0.7
#' phaseDiagram3S(A, dynamic, eta, state, TRUE, FALSE)

ILogit <- function(time, state, parameters) {
eta <- parameters[length(parameters)]

a <- parameters[-length(parameters)]
states <- sqrt(length(a))
A <- matrix(a, states, byrow = TRUE)
A <- t(A)

dX <- c()

for(i in 1:states) {
dX[i] <- sum(state * A[i, ])
}

etaVals <- c()

for(i in 1:states) {
etaVals <- sum(etaVals, state[i] * exp(eta^(-1) * dX[i]))
}

if(is.infinite(etaVals)) {
stop("Due to internal restrictions of R, please choose a greater value of
eta.")
}

for(i in 1:states) {
dX[i] <- (state[i] * exp(eta^(-1) * dX[i])) / etaVals - state[i]
}

return(list(dX))
}
```

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EvolutionaryGames documentation built on Aug. 29, 2022, 1:06 a.m.