| Title: | Constructing an Epistemic Model for the Games with Two Players |
|---|---|
| Description: | Constructing an epistemic model such that, for every player i and for every choice c(i) which is optimal, there is one type that expresses common belief in rationality. |
| Authors: | Bilge Baser |
| Maintainer: | Bilge Baser <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.2 |
| Built: | 2025-03-13 03:00:27 UTC |
| Source: | https://github.com/cran/EpistemicGameTheory |
This function eliminates strictly dominated choices.
esdc(n, m, A, choices.A, B, choices.B, iteration)esdc(n, m, A, choices.A, B, choices.B, iteration)
n |
an integer representing the number of choices of player 1 |
m |
an integer representing the number of choices of player 2 |
A |
an nxm matrix representing the payoff matrix of player 1 |
choices.A |
a vector of length n representing the names of player 1's choices |
B |
an nxm matrix representing the payoff matrix of player 2 |
choices.B |
a vector of length m representing the names of player 2's choices |
iteration |
an integer representing the iteration number of algorithm |
This function works for the games with two players.
The reduced matrices of players' that are obtained after eliminating strictly dominated choices
Bilge Baser
a=4 b=4 pay.A=matrix(c(0,3,2,1,4,0,2,1,4,3,0,1,4,3,2,0),4,4) ch.A=c("Blue","Green","Red","Yellow") pay.B=matrix(c(5,4,4,4,3,5,3,3,2,2,5,2,1,1,1,5),4,4) ch.B=c("Blue","Green","Red","Yellow") iter=5 esdc(a,b,pay.A,ch.A,pay.B,ch.B,iter)a=4 b=4 pay.A=matrix(c(0,3,2,1,4,0,2,1,4,3,0,1,4,3,2,0),4,4) ch.A=c("Blue","Green","Red","Yellow") pay.B=matrix(c(5,4,4,4,3,5,3,3,2,2,5,2,1,1,1,5),4,4) ch.B=c("Blue","Green","Red","Yellow") iter=5 esdc(a,b,pay.A,ch.A,pay.B,ch.B,iter)
This function takes the reduced payoff matrices and finds out the probabilities for the types that expresses common belief in rationality for optimal choices.
type(A, B, choices.A, choices.B)type(A, B, choices.A, choices.B)
A |
an nxm matrix representing the reduced payoff matrix of player 1 |
B |
an nxm matrix representing the reduced payoff matrix of player 2 |
choices.A |
a vector of length n representing the names of player 1's choices |
choices.B |
a vector of length m representing the names of player 2's choices |
This function works for the games with two players. It returns infeasible solution for the irrational choices.
Probabilities of the types that expresses common belief in rationality for optimal choices
Bilge Baser
lp
Ar=matrix(c(0,3,2,4,0,2,4,3,0),3,3) choices.Ar=c("Blue","Green","Red") Br=matrix(c(5,4,4,3,5,3,2,2,5),3,3) choices.Br=c("Blue","Green","Red") type(Ar,Br,choices.Ar,choices.Br)Ar=matrix(c(0,3,2,4,0,2,4,3,0),3,3) choices.Ar=c("Blue","Green","Red") Br=matrix(c(5,4,4,3,5,3,2,2,5),3,3) choices.Br=c("Blue","Green","Red") type(Ar,Br,choices.Ar,choices.Br)