Help1:=proc(): print(` GameDB(), Rand2PlayerGame(a,b,K), IsDom(v1,v2), IsStictDom(v1,v2)`):end:

#GameDB(): A list of length 5 consisiting of a a "data base"  of famous gamess (and less famous ones): 
#Prisoner's dillema, Boattle of the Sexes,  Matching pennies, Figure 1.1.1. in Gibbons, Figure 1.1.4 in Gibbons
#For example, to see the Prisoner's dillema, type
#matrix(GameDB()[1])
GameDB:=proc():
[
[ [[-1,-1],[-9,0]], [[0,-9],[-6,-6]]],
[ [[2,1],[0,0]], [[0,0],[1,2]]],
[ [[-1,1],[1,-1]], [[1,-1],[-1,1]]],
[ [ [1,0],[1,2],[0,1]], [ [0,3],[0,1],[2,0]]],
[ [ [0,4],[4,0],[5,3]],[ [4,0],[0,4],[5,3]], [ [3,5],[3,5],[6,6]]]
]:
end:


#added after class:
#Rand2PlayerGame(a,b,K): A random 2-player (static) game where the Row player has a strategies (Row 1, .., Row a), the Column player has b strategies (Col. 1, ..., Crol. b)
#and the pay-offs are from 0 to K. For example, to see a random game where Player Row has four strategy choices, and Player Column has five strategy choices
#and the pay-offs are integers from 0 to 20 type:
#matrix(Rand2PlayerGame(4,5,20));
Rand2PlayerGame:=proc(a,b,K)  local ra,i,j:
ra:=rand(0..K):

[seq([seq([ra(),ra()],j=1..b)],i=1..a)]:

end:

#IsDom(v1,v2): Given two lists of numbers is v1[i]<=v2[i] for all i. For example
#IsDom([1,3,2],[2,4,3]); should return true but IsDom([1,3,2],[2,4,1]); should return false
IsDom:=proc(v1,v2) local i:

for i from 1 to nops(v1) do
 if v1[i]>v2[i] then
  RETURN(false):
 fi:
od:
true:
end:


##Added Jan. 23, 2022, thanks to comments by Lucy Martinez, Rebecca Embar, and George Spahn
#IsStictDom(v1,v2): Given two lists of numbers is v1[i]<=v2[i] for all i. For example
#IsStrictDom([1,3,2],[2,4,3]); should return true but IsDom([1,3,2],[2,4,1]); should return false
IsStrictDom:=proc(v1,v2) local i:

for i from 1 to nops(v1) do
 if v1[i]>=v2[i] then
  RETURN(false):
 fi:
od:
true:
end: