Question 1160662: Helen and David are playing a game by putting chips in two piles (each player has two
piles P1 and P2), respectively. Helen has 6 chips and David has 4 chips. Each player
places his/her chips in his/her two piles, then compare the number of chips in his/her
two piles with that of the other player’s two piles. Note that once a chip is placed in one
pile it cannot be moved to another pile. There are four comparisons including Helen’s
P1 vs David’s P1, Helen’s P1 vs David’s P2, Helen’s P2 vs David’s P1, and Helen’s P2
vs David’s P2. For each comparison, the player with more chips in the pile will score 1
point (the opponent will lose 1 point). If the number of chips is the same in the two piles,
then nobody will score any points from this comparison. The final score of the game is
the sum score over the four comparisons. For example, if Helen puts 5 and 1 chips in her
P1 and P2, David puts 3 and 1 chips in his P1 and P2, respectively. Then Helen will get
1 (5 vs 3) + 1 (5 vs 1) - 1 (1 vs 3) + 0 (1 vs 1) = 1 as her final score, and David will get
his final score of -1.
(a) Give reasons why/how this game can be described as a two-players-zero-sum game.
(b) Formulate the payoff matrix for the game.
(c) Explain what is a saddle point. Verify: does the game have a saddle point?
(d) Construct a linear programming model for each player in this game;
(e) Produce an appropriate code to solve the linear programming model in part (c).
(f) Solve the game for David using the linear programming model you constructed in
part (d). Interpret your solution.
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
Answer by ikleyn(52788)  (Show Source):
You can put this solution on YOUR website! .
Alan wants to say that the entire semester is needed to read it to the end.
Regarding me, I think that it is difficult, in general, to find a person who will read it to the end.
My believe is that there is no Math problem longer than 5 lines of the standard text.
The common rule of life is that nobody will read so long text without vital necessity, unless it is EXTREMELY interesting.
Also, answering such post requires special knowledge in game theory and is far from the standard school Math curriculum . . .
At which "school" did you get this assignment ?
I hope my response will reduce and save your time from useless waiting a positive response from this forum,
so you should be thankful to me . . .
and therefore, I am ready to accept your "thanks".
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