Question

Prove that the first player in a game of (the usual 3 × 3) tic-tac-toe can always (at least) force a draw. Note that one way to do this is to draw the full game tree, but there is an easier proof.

Answer #1

**ANSWER:**

**Given that**

JAVA Programming
* create a 3 dimensional tic tac toe game. make 1 player
the computer.

Consider a modified version of the very famous tic-tac-toe game
in which player 1 moves, then player 2 moves, and then player 3
moves and the game ends. The number of strategies for player 1, 2,
and, 3 are respectively:
a.
9, 72, and 504.
b.
None of the available options in this list.
c.
9, 9, and 9.
d.
9, 8, and 7.

A Tic-tac-toe board has 9 spaces. The first player fills one of
the spaces with an X, then the second player fills a space with an
O. The players continue to alternate filling a space with their
respective symbol until no empty spaces remain on the board. How
many different arrangements of X’s and O’s are possible at the end
of the game? You must fully justify your answer.

Write a program that allows two players to play a game of
tic-tac-toe. Use a twodimensional char array with three rows and
three columns as the game board. Each element in the array should
be initialized with an asterisk (*). The program should run a loop
that:
• Displays the contents of the board array.
• Allows player 1 to select a location on the board for an X.
The program should ask the user to enter the row and...

Part 1: Create the grid tic-tac-toe gameboard using buttons and
iteration.
Part 2: Human user gets to select an open cell on the grid - place
an X on that button selected
Part 3: Check for a win using DOM iteration - new game option if
row or column matching X pattern
Part 4: Computer gets to select an open cell on the grid - place an
O on that button selected
Part 5: Check for a win using DOM...

Is it possible that which player goes first in a
sequential game can change what the Nash equilibrium outcome
is?
In this particular game, why or why not?
a. It is possible, since one player will prefer the
simultaneous-game Nash
b. It is possible, since the person going second will get to
know what the other player did first, putting them in a better
position
c. It is possible, since going first allows a player to commit
to their action...

Consider the original divide the dollar game of question (3).
How many strategies does player 1 have? How many strategies does
player 2 have? Write down all the strategies of player 1, and two
strategies of player 2. Explain briefly (in a line or two) why you
wrote the strategies of player 2 in the way you wrote them.
Question 3-Consider the following game of divide the dollar.
There is a dollar to be split between two players. Player 1...

Consider the following game. Player 1 has 3 actions
(Top, middle,Bottom) and player 2 has three actions (Left, Middle,
Right). Each player chooses their action
simultaneously. The game is played only
once. The first element of the payoff vector is player
1’s payoff. Note that one of the payoffs to player 2 has been
omitted (denoted by x).
Player
2
Left
Middle
Right
Top
(2,-1)
(-2,3)
(3,2)
Middle
(3,0)
(3,3)
(-1,2)
Bottom
(1,2)
(-2,x)
(2,3)
Player
1
a)Determine the range of values for x...

Q1. Consider the following game. A spy (row player) is trying to
get away from the villain (column player) by skiing down one of
three routes. The villain can choose to explode a bomb (which is
costly) and cause an avalanche or not explode a bomb. Payo↵s are
given by the following matrix:
Don't explode Explode
1 (12,0) (0.6)
2 (7,1) (1,5)
3 (9,3) (6,0)
a. Are there any routes that the spy should never to choose?
b. Let q...

Prove that for a square n ×n matrix A, Ax = b (1) has one and
only one solution if and only if A is invertible; i.e., that there
exists a matrix n ×n matrix B such that AB = I = B A.
NOTE 01: The statement or theorem is of the form P iff Q, where
P is the statement “Equation (1) has a unique solution” and Q is
the statement “The matrix A is invertible”. This means...

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