# In a game of tic-tac-toe, the first player has three different choices at the first move: the…

In a game of tic-tac-toe, the first player has three different choices at the first move: the center square, a corner square, or a side square. The second player then has different alternatives depending upon the move of the first player. For instance, if the first player chooses a corner square, the second player can select the center square, the opposite corner, an adjacent corner, an opposite side square, or an adjacent side square. We can picture the possible outcomes for the game in a decision tree as follows:

Nodes ➀ correspond to decision points for the first player; nodes ➁ are decision points for the second player. The tree is constructed in this manner by considering the options available to each player at a given turn, until either one player has won the game (i.e., has selected three adjacent horizontal or vertical squares or the squares along one of the diagonals), or all nine squares have been selected. In the first case, the winning player receives 1 point; in the second case the game is a draw and neither player receives any points.

The decision-tree formulation of a game like that illustrated here is called an extensive form formulation. Show how the game can be recast in the linear-programming form (called a normal form) discussed in the text. Do not attempt to enumerate every strategy for both players. Just indicate how to construct the payoff tables.

[Hint: Can you extract a strategy for player 1 by considering his options at each decision point? Does his strategy depend upon how player 2 reacts to player 1’s selections?]

The remaining exercises extend the theory developed in this chapter, providing new results and relating some of the duality concepts to other ideas that arise in mathematical programming

Calculate the price
Make an order in advance and get the best price
Pages (550 words)
\$0.00
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Upload your instructions
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with MyhomeworkGeeks
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
Testimonials
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.

Notice: Array to string conversion in /home/myhomeworkgeeks/myhomeworkgeeks.com/wp-content/themes/proxim-canyon/widgets/reviews.php on line 18
Array
Overall, I think it's a great service. I have yet to submit the assignment, so I don't know what kind of grade I'll get. But customer service was excellent. Reviews were made and the assignment proofed for satisfaction.
Customer 0, December 15th, 2021

Notice: Array to string conversion in /home/myhomeworkgeeks/myhomeworkgeeks.com/wp-content/themes/proxim-canyon/widgets/reviews.php on line 18
Array
Thank you so much for your help! :)
Customer 0, May 11th, 2022

Notice: Array to string conversion in /home/myhomeworkgeeks/myhomeworkgeeks.com/wp-content/themes/proxim-canyon/widgets/reviews.php on line 18
Array
great summery in terms of the time given. it lacks a bit of clarity but otherwise perfect.
Customer 0, June 9th, 2021

Notice: Array to string conversion in /home/myhomeworkgeeks/myhomeworkgeeks.com/wp-content/themes/proxim-canyon/widgets/reviews.php on line 18
Array
Love this writer!!! Great work
Customer 0, April 5th, 2021

Notice: Array to string conversion in /home/myhomeworkgeeks/myhomeworkgeeks.com/wp-content/themes/proxim-canyon/widgets/reviews.php on line 18
Array
First of all, the writer made sure that he completely understood my assignment and all the guidelines before he began writing. My paper was finished very fast and well before the specified deadline. I thought it was written excellently. He definitely completely grasped the topic. Overall, he is a great writer and I couldn't have asked for better.
Customer 0, November 29th, 2021

Notice: Array to string conversion in /home/myhomeworkgeeks/myhomeworkgeeks.com/wp-content/themes/proxim-canyon/widgets/reviews.php on line 18
Array
It was a very long paper, but she followed all the instructions, and she even finished the paper 5 days before the due date. Will write an essay with her again, thanks!
Customer 0, November 27th, 2021

Notice: Array to string conversion in /home/myhomeworkgeeks/myhomeworkgeeks.com/wp-content/themes/proxim-canyon/widgets/reviews.php on line 18
Array
very good paper thank you.
Customer 0, February 18th, 2022

Notice: Array to string conversion in /home/myhomeworkgeeks/myhomeworkgeeks.com/wp-content/themes/proxim-canyon/widgets/reviews.php on line 18
Array
The writer did not follow my choice of topic (Food/Water Insecurity, Hunger, & Poverty), the paper was instead written about Climate Change in Africa. However, the paper was still great and informative. Thank you!
Customer 0, January 28th, 2022

Notice: Array to string conversion in /home/myhomeworkgeeks/myhomeworkgeeks.com/wp-content/themes/proxim-canyon/widgets/reviews.php on line 18
Array
I am beyond eager to write this review for this writer. I received a grade of "Mastered"upon first submission on this assignment. I will shout to the rooftops ENCOURAGING you to hire him. I have used other writers but NONE have delivered such awesome work as this writer and NONE of their prices can compare to his. He does not try to "break the bank" and he works hard; it shows in the final paper and the grade. He is simply,THE BEST HERE!!
Customer 0, November 16th, 2021

Notice: Array to string conversion in /home/myhomeworkgeeks/myhomeworkgeeks.com/wp-content/themes/proxim-canyon/widgets/reviews.php on line 18
Array
Looks great and appreciate the help.
Customer 0, April 26th, 2021

Notice: Array to string conversion in /home/myhomeworkgeeks/myhomeworkgeeks.com/wp-content/themes/proxim-canyon/widgets/reviews.php on line 18
Array
I finished the first deliverable of a project presentation but had no time to finish my second deliverable. The writer revamped my first deliverable and made it much more appealing! Not only was I impressed with the content but I was so grateful for the time they took to redo the background. I have been under a lot of pressure at work and at home so this has been a great service when I have had little time! I appreciate the detail and help! Always on time and always exceeding expectations!
Customer 0, April 5th, 2022

Notice: Array to string conversion in /home/myhomeworkgeeks/myhomeworkgeeks.com/wp-content/themes/proxim-canyon/widgets/reviews.php on line 18
Array
On time and as always a great service! This semester has been very time consuming a tough for my family so this service has not only been a life saver but helped me keep up my grades! If you are in a time crunch or need help, don't hesitate! They are worth it!
Customer 0, April 4th, 2022
11,595
Customer reviews in total
96%
Current satisfaction rate
3 pages
Average paper length
37%
Customers referred by a friend
OUR GIFT TO YOU
15% OFF your first order
Use a coupon FIRST15 and enjoy expert help with any task at the most affordable price.
Claim my 15% OFF Order in Chat

Are You Looking For Assignment Help? We Can Certainly Assist You