This is an Excel spreadsheet that solves for pure strategy and mixed strategy Nash equilibrium for 2×2 matrix games. I developed it to give people who watch my YouTube course or read my game theory textbook the chance to practice on their own and check their solutions. (Note: If there are infinitely many equilibria in mixed strategies, it will not calculate them. Sorry!) The newest edition also calculates the minimum discount factor necessary to sustain cooperation in a grim trigger strategy equilibrium of an infinite prisoner’s dilemma. Enjoy!

I have included a couple of screenshots and video tour below:

Leave feedback below.

Edit: Someone asked for a Excel 2003 version of the calculator. I’m attaching it here. No guarantees that it functions properly.

Your excel spreadsheet doesnt work properly. I plugged in the exact same prisoners dilemma you illustrated in your youtube video. You said in your video that down-right was the strictly dominated strategy, but your excel spreadsheet says top left is. Once I realized that I decided to ignore the application entirely. Please fix it.

And I would appreciate it if you didnt password protect it. Its just math, you dont have a copyright privilege to pure mathematics. And I highly doubt there is anything particularly unique or creative about your coding. I could find the equations on wikipedia, for the love of god. There is no point frustrating the people who appreciate you and patron your site.

The calculator works properly, at least in the case you brought to my attention. In the prisoner’s dilemma, “up” and “left” (cooperate for the players) are strictly dominated. That is, there is another strategy (here, down and right, respectively) that strictly dominates it. Strictly dominated strategies cannot be played in equilibrium, and you will note that the calculator says that is the PSNE. The reason it lists strictly dominated strategies instead of strictly dominant strategies is that there is no guarantee that a player will play a strictly dominant strategy in equilibrium once you extend past 2×2 matrices.

As for why it is password protected, I know that this will get redistributed outside of my site, and I do not want it getting altered to something that functions incorrectly if it is associated with me. I obviously make no claim that the math involved in programming it is special. After all, there are many videos on YouTube from me that explain the process in painful detail. It is just the tradeoff if you want to use it.

The spreadsheet works very well and congratulations.I really do not know why the guy Cogito is claimming about. Why he do not make himself his own calculator. It is just math anyway… Thanks

Hi, I tried to download the excel spreadsheet, and it doesn’t seem to be working in excel 2003, could you or do you have an older version for this program. Much help would be greatly appreciated. Want to practice what I’m learning, and as far as I can find your calculator seems to be the only easiest best option available.

William,
Thank you so much! Your lessons will single handedly help me pass my public policy class! You explain the fundamentals of game theory so explicitly in an easy-to-follow manner. appreciated tremendously!

I’m not the first person to say this as evidenced above but without your YouTube lessons I would be struggling through my second-year game theory course. Much more helpful than my *actual* lecturer. I finished my assignment with the help of those, and just checked my answers on your calculator – I got it right! I’m sure that the people who have gone out their way to tell you how much they appreciate your work are only a fraction of the people out there who have used it, but it’s the least I can do!

I’m a real newbie in game theory and have been following your gametheory101 online class in YouTube for two weeks. I find it (and your blogs) SUPER-COOL as no one has ever made such simple-yet-substantial lectures about game theory before. So, thank you so much!

Taking one step further, I’m planning to develop my own game theory calculator for my next semester’s project– I’ll probably use Java/C# if it goes desktop or HTML/JavaScript if it goes web. Therefore, considering I’m just a newbie here, I need your suggestions of features and functionality that might be added/extended/improved from the current version of your game theory calculator. Your reply would be so much appreciated. (=

I am jumping back into this after almost 20 years,,, with John Maynard Smith’s “Evolution and the Theory of Games”. I am particularly interested in the ideas of honesty, bargaining, and commitment as these factor strongly in decision making in multi-stakeholder groups e.g., where bargaining/haggling/negotiating produces commitments.

we run into many situations where certain issues are bookend policies (0 or 1), but for which one side has a distribution of options that can be used to optimize, based on previous decisions made using such policies (a priori info from case studies).

I find the 2×2 matrix solutions tab very useful in summing up options. I am particularly interested in developing this approach further using iterative simulations and case studies to build an adaptive tool.

Your excel spreadsheet doesnt work properly. I plugged in the exact same prisoners dilemma you illustrated in your youtube video. You said in your video that down-right was the strictly dominated strategy, but your excel spreadsheet says top left is. Once I realized that I decided to ignore the application entirely. Please fix it.

And I would appreciate it if you didnt password protect it. Its just math, you dont have a copyright privilege to pure mathematics. And I highly doubt there is anything particularly unique or creative about your coding. I could find the equations on wikipedia, for the love of god. There is no point frustrating the people who appreciate you and patron your site.

Cogito,

The calculator works properly, at least in the case you brought to my attention. In the prisoner’s dilemma, “up” and “left” (cooperate for the players) are strictly dominated. That is, there is another strategy (here, down and right, respectively) that strictly dominates it. Strictly dominated strategies cannot be played in equilibrium, and you will note that the calculator says that is the PSNE. The reason it lists strictly dominated strategies instead of strictly dominant strategies is that there is no guarantee that a player will play a strictly dominant strategy in equilibrium once you extend past 2×2 matrices.

As for why it is password protected, I know that this will get redistributed outside of my site, and I do not want it getting altered to something that functions incorrectly if it is associated with me. I obviously make no claim that the math involved in programming it is special. After all, there are many videos on YouTube from me that explain the process in painful detail. It is just the tradeoff if you want to use it.

Very cool! Thanks for creating and sharing this!

The spreadsheet works very well and congratulations.I really do not know why the guy Cogito is claimming about. Why he do not make himself his own calculator. It is just math anyway… Thanks

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great site!!! must i say anything else…

Yay! it works on OpenOffice.

Thanks! Helpful for checking my homework

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Awesome!! Game Theory is a compulsory question in my upcoming finals… The calculator is great help.. Thank you so so much :D.

Hi, I tried to download the excel spreadsheet, and it doesn’t seem to be working in excel 2003, could you or do you have an older version for this program. Much help would be greatly appreciated. Want to practice what I’m learning, and as far as I can find your calculator seems to be the only easiest best option available.

Thanx

S

I have attached a 2003 version to the original post, but not guarantees it functions properly.

William

William,

Thank you so much! Your lessons will single handedly help me pass my public policy class! You explain the fundamentals of game theory so explicitly in an easy-to-follow manner. appreciated tremendously!

I’m not the first person to say this as evidenced above but without your YouTube lessons I would be struggling through my second-year game theory course. Much more helpful than my *actual* lecturer. I finished my assignment with the help of those, and just checked my answers on your calculator – I got it right! I’m sure that the people who have gone out their way to tell you how much they appreciate your work are only a fraction of the people out there who have used it, but it’s the least I can do!

That’s a cool tool !!!

Wow, this article is fastidious, my younger sister is analyzing

such things, thus I am going to inform her.

Hi Bill,

I’m a real newbie in game theory and have been following your gametheory101 online class in YouTube for two weeks. I find it (and your blogs) SUPER-COOL as no one has ever made such simple-yet-substantial lectures about game theory before. So, thank you so much!

Taking one step further, I’m planning to develop my own game theory calculator for my next semester’s project– I’ll probably use Java/C# if it goes desktop or HTML/JavaScript if it goes web. Therefore, considering I’m just a newbie here, I need your suggestions of features and functionality that might be added/extended/improved from the current version of your game theory calculator. Your reply would be so much appreciated. (=

Mean as, buddy! Works perfectly on LibreOffice.

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Read your book. Its nice.

Thanks! I’d appreciate it if you gave the book a quick review over on Amazon. They really help out authors!

I am jumping back into this after almost 20 years,,, with John Maynard Smith’s “Evolution and the Theory of Games”. I am particularly interested in the ideas of honesty, bargaining, and commitment as these factor strongly in decision making in multi-stakeholder groups e.g., where bargaining/haggling/negotiating produces commitments.

we run into many situations where certain issues are bookend policies (0 or 1), but for which one side has a distribution of options that can be used to optimize, based on previous decisions made using such policies (a priori info from case studies).

I find the 2×2 matrix solutions tab very useful in summing up options. I am particularly interested in developing this approach further using iterative simulations and case studies to build an adaptive tool.

Thank-you for sharing!