Hi, not a game theorist but im looking for some advice. For some background, im a Highschool sophomore looking into graduating 2 years early but one of the requirements is a capstone project. Ive always thought game theory is interesting so I’ve decided to try and do a project that models which colleges would be best to apply to with early decision (binding) based on game theory in order to learn more about the field. I am currently taking AP Calculus BC and have self studied linear algebra to an extent (at least up to eigenvalues, eigenvectors, etc) and know differential equations (up to the 2nd degree linear homogeneous kind) in case I need some math background.

I would like to know if its possible to model which type of colleges would be best to apply to with early decision with game theory. Some things to consider about the situation is the risk of applying for a college with early decision and being rejected, the prestige of the college, applying for a non optimal college with early decision while having better options and being forced to go, and many others. If it is possible, where do I need to start in terms of learning game theory and modeling the problem? Do I need to catch up on some other math fields before this? I have multiple months to do the project so time is not a major concern. Any advice would be appreciated. (Edit, I neglected to mention that other applicants could by represented as the other players in this situation with their choices possibly affecting others chances of getting in)

Imagine a team of three golfers competing together. While golf is an individual sport, the team’s overall success depends on everyone’s performance. Each golfer has two goals:

1.	Avoid Last Place: Each player wants to avoid being ranked last within the team.
2.	Help the Team: To boost the team’s overall score, each golfer can share insights or tips that could improve their teammates’ performance.

The dilemma? If a golfer shares too much information, they might help others perform better and potentially push themselves lower in the rankings. Each golfer has to decide how much to share to balance personal success with team success.

Question: Given these incentives, what’s the best strategy for each golfer to balance sharing and individual performance? Should they share everything they know to help the team or hold back just enough to avoid being last? What would you do to create the optimal balance between personal success and team performance?

Hi guys, so Im currently doing a game theory question and am kind of stuck. So I have a non symmetric zero sum game that I need to find the mixed strategy on but I cant find any vids teaching me how to do that(esp cause its non symmetric)

It looks something like this

    L                   C                   R

L (0.55, 0.45) ( 0.8,0.2) (0.9, 0.1)

C ( 0.9, 0.1) (0.1, 0.9) (0.8, 0.2)

R ( 0.9, 0.1) (0.8,0.2) (0.45, 0.55)

I have tried to use EU^L = EU^C = EU^R for the expected returns of player 1(using ō to denote sigma

Where EU^L = ōL(0.55) + ōC (0.8) + (1 - ōL - ōC)(0.9) =1-0.35ōL -0.1ōC

And so on and so forth for the other 2

So just an example of what I mean above in case I wrote something wrong (using ō to denote sigma)

Is EU^L = EU^C

1 - 0.35(ōL) - 0.1(ōC) = 1 + 0.1(ōL) -0.7(ōC)

Am I on the right track? Im not even sure if this is correct for the non symmetric games and if it is, im still rather confused on how to go about solving this. So if someone out there knows what im talking about, would appreciate some help. I know this is a long read, so Thank you!

I am struggling to do proofs like "show player A has a drawing strategy", etc. The games / situations vary a lot, and I am not able to think of a general method to tackle these problems.

Are there any resourses for me to practice on? And if possible, can anyone please share their experiences? Thanks!

Hello,

Can anyone help with explaining what a symmetric Markov SPNE is? And to proceed to find it with an example? I understand that it is a refinement of the regulat SPNE in the sense that players only condition on the relevant state, but how does that apply to solving infinitely repeated games (preferrably with an extensive stage game)?

Thank you!

I’m trying to improve my application of game theory to current events. Does anyone have any ideas for a current business event that I could analyze through game theory?

We are a charity that only serves a group of no more than 2000 people. If any of them donate (any amount) to us by March 2025, then they will be entered to win a $1,500 value prize. The catch is that these donations are in the form of a payroll deduction, so they are reoccurring donations on a bi-weekly basis, but they can choose to stop donating at any time. The payroll deductions began 6 months ago, so PRIOR to announcing the raffle, we have historic data showing how many people have signed up for donations as well as the amounts they are regularly donating.

With this information, is there a way to decide if it is worth it to offer the $1,500 prize to more than 1 winner? The goal is to be able to generate enough interest*/donations* in the raffle to at least offset the cost of prizes.

Hello, my fellow strategists, how are you all ?

I was recently wondering, if someone were given a chance to start learning about game theory from the beginning. What would be the most optimal path that they can take and why ?

Consider the game:

N={1,2,3}; v(1)=1, v(2)=2, v(3)=3; v(1,2)=5, v(1,3)=6, v(2,3)=6; v(1,2,3)=10

The core I found is the blue region

https://preview.redd.it/wp7z028k52zd1.png?width=1164&format=png&auto=webp&s=b6a71bb30a804c76454e3c9c141d25d4524b04de

However, I am stuck. I have no idea to continue.

Moreover, I am struggling to understand what is Von Neumann Morgenstern solutions and what does it represent.

Thanks!

Hello everyone! I'm having issued trying to show that for any bimatrix game, the mixed security level for a given player Pi is always smaller (i.e., better) than or equal to the pure security level for the same player
Pi.

I know this might seem pretty obvious but I cannot put my finger on an actual way to demostrate it.

I want to take this data and save it and use it for a project, I wish to learn how to gather the data and save the module. If someone can point me to a good tutorial or something that would be great.

Is there any book with a collection of games with winning strategies? will be glad to receive your recommendations

We have 3 points and a game: we could bet n (n>0, n is real number) from our points. With probability of 0.4 we get 2n, otherwise lose it. The goal is to get 8 points. What's the probability and the optimal strategy for winning?

The expectation is negative, so, we'll assume that the chances are higher with less games. Firstly, let's put 3, lose or get 6. Then put 2, win or have 4. Put 4, lose or win. So, the probability of winning is 0.256. Is this strategy optimal and how could I prove it or get a better one?

As mentioned in the title. The proof (open source. found from MIT) goes as follow:

https://preview.redd.it/pkzejhnjg0yd1.png?width=2038&format=png&auto=webp&s=356582b049b5c82c57d9e786aea7ba1441086c08

However, I don't really understand case 2 and 3.

For case 2, All trees are -+ which means a win for Richard, then why Louise(+-) has a winning strategy. Is it a typo or my understanding issue.

For case 3, Richard's best strategy is a drawing strategy, and thus it guarantees he will end in a draw, so L must be a drawing strategy for Louise. Is my understanding correct for this case?

Thanks!

https://preview.redd.it/ausp533i9yxd1.png?width=488&format=png&auto=webp&s=c8a61032bd9a20df79aa148391a48d4cdf2e0a20

https://preview.redd.it/be2fg1oj9yxd1.png?width=472&format=png&auto=webp&s=19ae5bb90c442326b78ad8a6cec6143db7e92914

I'm creating a general game theory page on nonzerosum.games and wondered if you thought there were other important aspects of game theory that should be included on this page.

My supervisor referred to a book on Game Theory but forgot the name. It was supposedly written by a lifelong practitioner who applied Game Theory to his own life (may be 50 years back?) and all his life situations (including with his kids) and the lessons are applicable in business and competition.
Sounded interesting. He shared with me knowing that I like reading books.

I was hoping the experts here can help me find the book.

Imagine a basic scenario:

The Government needs a new power plant built. Their goal is to get the power plant built to specification in time for the lowest price, thus saving taxpayer money.

They open the floor for Contractors to bid, following whatever method the Government prefers (open bidding, blind bidding, etc). Their goal is to be awarded the contract and maximize their profit.

At a glance these two goals work in opposition--the Government wants to drive bid price down, and the Contractors want to keep bid price high. In theory, the Government induces competition among Contractors, keeping costs low and incentivizing winning Contractors to be efficient with their time, budget, and materials. However, as observed in reality, Contractors have indirect methods of achieving their win condition.

A basic example of this is to bid as low as reasonably possible to secure the contract in order to lock competitors out, then to operate with little concern for efficiency. Since the power plant is critical infrastructure that the Government needs built, the Contractor has leverage over the Government. They can, in effect, hold the project hostage by saying that if additional time and/or budget are not allocated, the project will not be finished. They are instead incentivized to operate slowly and inefficiently with materials and budget so that they are able to induce a budget expansion.

The Government does have the option to, instead of approving a budget expansion, to terminate the existing Contractor and hire the second best Contractor to finish the job. However, this still means that the full budget for this project was already allocated and the power plant is still not built to specification. It also means that Contractors are able to get paid in full despite not performing their full duties, and simply puts another Contractor in the same position of power as the first, with all the same incentives in place.

In reality, many variables--capital, material, labor, political, emotional, environmental, and more--go into determining the precise outcome of any given project. However, I am wondering what Game Theory has to say about this very basic example.

Is bidding in this scenario a fundamentally flawed approximation of the real cost of the power plant? Is the push and pull between Government and Contractor a better system for approximating the real cost?

It seems in this scenario that the Government ultimately has less leverage than the Contractor. Short of violence (physical or political), what options does the Government realistically have (if any) to incentivize the Contractor to align with the Government's time and budget goals for the power plant while remaining within specification? If they strong-arm the Contractors too much, Contractors would be operating at a loss and could not complete the project, even in good faith.

i’ve been taught the definition of Weakly dominance as: strategy s' dominates s" if payoff is at least greater or equal or in some cases equal 2nd POINT: at least 1 strat for which you have something strictly greater

so technically a strict domination would also fit into this definition right? so all strict dominations are also weak dominations but not the other way around?

i found it to be w, y. z for player 2 and a, c, d for player 1. is this right? i’m still relatively new to this

“A strategy that, given the strategies played by all the other players, yields the highest payoff compared to all other strategies of the player”

i thought this definition was dominant strategy but now i’m thinking its best reply since it mentions “given the strat played by all other players.” thoughts?

How can I improve my life with this.

I tried out the newly popular game under the mode Liar's Deck - Basic, and I feel like there's lots of stuff to analyze using game theory and probability. At first there aren't a lot of clues as to if a player is lying or not, so people usually play it safe by passing. Towards the later stage of one round, the probability of playing a fake card increases because so many cards have already been played and it's always possible that among those contained some real ones. Especially if someone plays like 2 or 3 cards at a later stage, that's very suspicious.

But because of that thinking, players usually are greedy in the early stages hoping to not get noticed with playing fake cards and then leave the real cards towards the end to bait you to call them a liar.

Feels like there's lots of theory and probability hidden, and it'd be cool to see if there's a Nash in here. Psychological factors also exist such as the delay time in playing cards. If someone took a lot of time to think about what to play, then maybe that person is lying.

if i’m understanding correctly, no one has a dominant strategy here. then, is it that for strictly dominated strategies, it’s:

• bell strictly dominated (SR) by lapses
• bell SR by echoes
• moon SR by wall

is this correct? i’m not sure if i’m figuring it out correctly. it’s just whichever one row/column of the same color is less than the other right? any tips for understanding would be helpful!