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I understand for player 1 to randomise between a and b, they must be indifferent however I am struggling with the math to prove this. If someone can help that would be great!

I get that there’s no definitive Nash equilibrium for either player but I’m not sure how the fractions for each choice have been calculated. Thank you.

how do i set the normal form for such game and what would be the Nash equilibrium?

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what are the experimental results?

There are no pure strategies, and when I try to set equations equal to each other to find the probabilities, it never seems to work.

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Hello everyone,

I'm looking to model the ransomware problem using a simple game theory model. My goal is to find the game's equilibrium using a tool such as a payoff matrix or a decision tree, without resorting to complex mathematics.

I've studied the different type of conflicts and i first i thought it could be a prisonner's dilemma but i don't think so anymore because it's a sequential game. I also studied different method to solve the game and now i think i coudl use BRF (Best Response Function) or reverse induction but i'm not really sure.

I a bit lost now and i would be thankful if someone could give me some leads to solve this problem.

Here are the key elements I'd like to take into account:

1. The ransomware victim must decide whether or not to pay the ransom demanded by the cybercriminal.
2. The cybercriminal can choose to provide or not provide the decryption key after receiving the ransom.

Also the problem is that i dunno which numbers to use (i thought about using letters and making a curve in which the best choice for the victim would change whenever the cost of the lost files would be higher than the price of the ransom) but not sure either.

Thank you in advance for your responses and suggestions!

In Bayesian games, to show that a strategy, say A, is dominant over another strategy, say B, must it must it be shown that choosing A always gives a higher payoff than choosing B for all cases or is it sufficient to compare the expected payoffs?

Are positive-sum games cooperative by definition? Or can a non-cooperative game be positive-sum? Please explain your reasoning.

Imagine the scenario of a person who owes a lot of money in credit card debt. They are in over their head. Their income is fixed - no opportunity for the problem to get solved with a big raise or bonus. They have two options.

Option 1 is to put everything they make (after living expenses) toward paying off the debt. It will take 7+ years, and in that time their life will be unenjoyable because they won't have money for fun, hobbies, etc.

Option 2 is to file bankruptcy. This relieves them of the debt immediately, but they have bad credit for 7 years. However, they will be able to enjoy their life more because they WILL get to spend their money on the things they enjoy.

(Assume these are the only two options - no in-betweens. And assume there are no complications with the bankruptcy - all debts will be relieved.)

So my question is, is there a name for this dilemma?

Hi there people, full disclosure I don't know much about game theory, I got a question, looked around to find an answer but I don't seem to find it, so I thought I'd ask the experts.

The other day I was talking with a friend and referred to something as a zero-sum game. It is the term I heard that applied to this type of situation where you engage in something you can, in the best scenario, remain unscathed (you don't lose what you bet) or lose a varying amount of your bet up to zero, but never win anything. The best example I can come up with is a physical altercation where two people fight because of mutual dislike. Either one or both of them are going to get hurt but none won't benefit in a tangible way. He told me that wasn't a zero-sum game and reading a little about it I agree I was mistaken.

There are a lot of life situations that are like that and I find it useful to be able to identify them, but I want to use the proper term.

In the context of the Apple and Spotify strategic interaction, we will employ both the extensive form and a payoff matrix to model the sequential-move game between the two companies. This game involves Apple making initial decisions regarding its App Store policies, followed by Spotify's response to those decisions. By representing the game in this sequential manner, we can capture the dynamic nature of their interactions and analyze the implications of each player's actions.

For simplicity, we will assign arbitrary values to the outcomes based on the potential benefits or drawbacks for each player. These values will reflect the strategic considerations and incentives of Apple and Spotify in the context of their competition within the music streaming market.

Here is an example of how the payoff matrix might be structured:

• If Apple maintains its current App Store policies (A) and Spotify continues to file complaints (S), both parties may experience ongoing tension and legal battles, resulting in a payoff of 3 for Apple and 4 for Spotify.
• Suppose Apple adapts its App Store policies to comply with EU regulations (C), but Spotify explores alternative distribution channels (E). In this scenario, Apple may avoid significant fines and maintain its market dominance, resulting in a payoff of 7, while Spotify may gain access to a wider customer base, resulting in a payoff of 6.
• If Apple maintains its current policies (A) while Spotify adapts its pricing strategies (P), Apple may continue to benefit from its control over the App Store ecosystem, with a payoff of 8, while Spotify may mitigate potential price hikes and retain its user base, resulting in a payoff of 5.
• Suppose Apple adapts its policies (C) and Spotify continues to file complaints (S). In this case, Apple may incur some financial penalties but avoid more significant fines, resulting in a payoff of 6, while Spotify may maintain pressure on Apple to ensure fair competition, resulting in a payoff of 5.

These examples illustrate how different combinations of actions by Apple and Spotify can lead to varying outcomes for each player. By constructing a payoff matrix and analyzing the extensive-form representation of the game, we can identify equilibrium strategies for both companies and gain insights into the likely outcomes of their strategic interactions in the music streaming industry.

Is anyone interested in information Design? Literal (Bayesian persuasion) or metaphorical? I work on this topic and I realize that not many people seem to know about it. So, I thought it might be useful to have a topic about it. I will be posting links of the milestone papers but the following ones are very nice literature reviews that would help the beginners. Kamenica's literature review: https://www.annualreviews.org/content/journals/10.1146/annurev-economics-080218-025739 Bergemann and Morris' literature review: https://www.aeaweb.org/articles?id=10.1257/jel.20181489

I manage a grassland preserve in a rural area. We use hay harvest as an ecological restoration tool. We contract with local farmers who cut, rake, bale, and haul away the hay. According to our organization's policy, hay is considered surplus property and must be bid on competitively. Instead of money being exchanged, contractors pay with hours of "brushhogging" (using a tractor-mounted mower to cut and mulch up brushy areas which cannot be used for hay). The ecological effects of mowing+baling vs mowing+mulching are different. We have the ability to brushhog ourselves, but haying is time and equipment-intensive and we don't have the ability to do that ourselves, and we have little use for even good hay. Therefore, the contractors doing the haying is more valuable to me as the manager.

Hay contractors use the hay for their own animals or sell it. They are incentivized to bale "good" hay (grassy areas) and do not want to bale "bad" hay (weedy and/or shrubby areas) as it is not good forage and doesn't sell as well. However, the weedy/shrubby areas are the ones that would most benefit from hay baling, so I am incentivized to get them to bale hay on those areas. They are incentivized to do less brushhogging as it costs them time and fuel, and it is only somewhat useful for me as we can do it ourselves in a way that I'd prefer whenever we want. However, brushhogging hours are more useful to me than money. Some of the contractors only sell the hay, so they can get some money for low-quality hay, while the farmers using it for their personal use have little use for bad hay.

I am also incentivized to have multiple contractors working on multiple units so that the hay harvest is less affected by weather and mechanical issues, as it is therefore more likely to be done in the time frame I would prefer. The alternative would be a "winner take all" system that we used for a while, but when the one contractor has issues with their equipment or it is rainy, then they have to stop working and push the time frames I prefer. I would rather have 3 contractors working for 2 weeks each rather than 1 contractor working for 6 weeks, in other words.

I am considering using a system where

1. multiple units are available and can be won individually by different contractors
2. winning bids are for the greatest number of hours of brushhogging the contractor will later do in exchange for hay harvest on a particular unit
3. "good" and "bad" hay units are not treated differently by us - it is difficult for us to judge the value the contractors will see in a particular unit
4. contractors are allowed to bid negative values of brushhog hours, where a "winning" negative bid would be a "rebate" on the total number of hours of brushogging they would have to do later (assuming they also win other units with a positive winning bid). Negative total amounts would be reset to 0 each year.

I am hoping this would work this way: it would be more likely for multiple contractors to win bids, and they would be incentivized to hay low-quality areas (likely with negative bids), but no contractor misses out on "good" hay units because they weren't willing to hay low quality areas. A system that rewards more directly winning good hay in exchange for cutting bad hay would likely favor our contractors that sell their hay to the point where they could monopolize all the contracts, so that's not ideal (as describe above, I'd prefer multiple contractors). Attempts to negate excessively large positive bids on good hay with excessively low negative bids on bad hay could be thwarted by someone else bidding higher on the bad hay unit (if you bid -500 on a bad unit and 500 on a good unit, you will be beat by someone else bidding -499, 0, or 5 on the same bad unit...then you would have a lot of brushhogging to do). In this way, both the good and bad hay units are competitive.

Does this system make sense, and do you see a way it could be exploited to one person's advantage? Does it seem fair for all involved? Do you see another way this could be done given each party's incentives?

Thank you!

Have recently gotten interested in the game theory side of evolutionary biology. Is the book Evolution and the Theory of Games a suitable first book in terms of difficulty? Since I don't have much knowledge game theory.

I know tit for tat is the best in many situations, with pure evil (or whatever it's called) being the best in others. I was just wondering if there is a strategy or series of strategies that always loses regardless of the situation or else loses more often than not? Just curious! If there's not a definitive answer, then I'd love to hear your thoughts regardless! 👍

In order to further explore game theory I created a new version of my Zombie 2100 game called Zombie 2102. This version has an AI controlled opponent that cooperates or competes with you depending on circumstances.

https://labs.blueboxsw.com/z21/zombie2102/

It is registration-free, ad-free, download-free, tracker-free, and should play pretty much in any browser, desktop or mobile.

It still has a feature that will show you the strength of all available options at any point in the game. You can turn this on or off as needed to learn the game or if you get stuck.

Basically it is like a mashup of Oregon Trail and Zombie Dice, if you have ever played either of those. The rules are simple and you can pick it up in a couple minutes, but the strategies used can shift as you play.

Previous versions:

Zombie 2100 - Original, same setup each game

https://labs.blueboxsw.com/z21/zombie2100/

Zombie 2101 - New setup each day plus leaderboard

https://labs.blueboxsw.com/z21/zombie2101/

I need some assistance finding a real life example of game theory with a source linked. I need to compare my results with the real life results. If they don’t coincide I need to explain why.

Everyone in your workplace/university/whatever are offered a choice between taking a blue pill or a red pill.

• If over 80% take the blue pill, nothing happens
• If over 20% take the red pill, everyone who took the blue pill dies

The question is: which pill do you take? Here there are 2 slightly different formulations:

(a) Everyone is given this choice at once, without any time to prepare or agree on a strategy (b) You are given a chance to make a speech to the whole group, and immediately after everyone votes. What do you say in the speech and what do you vote?

What's it called when everybody adopts a sub-par strategy because everyone else did? The common example is how one spectator standing at a stadium can result in the whole stadium standing (so they can see), when the more efficient strategy would be for everyone to sit. Trying to find the name, but don't know what to search for.

Hello,

I'm not studying the field but has an interest in it. I kinda know the basics of it, but here is my question:

Was there some major breakthrough in game theory recently?

If so, what would you recommend that I read to keep up with it?

Thanks!

is this subreddit the official Game Theory subreddit?

I am really confused about this, I wanna scream so bad hahahahah. But for real, how?

I am a math major, my capstone focus is game theory. I’d like to write about game theory in backgammon. Anyone have any ideas or sources? Thank you! :)

Hey all, I'm hoping to get some insight into a personal project I'm working on. I wanted to create a program that allows users to input a wordle guess and then it would evaluate the guess based on several factors, including likelihood that a given letter is used, if the guess has duplicates, or things like that. I have the usage rates of each letter for every wordle answer from the first wordle puzzle until October 2027 as well as how common duplicates are, but i have no idea how to begin constructing a formula that will be even slightly coherent. Pls help ❤️