The question would probably be yes, but I'm simply interested in how that is the case. Would the correlation be a stretch, or would the connection be so good that it allows for thoughtful explanations/discussions? How so?

I really enjoy Inquiry courses and wanted to see if something like this can be applied to discussions among peers and such.

I said the only strategies were a,b,c, and e,f for p1. H is dominated by a mix of e and f, that g is dominated by e and f, and for p2 d is dominated and never optimal

You should do a game theory on the Papa Games. The Papa Louie Universe. Like the games Papa Sushiria and all the other ones.

Mixed strategy Nash equilibria always sound like a fascinating concept in theory, but it’s hard to imagine how they show up in real life. Most of the time, people expect clear, predictable strategies, but in situations like auctions, sports, or even military tactics, randomness can actually be the optimal move.

For example, penalty kicks in soccer or rock-paper-scissors-like games in business negotiations come to mind. But what are some less obvious, real-world examples where mixed strategies are not just theoretical but actively used? Bonus points if you’ve seen these play out in your personal experience or profession! Would love to discuss how game theory translates to the real world.

This is for one of my classes, is this question talking about if there is a mixed strategy (in this case, the other options aren't as good but a mix would work) that there could be a pure strategy as well?

If it's that's conditional statement, wouldn't it be false since you need the mix to have a dominant strategy so there can't be a pure strategy that can also dominate?

To preface this, I have very little formal experience in game theory, so please keep that in mind.

Say we modify the rules to Monty Hall and give the host the option to not open a door. I came up with the following analysis to check whether it would still remain optimal for the participant to switch doors:

1. The host always opens a door: Classic Monty Hall, switching is optimal
2. The host will only open a door when the initial guess is incorrect: not much changes and switching is still optimal
3. The host will only open a door when the initial guess is incorrect: assuming that switching when no door is opened results in a 50% chance of choosing either door, then both switching and not switching would result in a 1/3 chance of winning, meaning neither is better than the other
4. The host never opens a door: same as above, both are the same

So it's clear that switching will always be at least as good as not switching doors. However, this is only the case when the participant does not know what strategy the other will employ. Let's say that both parties know that the other party is aware of the optimal strategies and is trying their best to win. In that case, since the host knows that the participant is likely to switch, they could only open a door when the participant chooses the right door, causing them to switch off of the door, and give the participant a 1/3 chance if they initially chose the wrong door. However, the participant knowing that, can choose to stay, and the host knowing that can open a door when the participant is initially incorrect. Is there any analysis that we can do on this game that will result in an optimal strategy for either the host or the participant (my initial thoughts are that the participant can never go below 1/3 odds, so the host should just not do anything), or is this simply a game that is determined by reading the other person and predicting what they will do. Also, would the number of games that they play matter? Since they could probably predict the opponent's strategy, but also because the ratio of correct to incorrect initial guesses would be another source of information to base their strategy upon.

Hi All - I am just beginning to learn about game theory. I would like to begin with learning about incidents where game theory was successfully applied and won in real life political, criminal negotiations or any interesting situations. Are there any books to such effect?

Hi, I’ve decided on writing an essay about game theory and have been recommended to focus on one field where it is utilized. I’ve gone through a couple of them and can’t really seem to choose one I’m content with.

I’m looking for something that’s up-to-date and also for some book recommendations.

I appreciate any kind of help 🙏

I need to do a project for my university. It's a Markov game, that I should model and then solve it (find the optimal/almost-optimal policy for it using different methods. It is a two-player zero-sum game. What approaches I can use for solving it? How would you usually approach this kind of problem? Where to start? I know how to model it in Game Theory, but I have problem in actually solving it with different algorithms, having good visualizations for it and things like that.

Any tutorial that actually doing it and is beginner friendly?

Hello everyone,

I am learing for my economy exam and I would really appreciate some help.

How do I tranform this tree shape graph into matrix style one?

The third and fourth paragraphs of this book seem somewhat disconnected. The third paragraph explains that Von Neumann's theory takes individuals' preferences for risk aversion into account, while the fourth paragraph states that the theory assumes players are entirely neutral toward the actual act of gambling. Did I misunderstand something?

https://preview.redd.it/09drumn0kcfe1.png?width=602&format=png&auto=webp&s=b1b3f7afb4ddfee65466515bcc77233a34f9bb79

Framing negotiations in life as contained one-shot decisions made in the dark with no communication or trust, between "rational" (nihilistic) criminal agents?

It seems to me this never eventuates in real life, every pair of negotiators has some sort of history and/or future together, there are external factors, and there is often communication as well as common ("irrational"/non-nihilistic) values that can be appealed to.

It seems to me that selling the idea of the Prisoner's Dilemma as the first port of call for almost any application of Game Theory to real life, is not only mismatched but potentially corrosive to society.

Thoughts?

PS: I appreciate all the points in support of the PD as a worthwhile and interesting example, leading to the more interesting and applicable iterated version. I’m more interested in what influence people think the one-shot PD becoming universally known by laypeople might have on society. People seem to be missing this question, in favour of supporting the PD as a valid game theory example (all fair points).

So I am trying to apply some game theory principles in stock trading and I learned everything about game theory basics like equilibrium and prisoner's dilemma stuff. What I really keep getting in stock trading is the concept of "priced in". So the stock prices are assumed to have applied to their price all the news that already publicly known. What my problem is that if you get to the next level and ask a question: "OK, the investors already priced in all the news then what if they buy futures for the stock prices that are expected to change in the next few months". Then if you get to another "level" and ask a question "what if futures traders understand that those investors priced in what is expected in the futures". So you see my point you get this endless "what if" circular logic where an "absolutely smart" player can go endlessly thinking what the other player thinking.

First of all I want to know if in mathematics there is a formal term for this. Also would love to see some papers addressing this circular logic.

It's 1:30am and I've been thinking about Monty Hall. I got to thinking, what if the contestant lies about their intentions? How does it affect the statistics of the situation?

Three doors, prize behind one of them: D1, D2, D3.

You are asked to pick a door. You secretely decide on D2, but lie to the host, saying you'd like to pick D1. The host then opens a door to reveal what is behind it.

The host will then reveal what is behind either D2 or D3, and will never reveal the door which has the prize, which is information he has.

If the host exposes D2, then your original secret pick is no longer an option - you must decide on either D1 or D3. Functionally, I guess this is identical to the standard monty hall problem, and you'd be best to choose D3 on the basis of the host being rational and informed.

But what happens if the host exposes D3? do you still gain an advantage from "switching" to D2, which was your real pick from the beginning? As I understand, the advantage you gain from switching is because of your knowledge of the host's knowledge, therefore, you should always choose the option that the host didn't understand you to intend on taking.

Is this correct? Am I going crazy?

Hey! I'm trying to do a study on trust using Berg's investment game. I want to run it online, and am wondering if anyone has suggestions of how to do that. Also am open to other games that measure trust! Thanks! :)

So I've just started looking into the concept of game theory and I think it'd be a great idea for a school project, can you give me one real life scenario that follows the fundamentals and applications of game theory but is also heavily backed up by mathematics?

I've been using this https://axelrod.readthedocs.io/en/fix-documentation/index.html python library to have a bit of fun with Axelrod's Tounament.

Some of the final results I get are different from the scores found in 'Effective Choice in the Prisoner's Dilemma' paper by Axelrod. Namely the result for FirstByDowning vs FirstByTidemanandChieruzzi gives 203-223 in python; but in the paper the results were 591-596.

Is this library reliable? has anyone else used it? I am using it wrong?

Should I not be bothered about the differences?

thanks for any answers

Hello all,

I have hopefully a quick question regarding 2x2 matrices and pure strategy nash equilibria. Firstly, how many pure strategy nash equilibria can exist in a case where we have 2 players who can only choose between 2 actions (2x2 matrix)? Initially I thought the answer was 2, but I am now presented with the following matrix which I believe (could totally be wrong lol) has 3 pure strategy nash equilibria:

R L

R (6,6) (2,6)

L (6,2) (0,0)

I believe the pure nash equilibria are: (D,D),(H,D),(D,H) because in those instances no individual can make a unilateral change to increase their utility. However, as previously stated I am unsure of how many pure strategy nash equilibria could exist in a 2x2 matrix.

Any help on the matter would be greatly appreciated!!

Looking for a textbook that is mathematically rigorous but also relatively accessible.

My course topics are: Game Theory, Imperfect Competition, Externalities and Public Goods, Adverse Selection (Signalling and Screening), Moral Hazard and Mechanism Design/Applications.

Textbook Recommendations by my professor:

Robert Gibbons, Game Theory for Applied Economists, Princeton University Press, 1992.

Hal Varian, Microeconomic Analysis, 3rd edition, Norton, 1992.

Andreu Mas-Colell, Michael D. and Jerry R. Green, Microeconomic Theory, Oxford University Press, 1995.

Tirole, J., The Theory of Industrial Organization, MIT Press, 1988.

David Kreps, A Course in Microeconomic Theory, Princeton University Press, 1990

Was hoping to look into experiences by others who've read the above texts already, as to which text is good for which topic, and if there any unmentioned textbooks that could be good for learning my course topics.

can anyone solve the question below? (its frustrating because simultaneous move games shouldn't normally be solved using backward induction, but this what I think must be done for the last subgame part). thank you for your help!

Consider the following two-player game. Player 1 moves first, who has two actions
{out1, in1}. If he chooses out1, the game ends with payoffs 2 for player 1 and −1
for player 2. If he chooses in1, then player 2 moves, who has two actions out2, in2.
If player 2 chooses out2, then the game also ends, but with payoffs 3 for player
1 and 2 for player 2. If she chooses in2, then next, the two players will play a
simultaneous game where player 1 has two actions {l1, r1} and player 2 has two
actions {l2, r2}. If player 1 chooses l1 while player 2 chooses l2, then the payoffs
are 4 and 1, respectively. If player 1 chooses r1 while player 2 chooses r2, then
the payoffs are 1 and 4, respectively. Otherwise, each of them will receive zero
payoff.
(i) Show the corresponding extensive form representation. How many subgames
does this game have? Show the subgame perfect Nash equilibria (in pure
strategies).

https://preview.redd.it/g4raczu29kce1.png?width=479&format=png&auto=webp&s=b2b80ba35afaded90c0be169760ad0fb22a9951a

Assume A is a payoff matrix of an evolutionary game, I am asked to find all evolutionary stable strategies.

Entries in A represent the payoff for player 1. For example, consider entry (2,1), then player 1 gets payoff of 2 and player 2 gets -2.

https://preview.redd.it/97dmbmryakce1.png?width=1246&format=png&auto=webp&s=0e011736e59d8a577059159a3999ba4eb345b9ea

However, sigma* is not valid. Are there any errors in my method? Or is there other methods?. Thanks!