# Questions tagged [game-theory]

The study of mathematical models of conflict and cooperation between intelligent rational decision-makers

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### Shapley, cooperative games and linearity

Shapley values grant that the additivity property hold. However, I am in understanding cases where additivity in cooperative games does not hold. Specifically, I am looking for a practical example of ...
• 747
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### How to approximate the point a sequence is converging to?

I have created a poker solver as part of my Master's Thesis. This solver uses Counterfactual Regret Minimization (CFR) to compute a Nash Equilibrium of Hold'em or Omaha Poker. The solver uses existing ...
61 views

### Variation on St. Petersburg Paradox, with total loss at the end

I’m not too sure how to answer these variations I thought of and was hoping someone could enlighten me. A casino offers a game of chance for a single player in which a fair coin is tossed at each ...
• 83
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### Probability of winning in the specific case [duplicate]

With 3 boxes, two of which are empty and one full, what is the probability of winning the full box by switching when there are two left? Considering that I initially choose one box, and then one empty ...
280 views

### One Card Poker Expected Value

At my local casino there is a one card poker game with the rules as follows: The game is essentially WAR you get a card and the dealer gets a card. To beat the dealer you need a higher value card (in ...
• 131
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### Analyzing Optimal Search Strategies for Rewards in a Game with Unbalanced Odds

I have received an invitation to participate in a game show where the amount I could potentially win depends on how well I perform. The game requires me to find diamonds hidden in 30 vases that are ...
1 vote
29 views

### Given a set of random variables, how can I find a linear combination of these variables satisfying a constraint on the sum of their permuations?

Say I have n random variables, {X0...Xn}, n>9. I also have another set of random variables constructed from the first set, where each of these are the sum of 9 ...
• 11
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• 351
1 vote
202 views

### How to deal with unknown distribution?

I have a game with two players. Player 1's type is publicly known, while player 2's type is unknown (privately known to him) and distributed, say, from 0 to 1. Both players play their payoff ...
• 11
6k views

### In simple Russian Roulette how many times should you shoot before handing it off to the other person?

I'm assuming a game of Russian Roulette where you have a gun with 1 bullet and six chambers, and two people playing. The rules are: You must shoot at least once on your turn. After shooting once, ...
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1k views

### Shapley Value with incomplete information

I'm building an algorithm in R to calculate the Shapley Value for players in a collaborative game. However, I do not have an outcome value for all possible coalitions, partially because the number of ...
• 83
1 vote
116 views

### How to know which method to use to work out hand probabilities in Texas Hold'Em Poker?

So I just asked earlier about how to calculate the probability of a starting pair making quads (four of a kind) on the flop and was informed that it's a hypergeometric distribution and essentially it'...
52 views

### How to make a confidence interval in a binomial model with fakes?

I'm writing a concept recognition self-test. (This is less weird than it sounds, but only slightly. Don't worry about it.) Partly to prevent people from clicking everything in sight, but mostly just ...
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### Specifying a good goal in Multi-agent RL

I am reading a survey paper on Multiagent reinforcement learning (MARL) by Busoniu, Babuska, De Schutter (IEEE Transactions on Systems, Man and Cybernetics March 2008). Under 'Challenges in MARL', ...
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### What's the relation between game theory and reinforcement learning?

I'm interested in (Deep) Reinforcement Learning (RL). Before diving into this field should I take a course in Game Theory (GT)? How are GT and RL related?
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1 vote
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### Probability the next draw from a distribution is greater than some number given a previous draw

I'm working on a game theory model of incomplete information, where players observe certain attributes via noisy signals. I am looking to solve for two different probability functions, though I think ...
• 99
852 views

### Statistics guessing game

This is a game that I wanted to know the answer for. The Game There are many players in the game, who each get a guess. There is a loss distribution, $L$, where: $L$ ~ Gamma($\alpha$, $\beta$) i....
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