Questions tagged [game-theory]

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

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1answer
49 views

Problem of accepting a prize versus trying to get a better one

I don't know how to better formulate the general problem I am thinking about, let me try formulate an example. Assume you are playing a game with N rounds, and at each round the following happens: ...
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0answers
9 views

Select coefficients of significance for user ratings

I create an application with some social interaction between users. Users will have ratings that determines your recommendations - users are recommended to users with the same rating.Total rating of ...
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0answers
22 views

Neural Network and equally good predictions

There is a two-player game (discrete, deterministic, perfect information and so on) where - in some but not all states - a few moves may be equally good; i.e. they are symmetric and expert player will ...
2
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2answers
49 views

Best strategy to cheat on a lots game

Consider the game: 100 (n=100) people (inclusive you) are putting their names in a bowl for drawing a lot There is 5 (p=5) prices, thus 95 wins nothing Cheating You can just throw instead of 1 ...
0
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1answer
74 views

Stochastic vs Adversarial Multi-Armed Bandit Problems

I know that the multi-armed bandit can be formalised in multiple ways - two of them being the stochastic and adversarial ways. I am familiar with the fact that adversarial way is a game theoretic ...
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0answers
28 views

Expected payoff from a weighted random sampling without replacement?

In an evolutionary game theoretic context, I am interested in calculating expected payoffs of different strategies in a 2x2 game, given a weighted random sampling without replacement from a population....
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1answer
262 views

Parameterizing Reinforcement Learning card game state space

I want to model a particular card game as a reinforcement learning problem. For simplicity let's say it is a single standard 52 card deck, and let's say it is just 2 players. The exact details are not ...
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1answer
273 views

What is the relation and/or difference between Game Theory and Markov Chain Model? [closed]

I am doing some work regarding my master's thesis in networks security. I have decided to work with Game Theory, calculating the Nash Equilibrium for a two player zero sum game. However, I have also ...
2
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1answer
54 views

Strategy to win a card game that follows Wallenius' noncentral hypergeometric distribution

Let's say that you have a two valued deck of N = 53 cards. Win and lose are the only values and we know that #win = 26 and #lose = 27. To play, we pay 1 unit of value. We draw one card at a time, but ...
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0answers
122 views

Multi-agent reinforcement learning: An introduction

I would like to make a Tic-Tac-Toe game with 10X10 board and I want to have 2 agents playing against each other and learning to play from interaction. A naive approach could be taken - to simply let ...
2
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0answers
379 views

How to calculate Shapley value when order matters?

I am trying to figure out the Shapley value when order matters. When using the R package GameTheoryAllocation you have to input the characteristic function. For ...
4
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0answers
40 views

“Approved” switch criterion for the Secretary problem

The secretary problem ( 1, 2, 3, 4, 5 ) optimal stopping, says "stop and keep the best" in a randomized sequence of known length "k" where you can't select previously elements of the sequence. One ...
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0answers
125 views

Why in fictitious self-play only average strategy converge to the Nash equilibrium?

What are the reasons that in fictitious self-play only average(not the best-response) strategy converge to the Nash equilibrium?
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1answer
108 views

Simulation of Secretary problem: optimal pool size given k=2?

Question: Is it incorrect to think there is a "sweet spot" where more samples slightly decreases the likelihood of a "Best pick" in the Secretary Problem? Details: The "Secretary Problem" from "...
2
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1answer
154 views

Uniform random variables and optimal strategy

This comes from Fivethirtyeight's riddler weekly challenge... Toddler poker is played by two players. Each is dealt a “card,” which is actually a number randomly chosen uniformly from the ...
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0answers
121 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 ...
2
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2answers
217 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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0answers
719 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 ...
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0answers
63 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'...
2
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1answer
42 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 ...
3
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1answer
60 views

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', ...
10
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2answers
4k views

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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1answer
97 views

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 ...
2
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1answer
158 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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0answers
714 views

How to deal with negative Shapley coalitions/contributions

I have a moderate understanding around the Shapley value/theorem (I've been digging into many papers and research articles lately). Up front statement -- I'm not a statistician/mathematician -- I ...
1
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1answer
39 views

Expectations versus returns

I have calculated the probability of winning an event, say a horse race, and am comparing it with the odds on offer. I have two horses which look good prices. My model says horse A has a 5% chance of ...
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1answer
151 views

How to get payoff function from probability?

Okay, I am studying for my game theory midterm tomorrow and I am stumped at the practice final and I don't want to just look at the answer key. I would like some knowledge to substantiate my work. I ...
4
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1answer
2k views

What is the formal definition of an “atomless” distribution?

The use of atomless (continuous) distributions is ubiquitous in applied works. While the general idea is somewhat clear to me, I was looking for a formal definition or some useful references on the ...
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0answers
44 views

Probability in the game Risk? [duplicate]

I've been playing a board game called risk lately, and I'm very interested in the probability behind it. Sorry if this question is it the wrong category, but I assumed that it was largely statistical. ...
3
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1answer
341 views

Why are inf and sup used in the definition of minimax estimators?

An estimator $\hat{\delta}$ is minimax iff $$\sup_\theta R(\theta,\hat{\delta})=\inf_\delta\sup_\theta R(\theta,\delta)$$ or in english iff out of all estimators it has the least maximum risk. For ...