Questions tagged [game-theory]

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

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4
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1answer
59 views

How can we allocate when we have 150 open slots every day (5 days a week) for those 200 arrivals every day

My question is to solve a very basic problem related to the allocation of slots. Say there are 20 teams with 10 persons in each team. I have 150 open slots every day (5 days a week) for those 20 teams ...
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1answer
67 views

(Open-ended?) Stat puzzle about expected value

A fair coin is flipped $200$ times and each time it lands on heads, $1$ dollar is added to a pot. After this process is over, an auction is held for the pot. There is exactly one other person at the ...
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1answer
51 views

Bernoulli distribution

Definition 3.3.1 (Bernoulli distribution). An r.v. X is said to have the Bernoulli distribution with parameter p if P(X = 1) = p and P(X = 0) = 1 − p, where 0 < p < 1. We write this as X ~ Bern(...
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0answers
26 views

Difference between types of solutions in network matchings? [closed]

So there are so many different types of solutions: pareto, stable, rank-maximal, etc. etc. How do anyone know which one to use for any given problem? Particularly when some of them may not exist? And ...
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0answers
14 views

Confidence Level for mean comparison among control and treatment group

I collected data where two players interacted with two choices each, where a 2x2 table resulted when representing the game in strategic form. The 4 outcomes are (A, A) ; (A, B) ; (B, A) ; (B, B). My ...
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0answers
16 views

What are common statistical techniques applied to Game Theory?

I have been examining stochastic Bayesian games as a framework for modeling multi-agent games. As this looks like an active area of research, I was wondering if any particular techniques have emerged ...
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1answer
100 views

Kelly Criterion for game with payoff equal to normal distribution

I'm struggling to come up with an answer to a problem I've asked myself, if the answer is out there I must not be searching for the correct things. The problem formulation is this: You're given the ...
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0answers
18 views

Example of a Game for which Shapley Values are Clearly the Most Fair Assignment of Payout

What is an example of a (simple) game in which it is clear that paying the contributors according to their Shapley value is more fair (or otherwise makes more sense) than paying them proportionally to ...
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0answers
1k views

Interpreting SHAP Dependence Plot for Categorical Variables

I'm reading about the use of Shapley values for explaining complex machine learning models and I'm confused about how I should interpret the SHAP independence plot in the case of a categorical ...
76
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7answers
10k views

Do not vote, one vote will not reverse election results. What is wrong with this reasoning?

Do not vote, one vote will not reverse the election result. What's more, the probability of injury in a traffic collision on the way to the ballot box is much higher than your vote reversing the ...
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1answer
142 views

Queuing theory for elevators

It's been a while since I had my probability course based on Sheldon Ross' book "Probability Models", and while I never went into econometrics, I was very interested in the queuing theory section. I ...
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0answers
14 views

How to optimize a number of games with a limit set of second chances at guessing other options given probabilities?

Let's say I have a game with $M$ outcomes $\{O_i\}_{i=1}^{M}$ and I have a predictor $P$ that gives me probabilities for the outcomes of a game. I now have $N$ independent games that I want to ...
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0answers
428 views

Why is Nash equilibrium stable?

As I understand it, a Nash equilibrium is an equilibrium because no player can single-handedly improve their situation. But now consider a game where one of the Nash equilibria is worse for TWO of ...
2
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1answer
158 views

Strategy for game where larger number wins. Drawn from standard uniform distribution with one redraw allowed

Two players are playing a game where they each draw a secret random number uniformly between 0 and 1. If they are not satisfied with their draw they may redraw. The players do not know whether or not ...
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0answers
39 views

How to model game theory of poker-like card game

I'd like to get a general understanding of the optimal strategy from a game called Team Fight Tactics. To reduce this problem into a simpler form I'd like to analyze a simpler card game problem I've ...
1
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1answer
37 views

Two different dice games. What are the odds the game will be won?

Based on the images above, is it correct that the first game should be won 1 out of six times, the second game every time, and the 3rd game 1 out of six times?
4
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1answer
66 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
23 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 ...
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2answers
103 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 ...
2
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1answer
590 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
43 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
418 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
614 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
81 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 ...
4
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0answers
207 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 ...
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0answers
536 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 ...
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0answers
51 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
142 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
151 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 "...
4
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1answer
600 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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2answers
2k views

Martingales: Why must expected posterior equal prior?

For a posterior distribution to be plausible in the Bayesian sense (Bayes' Plausible), it is said that: $\mathbb{E}(\mu_{t+1} | \mu_t) = \mu_t$ where $\mu_t$ is the posterior distribution at time $...
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0answers
153 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 ...
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2answers
2k 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
954 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
86 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
45 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 ...
4
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1answer
75 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', ...
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3answers
9k 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
138 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 ...
3
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1answer
583 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
1k 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). I'm trying to derive weights/attribution for each player when ...
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1answer
45 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
240 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
4k 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
45 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. ...
5
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1answer
559 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 ...