Questions tagged [game-theory]

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

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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 ...
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 ...
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(...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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?
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: ...
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 ...
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 ...
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 ...
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....
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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?
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 "...