# Questions tagged [game-theory]

The study of competitive and non-competitive games, equilibrium concepts such as Nash equilibrium, and related subjects. Combinatorial games such as Nim are under [tag:combinatorial-game-theory], and algorithmic aspects (e.g. auctions) are under [tag:algorithmic-game-theory].

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### Question on John von neumann's minimax theorem.

in the process of proving the theorem there is this step Suppose $Κ(x,y):X\times Y\rightarrow \mathbb{R}$ continous function and strictly convex wrt $y$ and strictly concave wrt $x$ where $X\times Y$ ...
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### Modified Balls in Bins Game Theory Problem

There are 3N players playing N gambles and each player has the same amount of money. For each game, each player could choose to bet some money (from 0 to 100%). The player who placed the highest bet ...
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### Is the Game of Life predictable?

I played the Game of Life intensively for a while. I tried to keep things alive from all kinds of initial configurations and succeeded up to about 1000 iterations maximally. Everything died all the ...
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### correct terminology for "dead-end game"

Apologies if this question has an obvious answer! My research is in pure math, but I've started to think about some applied problems that are similar to this game. The player arranges numbers 1-19 ...
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### Winner of impartial King placing game

The game is played on an $n\times n$ board. Two players take turns placing kings, such that no two kings attack each other. The last player to move wins. If $n$ is odd, I think the game is a win for ...
1 vote
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### I canot find what does $\langle,\rangle$ mean in a cooperative game theory book [closed]

Does anyone know what here on the page 83 it holds that $\langle x,y\rangle\geq \langle x,y'\rangle$ in taking the minimum ? I.e. I cannot find the notation $\langle,\rangle$ in the book.
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### Combining Rate of Winning | Multiplication or Addition

Problem Imagine I play the lottery and have a $2\%$ rate of winning. My friend also plays the lottery and has a $1\%$ rate of winning. Whoever wins, we will share the prize. We could think our ...
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### The win rate of three player rotation battle

Three players $A,B,C$ are playing a game. Players play against each other in round, the order of battle is $$AB \to BC \to CA \to AB \to \cdots$$ Players need to win two consecutive rounds to win the ...
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### Branches evaluation in infinite binary tree

I have been thinking about a proposition on infinite trees, which seems to be false but I can't find any counterexample. The problem : Let $T$ be an infinite binary tree, where all nodes are of ...
1 vote
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### Assume unknown tennis players B & D in three set match. Find Relation in $p$ [Probability B wins First Set] & $q$ [Probability Match ends in two sets]

Problem If we assume that two completely unknown tennis players B and D are facing each other in a three set match. Let $p$ be the probability that B wins the first set Let $q$ be the probability ...
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### Construct a fair game with a $N$ sided die

You have a $N$ sided die. And $X$ players. You have to devise a game, such that only one player wins and every player is equally likely to win. Also, the game should be finite (there shouldn't be a ...
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### mixed strategies when strategic space is convex

I am new to game theoretic concepts. I have read that "in a two player zero sum game, if the strategy space of a Player is convex then she may need not consider any mixed strategies". Can ...
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### Model team strength based on outcome of games

Say I have four teams, $A, B, C,$ and $D$. I have a data set that looks roughly like teamOne teamTwo win? A B 1 C B 0 ... ... ... D A 1 where whether a team is teamOne or teamTwo is random and ...
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### Mechanism Design problem about IC and IR conditions

here I have some doubts about the mechanism-design exercise in the image. Since there are 2 options that B can choose to default, not default, and 2 types including type 1, type 2, and having loan, ...
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### Why Nash or correlated equilibrium require complete information?

In games of complete information, there are common solution concepts such as Nash equilibrium and correlated equilibrium. The idea is that each player is playing a best response. My question is - Why ...
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### Calculate card percentage return [closed]

No sorry this isn’t how things work around here
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### PUCT Analoge for Adversarial Bandits

Many people are familiar with PUCT, the multi-armed bandits algorithm that produces good results (logarithmic regret) in the stochastic regime that utilizes 'predictions' of the best arm. This ...
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### Can one use Combinatorial Game theory in PvP video games, specifically Fighting games?

I have always loved the idea of combinatorial games like Chess and Go, and in my head, I always believed that Fighting games can follow that same logic. So I decided to start writing a simple High ...
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### Optimal strategy to win this football match

You're the trainer of a football team playing an opponent, and you can let your team play either in a defensive tactic, or an attacking one. You can switch between tactics at any moment, as often as ...
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### A Combinatorial Game Riddle - two players dividing towers

I have recently been struggling on a riddle- it's a Nim type of game. In front of two players, there are $n_1, n_2, \dots, n_k$ height towers ($k$ towers, each of them of some integer height). On each ...
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### Game Theory - What is the equilibria?

I think i'm braindead from the amount of time i've stared at this. What is the equilibria in each of the scenarios in this? and preferably the subgame perfect equilibrium? Is there even any, as player ...
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### What was so "Groundbreaking" about Bellman's Equations?

In the context of Decision Making and Game Theory, "Bellman's Equations and Bellman's Conditions of Optimality" are said to be some of the most important mathematical principles in this ...
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### Equivalent representation of a system of linear (in)equalities

I am reading about the equivalence between zero-sum games and LPs from Adler's 2012 paper. Right after lemma 3, he writes that it is equivalent to represent  (\mathsf{A}) := \{x:Ax=b\} = \{x:Ax\geq ...