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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].

Game theory is the study of mathematical models of strategic interaction between rational decision-makers. Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics.

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rock, paper, scissors, well

Everyone knows rock, paper, scissors. Now a long time ago, when I was a child, someone claimed to me that there was not only those three, but also as fourth option the well. The well wins against rock and scissors (because both fall into it) but…
celtschk
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How is prisoner's dilemma different from chicken?

Chicken is a famous game where two people drive on a collision course straight towards each other. Whoever swerves is considered a 'chicken' and loses, but if nobody swerves, they will both crash. So the payoff matrix looks something like this: …
Larry Wang
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Is Rock Paper Scissors with two players but three contestants a fair game?

In a game of Rock Paper Scissors with two players, there are $3$ outcomes every round each with multiplicity $3$. Player 1 can win. Player 2 can win. Both players can draw. If we were to assign a winning result to a third "Player" when Player 1…
Axoren
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Optimal strategy for the Rope Climbing Game

Define a two-player, turn-based climbing game as follows. Each turn, players have the option to climb or tie a knot at his current position. If the player chooses to climb, there is a 50% chance that he advances his position by $1$, and a 50% that…
Alexander Gruber
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How to choose the smallest number not chosen?

So there are $n$ people, each choosing some non-zero counting number. You don't know what any of them choose. To win, you must choose the smallest number; but if you choose the same number as somebody else, you are disqualified. How would you decide…
Vedvart1
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Game Theory - Choosing the smallest number not chosen yet

A company has a competition to win a car. Each contestant needs to pick a positive integer. If there’s at least one unique choice, the person who made the smallest unique choice wins the car. If there are no unique choices, the company keeps the car…
Chuck
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A game played on a rectangle

Suppose two players play the following game on a $m$ by $n$ rectangle. Alternatingly they have to make a cross in some empty $1\times 1$ square. They are not allowed to make a cross next to another cross (Diagonally is OK, not just right next to…
HenrikRueping
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The Goblin Game

Goblin Game is a Magic: the Gathering card. The full text of the spell is: Each player hides at least one item, then all players reveal them simultaneously. Each player loses life equal to the number of items he or she revealed. The player who…
Brian S
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Difference between Minimax theorem and Nash Equilibrium existence

Von Neumann's Minimax theorem (quoted from Wikipedia): For every two-person, zero-sum game with finite strategies, there exists a value V and a mixed strategy for each player, such that (a) Given player 2's strategy, the best payoff possible for…
Ziv
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Alice has two bags, having random values in [0, 1]. She reveals one bag to Bob. Bob picks one bag, Alice gets the other. What is the optimal strategy?

Alice is given two bags. The values of the contents of the bags are each uniformly (and independently) distributed over $[0, 1]$. She looks in both bags and finds out their value. She then reveals the value of one of the bags to Bob. Bob then picks…
Superty
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Computer software for solving mixed strategy Nash equilibrium

Is there any computer software available for solving for mixed strategy Nash equilibria for two players given each player's payoff matrix?
Duncan
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pure strategy vs mixed strategy

Apparently, I'm not understanding this simple concept. What are the differences between the two? Can a person have multiple pure strategies that change throughout the game?
larry
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A number guessing game

Alice chose a positive integer $n$ and Bob tries to guess it. In every turn, Bob will guess an integer $x$ $(x>0)$: If $x$ equals $n$, then Alice tells Bob that he found it, and the game ends. If not, then Alice tells Bob whether $x+n$ is prime or…
Sayakiss
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Can two queens win against a knight on an infinite chess-board?

Inspired by this question : A simple game on infinite chessboard I ask whether the special case ($0$ bishops) will already be sufficient. More concretely : The game is as follows. Player $A$ places two queens, then player $B$ places a knight on an…
Peter
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Optimal Strategy for this schoolyard game - (Charge, block, shoot)

I encountered this game when I was a kid (we called it Street Fighter back when it was all the rage) and recently saw it again with my nephews playing the same game with a different name and slightly different rules. The basic game is an RPS-style…
Javier I.
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