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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].

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Show that the second player can always achieve a draw in the defined game

currently at it working on my discrete mathematics assignment, where I now have one assignment, that I just can't crack. I feel like I am very close, but miss something critical to it. So, I have the ...
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Three players mixed strategy nash equilibrium problem

The table above represents payoff for three players game accordingly. The probability for z1 is z and z2 is (1-z), r1 is r and r2 is (1-r) meanwhile for p1 is p and p2 is (1-p). Firstly, I would like ...
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44 views

Optimal Strategy in a money compounding model where one's interest is only consolidated at a fee

Say I have my main account with $ \$ 10000$ that gains interest at a rate of .1% a day. The interest collects in a separate account and I have to pay a certain fee, say $\$1$, to consolidate this ...
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37 views

States of the world/Game theory and Beliefs

This post consists on 3 parts: the question itself, hint and a table. The question will make sense to you only after you have read the tables and the hint attached. The problem is about beliefs of a ...
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11 views

Multiplayer zero-sum games theory and algorithmic solvers

My apology if either this question has been asked elsewhere or it is well known (but not to a beginner in game theory like me). Firstly, I haven't seen much work/literature on multiple player games ...
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26 views

Can a game theorist predicted a human using mixed strategy? [on hold]

Here, I really confused that every game have a mixed strategy, but not every game can perform a mixed strategy. I believe that human cannot perform a pure randomize task. Example: Asking someone a ...
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method of maximizing a welfare function in queuing problem.

We consider two agents queuing to access a server. Both agents have the same value for the job and the value is normalized to $1$. Agents draw independently their waiting cost from the same ...
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Is there a reasonable one hour summary of Game Theory?

In his Topology and Geometry course on Youtube (http://www.youtube.com/watch?v=QzfZS3iopR0&t=10m7s), Tadashi Tokieda claims he can teach all of game theory in an hour. He seemed very sincere and ...
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Two equally strong teams, one having the upper hand for a long time [on hold]

On one of my courses (applications of probability theory) the lecturer mentioned an interesting theorem. It was something along the lines of two, equally strong teams playing against each other and ...
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Min max and max min in Zero sum games

In zero sum games, is the max min payoff to player I equal to the min max payoff to player II? (and vice versa)?
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1answer
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Generalizing Rock, Paper, Scissors game?

Problem of playing rock-paper-scissors with $n$ elements and keeping it balanced How to extend the rock-paper-scissors game to more than just $3$ elemetns, and keep it balanced? In a ...
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Existance of concave balanced function

We know that the core of a balanced game is non-empty. The convexity ensures balancedness. However, I was wondering if a concave function too satisfies balancedness condition. The balancedness is ...
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A question about the solutions of min-max problems

The minimax theorem states that for compact sets $X$, $Y$, if $f(x,y):X\times Y \rightarrow \mathbb{R}$ is convex for fixed $y$ and concave for fixed $x$, we have $$ \min_{x\in X}\max_{y\in Y} f(x,y) =...
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Exhibition where children were playing Tic Tac Toe against their parents

I recall that there was an exhibition, in some place in the US I believe, where children could play tic tac toe against their parents. The catch was the following: both were sitting in front of a ...
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20 views

Possible worlds/beliefs/Probability Matrix/Example 3

I the snippet below, copied from the Handbook of Game Theory with Economic Applications, the condition (2.1) says that we can rearrange the columns so that the matrix becomes block diagonal with each ...
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14 views

Optimal strategy of a stochastic game

In a game with $n$ players where they can not communicate with each other, each player bids a positive integer. The chance they get the number they bid for is $p^n$ where $p$ is a predetermined ...
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32 views

Minimize or Maximize The NimSum at a certain step?

Suppose, we are playing a nim game. And We can make say N possible moves, each generating some NimSum Value. For a Winning, Strategy, Should we chose the move with minimum nimsum?
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Core of the game and shapley value

Five political parties, A, B, C, D, E take part in the following cooperative game. The number of votes controlled by individual parties are a = 9, b = 9, c = 10, d = 60, e = 60, Any coalition that ...
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Subgame Perfect Equilibrium Commitment Game

enter image description here If we turn this game into an extensive form where player I moves first and commits to a probability of playing A with a certain probability p, what would that probability ...
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1answer
24 views

Mixed Strategy Without an Option = Option is Dominated?

If a matrix game has a Nash equilibrium strategy in which certain options are not used (i.e. chosen with 0% probability), does that mean that those options are strictly dominated? If so, is it also ...
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1answer
30 views

Game theory problem - two towers

I'm asking that question because I still cannot figure out the solution after hours of thinking. You are given two towers where first has exactly n stones and second has exactly m stones. You are ...
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English Auction & Second-Price Sealed-Bid Auction

I am currently new to studying auction theory and I came across the following web page which explains the different mechanisms and strategies used in the two auctions (See title) I do not understand ...
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39 views

how do you calculate the grundy number?

I want to calculate the grundy number of these 4 normal-play nim heaps: 0, 7, 7, 7 I'm confused when comparing two wikipedia pages: sprague-grundy suggests I should ...
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Playing a normal-form game against another player

Suppose we have the following game: Game and we need to play the game twice against another player who we do not know. First I have to play as the row player and then next as the column player ...
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Proof of the Existence of Bayesian Nash Equilibria

I found the following two Theorems when studying games with incomplete information. "Consider a finite incomplete information (Bayesian) game. Then a mixed strategy Bayesian Nash equilibrium exists." ...
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Possible worlds/beliefs/Probability Matrix/Example 2

I have posted a similar question elsewhere, but this one is different. Take the definition and example as below as copied from the Handbook of Game theory with Economic applications. I want to design ...
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Probabilites of different players winning a simplified 2-person version of ludo

Consider a game in which players A and B both start on square 0. Player A goes first, flipping a coin, and advances one square if heads (stays on same square if tails). Then Player B goes does ...
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I need help understanding the shapely value formula for voting games

A company has 4 shareholders with 10 20 30 40 stock respectively, a decision can be made by the shareholders with the majority of the shares ie over 50 percent, determine the voting power of each ...
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The Trust Game: what is the Nash equilibrium?

Here is how the experiment goes: Half of the participants were given the role of a first mover, and half that of the second mover. In each round, it was common knowledge that a first mover would be ...
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How to solve this variation of nim that has division?

I ran into this problem, that consist of two stacks of coins each with different amount of coins, there are two players p1 and p2. p1 plays first and each take one turn. The turn consist of removing ...
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Playing a Minimax strategy in Zero-Sum games: how to bound the average loss $\limsup_{n \to \infty} \frac{1}{n} \sum_{t=1}^nl(I_t,J_t)$

I am currently working my way trough Chapter 7 of "Prediciton, Learning and Games" by Cesa-Bianchi and Lugosi which connects the field of Prediction with Game Theory. http://www.ii.uni.wroc.pl/~...
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20 views

Mixed Strategy subgame perfect equilibrium

enter image description here If player I can commit to a mixed strategy (1-p,p) for strategies (A,B) and player II knows the probability (1-p,p) applied to both strategies, what is the value of p in ...
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42 views

Possible worlds/beliefs/Matrix Game/Example

In the page copied from the Handbook of Game Theory with Economic Applications, I have a problem with the condition $$\pi_i(\{\nu\};\omega)>0.$$ I.e. I'm looking for an Event $E$ and states $\nu$ ...
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Best strategy in the game of Shoot-charge-dodge

The rules of the game are the following: There are 2 players, each of them have a gun and plays at the same time in every turn, in a turn they must perform one of three actions, shoot, charge or ...
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A game relevant to moving a stone.

There is a straight line of $10000$ cells connected together . It contains $n$ stones at coordinates $p_i(1\le p_i\le 10000,i=\overline{1,n})$. A and B plays a game as follow: 2 players take turns ...
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61 views

A game relevant to piles of coins.

There are $N$ piles of coins, the number of coins of a pile is $p_i(1\le i\le N)$. ($N$ is a prime number and $2\le N\le 30$). A always plays first. A and B move in alternating turns. During each ...
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Winning strategy using prime divisors. NIM varient.

In this game, two people take turns removing sticks from a pile that begins with x sticks. The person who takes the last stick wins. A person removes either one stick or p sticks, where p is a prime, ...
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Combining Nim Games

I was reading the Wikipedia article on the Sprague-Grundy theorem, and I can't get through their example for combining games. The example combines two sets of three heaps. The first set has 1, 2 and ...
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Accept or Reject Optimization

Let's say that a player has some general idea of a distribution that random numbers will be drawn from. The player will be presented a number and he can either accept or decline it. He will be ...
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55 views

A game based on cutting rectangles from paper

You are given a piece of paper that consists of $w \times h$ squares. You can cut the sheet in a vertical or horizontal axis at the positions with integer coordinates so that the paper becomes two ...
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1answer
39 views

A game relevant to sum and sequences.

We have a set of k positive integers $a_i$ and $x$ coins. A and B take turns picking up the coins so that the last picker is the winner. Each turn, one person can only pick up a positive number of ...
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22 views

Does there exist MATRIX games for more than two players

I am in a game theory course and I need to come up with an example of a Matrix game with more than two players I have consulted https://en.wikipedia.org/wiki/List_of_games_in_game_theory, but the ...
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A coin flipping game

I've been thinking about the following game for a while and am curious if anyone has any ideas of how to analyze it. Problem description Say I have two biased coins: coin 1 that shows heads with ...
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1answer
59 views

Who will be the winner if $A$ is always the first to go?

$A$ and $B$ play a folk game as follows. There are $n$ sticks on the table. Each person takes turns picking up the number of sticks that are one of three numbers $1,2$ or $3$. If the last person is ...
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1answer
36 views

Expectation value of fighting time of Knight vs Monster problem

I get this problem when I play computer game. When I see my knight is attacking the monster, I think what is the expectation value of fighting time. My knight is much more powerful than the monster, ...
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2answers
107 views

The Connect Infinity game

Recently Joel David Hamkins posted an entry on the Connect Infinity game. Connect-$\omega$ is Connect Four but played on an $\omega\times n$ grid ($n$ finite)! The above shows $n=6$. The difference ...
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Commitment Games: Game Theory

For the given game (with left payoff to player I and right payoff to player II), after drawing the extensive form/game tree of the commitment game where player I moves first and player II second, how ...
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Image of a first category set for a typical continuous function

Given a first category set $A \in [0,1]$, is the set $X = \{f \in C[0,1]:f(A)\text{ is first category}\}$ residual in $C[0,1]$? I tried two strategies: First I tried to play the Banach-Mazur game on $...
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MIP programming for fairness

I have a MIP model that allocates 24 rides between 6 drivers (with many constraints irrelevant here), and an important part of my objective is splitting the rides fairly. The easiest implementation ...
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How Stackleberg game works?

I'm a student of computer science and currently doing a term paper documentation, where actually I got the term. Now, it is stated that Stackleberg game is applied in a fog network, where service ...