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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Game theory: how is law of large number applied here?

This is a claim rephrased and lifted from from Herbert Gintis' book "Game Theory Evolving" Pg187 Consider an evolutionary game with $n$ pure strategies $i = \{1, \ldots, n\}$, and time periods $t ...
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31 views

Finding the unique Nash equilibrium

$$ m^2(1-m)[(1+m)^2 - R] x^3 + [6m^2R + 12mR - 2m(1-m^2)(6+2m) - 4tm^2(1+m)^2] x^2 + [(1-m)(6+2m)^2 + 8tm(1+m)(6+2m)] x - 4t(6+2m)^2=0 $$ where: m ∈ (0, 0.5), R ∈ [0, 0.25], t ∈ [0, 1], x ∈ [0, 2]...
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1answer
30 views

A question about interval operation result in a game

A state is:$A_{q}=(A_{q}^{0},...,A_{q}^{E})$ where $A_{i}^{j}$ is interval, $q$ and $E$ are positive integer The initial state is $A_{m}=((0,1),\emptyset...,\emptyset)$ , $m>E$ Procedure: Every ...
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2answers
27 views

Expected value and variance of a random variable, defined as the largest of $6$ randomly drawn numbers

Let each of the numbers from $1$ up to $49$ be written on a ball, and let all these balls be contained in a box. From this box, we randomly draw exactly $6$ numbers (without putting them back, so we ...
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9 views

About those equivalences in games, is it posible to…

I've heard about some games which can be reduced to TicTacToe, i guess in general there should be some simplier games and other complex games could be reduced to them. I've been wondering, is it ...
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12 views

Which type of games can I model this problem

I'm dealing with Smart grid retailers and I'm dealing with retailer's price decision , there are multiple retailers which sell electricity to users and they are competing in Price with capacity ...
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20 views

Generalized First Price Auction or Generalized Second Price?

Sorry if I ask the same question again but in the other post I'm not able to edit my question because I wasn't using an account. By the way, the question: I'm running some tests to decide which type ...
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19 views

First Price Auction or Generalized Second Price

I'm running some tests to decide which type of auction is better. My settings are set randomly, I mean that budgets are random, advs' value are random .... My goal is to maximize the revenue. Which ...
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16 views

Compute the set of subgame perfect equilibria for this game (mixed strategies help)

In the above game there are 2 proper subgames (not including the whole game itself). I know there's 9 sub-game perfect equilibrium i have to figure out. I've managed to work out 4 of those, the ...
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1answer
57 views

How exactly is the St Petersburg Paradox giving bounded payoff in average-of-N-trials?

I understand why the expected value of the St Petersburg Paradox is algebraically infinite, but intuition tells me that in practice any given round of the game will not go on multiplying the pot for ...
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1answer
15 views

How to create a fair dynamic scoring system?

I am currently in the process of creating a game consisting of a fixed set of tasks of varying difficulty. Each player gets the same set of tasks to choose from and is awarded a certain number of ...
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1answer
12 views

Incentive compatible revenue maximizing multiunit auction

The Vickrey-Clarke-Groves Auction is an example of incentive compatible (truthful reporting) multiunit auction, but it is only maximizing social utility, not the seller's utility. If my ...
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14 views

Two variable integral arising from an application of myersons lemma

We have the following equation. $f:[0,1] \times[0,1]\to [0,1]$ f is monotone. $$(x+y-1)f(x,y)=\int_{0}^{x} f(t,y) dt +\int_{0}^{y} f(x,t) dt$$ further we have the symmetry condition that. $$\...
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34 views

Optimal strategy in an idealized dating scenario

The question I have is in some ways a variation on the stable marriage problem adapted to the situation of dating. Suppose there are $n$ boys and $n$ girls, where every boy ranks the girls from $1$ ...
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28 views

A two player game with tokens

Consider the following two-player game. The game begins with k tokens placed at the number 0 on the integer number line spanning [0,n]. Each round, one player, called the chooser, selects two disjoint ...
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86 views

calculate malus value of a urn

In an urn, I can put 20 balls having a value from 1 to 7. So I got Ni, with i $\in$ [1,2,3,4,5,6,7], where Ni is the number of balls with a value i in the urn. And $\sum_{i=1}^7 Ni = 20$ The game ...
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1answer
35 views

Calculating the odds of winning a game

Problem: You, the user have 3 lives. In front of you are 5 cups - in each cup there is a piece of paper with 1 random number between 1 and 5 (inclusive) written on it. You must guess the number in ...
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1answer
25 views

Pareto optimum in game matrix

I have to find Pareto optimum squares in game matrix. They are marked in following picture What questions do I have to ask myself for every square to decide if it is Pareto optimum? Why square E/A (...
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1answer
39 views

Complementarity and Substitutability

I am reading a paper in the international journal of game theory entitled Unequal Connections by Goyal and Joshi (2006) and it has the following sentences: "If strategic complementarity obtains... In ...
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1answer
26 views

Finding NE and SPNE

Given the diagram find SPNE and NE: In my opinion NE is: (6,4),(8,5) and (4,6) but i have problem with SPNE. How to find SPNE ?
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1answer
32 views

Game Theory: How Behavior Can Effect Win Rate

My question relates to how behavior can change win rate in a game Imagine a game that gives a bonus for the first win of the day. A behavior may arise where a player will play a series of games each ...
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1answer
20 views

What is a chance move?

I am studying the book Game Theory by Guillermo Owen and in the next paragraph I do not understand what means a chance move. Could anyone explain to me, please? The elements of a game are seen ...
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1answer
35 views

nash equilibrium and best response dynamics

I have a very basic question : How is nash equilibrium found in real life problem. I mean, in theory it exists and we can prove it but how this knowledge will be applied in real life especially with ...
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524 views

Optimal Solution

Players $1$ and $2$ are playing a game. They have a pile containing $N$ coins. Players take alternate turns, removing some coins from the pile. On each turn, a player can remove either one ...
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1answer
37 views

'Guess 2/3 of the average' normal form

I wanted to represent the 'Guess 2/3 of the average' problem in normal form. The rules for this game are below: There are two players. Each player names an integer between 1 and 100. The ...
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1answer
36 views

Decision theory references for advanced undergrad/early grad students?

I'm studying measure theoretic stochastic calculus, and I was hoping to pick up some knowledge of decision theory along the way. I'm very happy with Rudin or Karatzas in level of rigor, and I was ...
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15 views

Public Good Game with Joint Distribution of types

I have been working a public good game given as $$\begin{bmatrix} & C& D \\ C& 1-c_1,1-c_2 & 1-c_1,1 \\ D & 1, 1-c_2 & 0,0 \end{bmatrix}$$ Suppose $c_i$ is only known to ...
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1answer
41 views

Hunter and Rabbit Bayesian Probability [closed]

I've been asked to do this by process of game theory and probability (namely Bayesian theory). Here is the problem: There is a Hunter (H) and a Rabbit (R). They are playing the following game: - ...
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2answers
38 views

While finding an optimal strategy for a mixed nash equilibrium, why do we not consider strategies which are never a best response?

"A strategy cannot be plausibly chosen by a rational player if and only if it is never a best response." I understand the logic behind neglecting the strategies that are strictly dominated. But why ...
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116 views

A variation of Nim game

There are two players X and Y . They write N integers on paper ( A_1 , A_2 , A_3 , .... A_N ). They have also p integers (b_1 , b_2 , b_3 , .... b_p ) . Now , Player X always takes turn first . He ...
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103 views

Mathematical game with numbers

We invented a mathematical game, which i am going to explain here. The first player choose a natural number, lets call it $n$ (if you play it for real, you must choose a sufficiently big number so ...
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190 views

Alice and Bob make all numbers to zero game

Alice and Bob are playing a number game in which they write $N$ positive integers. Then the players take turns, Alice took first turn. In a turn : A player selects one of the integers, divides it ...
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1answer
34 views

Three games of two-players each being played by three players simultaneously

Has the game theory literature considered situations wherein there are three two-player games being played by three players concurrently with each other; and the outcomes of those games may impact the ...
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2answers
89 views

How can the policeman catch the gangster?

I try to solve the following problem (Moscow Mathematical Olympiad, 1978) There is a town with six streets: four sides of a square and two its middle lines. Policeman tries to catch a gangster. If ...
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11 views

Looking for info on game theory for a scenario where participants earn points, and the top K earners receive a reward determined by rank

Say there's some competition that lasts for a week and takes place in a community. Participants receive points for collecting littered cans in the streets. Each can collected is a point. At the end ...
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1answer
33 views

Strategy optimisation

This is a question from the Singapore Invitational Mathematics Challenge 2016. The question paper can be found here. (Part C:Question 2) http://www.nushigh.edu.sg/qql/slot/u90/file/simc/...
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2answers
28 views

Dice role: What is the probability to observe 2 times 1 and 2 times 5 with the outcome of a fifth die role being unknown?

I tried to solve the following exercise: Given a dice with $P(X=2) = P(X=4) = P(X=5) = \frac{2}{15}$ and $P(X=1) = P(X=6) = P(X=3) = \frac{2}{10}$. What is the probability to observe 2 times 1 and 2 ...
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1answer
37 views

A bin-assignment infinite 2-player zero-sum game

What is known about the following infinite 2-player zero-sum game? There are $k$ bins. Each player has 1 unit of mass and, simultaneously, divides it arbitrarily among the $k$ bins. The player wins ...
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1answer
28 views

Enunciating utility maximization problem using set theory

I need to enunciate a problem using set theory and I am not sure how to start. The problem goes like this: You are a car manufacturer and need to decide how many colours to use in your next bash of ...
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121 views

Variation of Nim, where one has to divide a pile into any number of piles.

I am learning the basics of combinatorial game theory (impartial games). After learning about decompose a game into the sum of games, I feel comfortable with games that can divided into the sum of 1 ...
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1answer
148 views

He who has the largest real number in $[0,1]$ wins

Let's play a game: Let $X,Y \sim U (0,1)$ be random variables uniformly distributed over $[0,1]$. The game is as follows: I obtain a realization of $X$. You obtain a realization of ...
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1answer
41 views

Stackelberg problem?

Suppose that two firms have different production costs: Player I's cost of producing x is x+2, while Player II's cost to produce y is 3y+1. Suppose that the price function is p(x,y)=17−x−y, where x ...
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1answer
39 views

Bertrand Duopoly

Consider the following version of the Bertrand model with differentiated products. Specifically, if player I sets price $p_1$ and player II sets price $p_2$ for goods, then the demand is given by $$...
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1answer
65 views

Tic Tac Toe: What is the probability that a random player draws against an infallible player?

I have simulated a tournament between an infallible Tic Tac Toe player and one that chooses its moves randomly. Even after 5 million games, the infallible player wins every single game. I know that ...
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94 views

Position games: how to fill a matrix with dominos? [duplicate]

Dominos of size $2 × 1$ can be placed on a $m × n$ board so as to cover two squares exactly. Two players alternate placing dominos. The first one who is unable to place a domino is the loser. I can ...
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110 views

Guess the number despite false answer

This is the Guess-The-Number game with a twist! Variant 1 Take any positive integer $n$. The game-master chooses an $n$-bit integer $x$. The player makes queries one by one, each of the ...
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1answer
17 views

Explanation of Nash Equilibrium using Gambit software

I am trying to understand how Nash Equilibrium works in the Gambit software but I can't figure it out. I have created a simple game shown below and I have calculated just one Nash equilibrium by ...
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1answer
16 views

Upper and Lower Value of a two person zero sum game

I understand that if a game's lower value V$_{L}$ is equal to it's upper value V$_{U}$ then the game has a value V$=$V$_{U}$=V$_L$. Just to be sure it is also the case that if a game has a value V ...
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1answer
23 views

Two person cooperative non-zero sum game

This a two person cooperative non-zero sum game. The shaded area is the negotiation set. $s_a$ and $s_b$ are the security levels for $A$ and $B$ respectively. I do not understand the part I have ...
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38 views

Big Two's classification according to game theory

Is the game Big Two, as described in https://www.pagat.com/climbing/bigtwo.html, classified as: a game of perfect or imperfect information? deterministic or stochastic? EDIT: I am fairly certain ...