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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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
27 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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1answer
395 views

Odds of winning a two part drawing

There is a local drawing that involves being selected out of an estimated 6000 entries, and then correctly selecting 1 of 3 numbers in order to win. The numbers have are actually cards in a deck that ...
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2answers
25 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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364 views

When is the “Taxman Game” winnable?

I recently came across the "Taxman Game" the rules are in the link, but I'll repeat them here: We start with a pile of integers, from 1 to some number that you choose [$n$]. You take one, and I ...
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8 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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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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11 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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2answers
1k views

Splitting the dollar Nash equilibrium

I'm working on a game theory problem I can't seem to figure out. Players 1 and 2 are bargaining over how to split $\$10$. Each player names an amount $s_i$, between 0 and 10 for herself. These ...
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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
55 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
11 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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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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1answer
763 views

Relationship between regular Nim and Lasker's Nim

So I'm trying to do qn $6$ (on pg I-13) about staircase Nim in Game Theory by Ferguson Game Theory, Ferguson and it's asking to prove that $(x_1, x_2, \ldots, x_k) \in P $ only if $(x_1, x_3, x_5, \...
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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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1answer
646 views

Calculating the Shapley value in a weighted voting game.

Given a special case of WVG (Weighted Voting Game) of $a$ 1s and $b$ 2s and a quota q, $ [q:1,1,1,1..1,2,2,..2] $. I need help with calculating the Shapley value of a player with a weight of $2$ and a ...
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1answer
23 views

How do you seed a “non-binary” tournament?

In a typical tournament, seeding is arranged to provide proportionate advantage to competitors based on their perceived relative ability. (Good teams get to play bad teams, bad teams have to play good ...
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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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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
2k views

Mixed Strategy Nash Equilibrium of Rock Paper Scissors with 3 players?

It seems like most game theory tutorials focus on 2-player games and often algorithms for finding Nash equilibria break down with 3+ players. So here is a simple question: Is $(\frac{1}{3},\frac{1}{3}...
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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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2answers
793 views

Nash equilibrium in first price auction

I'm trying to understand Exercise 18.2 from Martin J. Osborne and Ariel Rubinstein A Course in Game Theory about finding pure Nash equilibria in a first-price auction. There are $n$ players, named ...
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1answer
37 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
616 views

Game Theory. Repeated Games. Strategy set.

I'm reading the book "Strategic games" by Krzysztof R. Apt. I have a question about the strategies in Prisoner Dilemma repeated game. On page 63 there is expression: "In the first round each player ...
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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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1answer
30 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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1answer
409 views

Finding values such that the game is strictly determinable

Please help me to solve these two problems. Q1)Find the range of values of p and q that will make the entry (2,2) a saddle point of the game. $$ \begin{pmatrix} &player B\\ ...
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4answers
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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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
36 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
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
2k views

The Notion Of Degenerate Two Player Game

I try to get the intuitive understanding of the notion "degenerate two player game". Definition. A two-player game is called non degenerate if no mixed strategy of support size $k$ has more than $k$ ...
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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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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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1answer
240 views

Coordination game

Consider the following game in normal form: $$\begin{bmatrix} & x_B=0& x_B=1 \\ x_A=0& 1-\theta_A,1-\theta_B & 0,0 \\ x_A=1 & 0,0 & 1+ \theta_A,1+\theta_B \end{bmatrix}$$ ...
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0answers
56 views

Probabilities in this blackjack variation

Let's say I play blackjack (52 cards, figures count for 10, aces count for 1 or 11) and alone (no dealer). The cards I use for one particular game are always removed at the end of that game and won't ...
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114 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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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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1answer
797 views

I can't find the Nash equilibrium of this 3x2 game.

Sorry for my English, I am French but i couldn't find help on the French website (so I am here). I have a question about this two-player game: $$ \begin{array}{c|cc} & y_1 & y_2 \\ \hline ...
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2answers
88 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 ...