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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Gambling to pay off debt?

Someone told me something interesting today. They said they were going to take their bonus check from work, to the casino because they have "better odds" of paying off more debt then if they would ...
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24 views

A minimum settlement for a bargaining problem

Question: Alpha and Beta are 2 companies. Now Alpha thinks that Beta has violated Alpha's trademark. Beta denies that. Now, Alpha is threatening to go to the court and claim 5,000,000 EUR from Beta ...
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1answer
72 views

Brouwer's fixed point continuous function

Can anyone point me out the continuous functions without brouwer fixed point's for the following sets $$A = \{x \in \mathbb{R}^2 | x_1,x_2 \geq 0 \text{ and }x_1^2+x_2^2 = 1 \}$$ $$B = \{x \in ...
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1answer
62 views

Game theory question- no idea how to proceed

A monopolist sells two products, X and Y . There are three consumers with asymmetric preferences. Each consumer buys either one unit of a product or does not buy the product at all. The per-unit ...
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2answers
38 views

Mixed Strategy Nash Equilibrium in this game?

L (q) R (1-q) l (p) [(2, 1), (0, 1)] r (1-p) [(-1, 0), (1,7)] I'm having a lot of trouble understanding what the mixed strategy nash equilibrium is ...
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1answer
16 views

Algorithms for computing Nash equilibria

Excuse me, since I am modeling a situation into a nonzero-sum n-player non-cooperative game. I wonder if there is any algorithm for computing its Nash equilibria?
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1answer
50 views

Game theory question- boxes

There are two players 1 and 2, and the game begins with player 1 selecting one of the boxes marked 1 to 16. Following such a selection, the selected box, as well as all boxes in the square of which ...
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1answer
34 views

How much is it worth to participate in a second price auction?

You have a valuation for an object (say $v_a$), which you don't know yet but you know is distributed U[0,1]. You will be competing in a second price auction against a completely identical guy as you, ...
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1answer
39 views

What is a two person constant sum game?

I read that a two-person constant-sum game is a two-player game in which, for any choice of both players strategies, the row player's reward and the column player's reward add up to a constant value ...
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3answers
52 views

Looking for the function of x for a line that approaches, but never reaches 100

I'm looking for the function of x for a line that intersects at (0,0) and (100,80), and as x goes off into infinity, the line approaches, but never touches 100. See image attached. I am writing a ...
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1answer
28 views

A proof related to diameter of a simplex S

Question: Prove that the diameter $\mathcal p(S)$ of a simplex $\mathcal S$ equals the greatest Eucledian distance between two vectors in the simplex. My opinion: We all know what every vector in the ...
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1answer
36 views

Mixed strategy Nash Equilibrium

How do I solve this problem by using mixed strategy Nash equilibrium? \begin{pmatrix} (2,0)& (1,1)&(4,2)\\ (3,4)&(1,2)&(2,3)\\ (1,3)&(0,2)&(3,0) \end{pmatrix} I tried to ...
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0answers
39 views

Has two player five-card draw poker been solved?

I know that some other types of Poker have recently been solved with computers but has five-card draw poker been solved and if so, is there any place for mathematical analysses in the game? I need to ...
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0answers
56 views

Cournot competition: profit maximizer vs. market share maximizer

Today during an informal conversation with an established business researcher, I learned such a fact: In the classical Cournot competition model, if one player is a profit-maximizer, the other ...
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1answer
87 views

Do you need true randomness to beat the two-envelope game?

A well-known (non-)paradox in probability involves a two-envelope game played between two players, $A$ and $B$: $A$ selects two distinct (real) numbers, $x$ and $y$, writing each one down on a card ...
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1answer
32 views

Probability of number of drawing cards in a scenario being equal to that in another scenario

I came across the following question in a book:- $Q.$ Cards are drawn one by one at random from a well shuffled pack of $52$ cards. $(a)$Find the probability that exactly $n$ cards are drawn before ...
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0answers
31 views

Finding the core of a coalition game

I need to find the core of a 3-player coalition game graphically, given that $v(\phi)=0$, $v(1) = 9, v(2)=8, v(3) = 9, v({1,2}) = 14, v({1,3})=15, v({2,3}) = 13, v({1,2,3}) = 21$ So I'm following the ...
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0answers
68 views

Wizard against two dwarfs: guess the whole function

An evil wizard plays the following game with two dwarfs $A$ and $B$: he thinks of a function $f:\mathbb{R}\to\mathbb{R}$ (which is not required to have any regularity properties, such as ...
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26 views

Unfair coin tossing game,target,optimal fixed investment,

Suppose the player has capital 1\$. He chooses a number $f\in[0,1]$.He tosses an unfair coin repeatedly, which wins for him, with probability $p$, a gain $q\times f \times$ current capital \$,where ...
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0answers
32 views

Finding the expected revenue of a first price auction

I'm currently trying to solve for the expected revenue of a first price auction involving n players who draw their values v independently from F with support $[\underline{v}, \bar{v} ]$ and positive ...
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1answer
19 views

Example of a matrix which is copositive plus but not PSD.

This came up in our game theory course. While doing the Lemke's algorithm for solving LP, it was said that the process terminates when the matrix $M$ is copositive plus. Now copositive plus has a ...
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1answer
43 views

game theory question

For a non-cooperative bimatrix game the feasible set is $$\{(u,v)=(\mathbf{p}^TA \mathbf{q},\mathbf{p}^TB \mathbf{q}):p \in X^*, q \in Y^*\}$$ graph the non-cooperative feasible set for the Battle ...
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0answers
39 views

Forming a differential equation from game

I was wondering if someone could help me form a differential equation from the following game: A population consists of two types of diets, fish and veg. People play a with every other person and the ...
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1answer
29 views

show no equilibrium pairs exist in a non cooperative game using pay-off set?

I am trying to understand the following exersice from the solutions of my professor and I really don't understand what she is doing. The exersice is the following: Suppose the matrix below is a pay ...
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0answers
27 views

calculating expected gains.

A game costs \$100 to play. Toss a coin repeatedly, and win \$1 if you get heads for the first time, \$2 if you get heads both of the first two times, \$4 all of the first three times, \$8, and so ...
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1answer
61 views

Why “Ann believes that Bob assumes that Ann believes that Bob’s assumption is wrong” is paradoxical?

In a paper(see here) by Adam Brandenburger and H. Jerome Keisler, they give a game-theoretic impossibility theorem akin to Russell’s Paradox: Ann believes that Bob assumes that Ann believes that ...
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1answer
95 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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0answers
29 views

Quasiconcavity of $g(x)=xf(K-x)$

The function $f(x)$ is strictly increasing, finite, positive and twice continuously differentiable on the compact interval $[0,K]$, and $f(0)=0$. I'm trying to either find a counterexample to, or a ...
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0answers
87 views

Fastest way to meet, without communication, in a toroidal palace?

I was interested by a similar question asked here, but wanted to pose a slightly different variant that avoids some of the pitfalls and ambiguities in the first question in order to ask something more ...
2
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0answers
33 views

Cournot Oligopoly in Bayesian Game Theory

I have this Cournot game in which $n$ firms produce quantities $q_1, \ldots, q_n$ with respective marginal costs $c_1, \ldots, c_n$. They all sell at price $P=1-(q_1 + \cdots + q_n)$. For any $i$ ...
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1answer
47 views

Nash equilibrium in mixed strategies with p = 0

I am currently writing a program to calculate nash equilibria in mixed strategies. My algorithm simply tries a lot of different probabilites and then decides which one is the best. However I came ...
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0answers
59 views

How can I find the Nash equilibrium for this 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 ...
3
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1answer
52 views

Core vs. Strong Core in Housing Allocation Games

I am presently reviewing the course notes for my Game Theory course, and I'm struggling with the concepts of the core vs. the strong core. In the notes, we have three players, with preferences ...
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2answers
39 views

If $e_0 = \frac{1}{2} $and $\forall n\in\Bbb{N}:e_n=\frac{(2n-1)^2}{2n(2n+1)}e_{n-1}$, find $\sum_{n\geq 0} e_n$

Consider the following optimal stopping game: The controller is presented with steps in a fair random walk (fair coin flips, $P(h)=P(t) = \frac{1}{2}$) and at each stage of the game, the controller ...
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95 views

StackEgg optimal algorithm

What is the minimum number of days that is needed to complete the StackEgg game? (It's on the right if anyone didn't notice.) There are four markers (Questions, Answers, Users, Quality) I believe each ...
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1answer
51 views

Perudo Game - probability of succes for my call

I'm making a computer program that should play as a bot against other student's bots as ICT project at school. The game is Perudo. In this part of the program I want to know what's the probability of ...
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1answer
24 views

Convergence of nested converging measures

Sorry for the poor title. Not sure how to ask this question without formalism. Let $X$ be a metric space and $\Delta(X)$ be the space of all probability measures, endowed with with topology of weak ...
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18answers
8k views

Fastest way to meet, without communication, on a sphere?

I was puzzled by a question my colleague asked me, and now seeking your help. Suppose you and your friend* end up on a big sphere. There are no visual cues on where on the sphere you both are, and ...
2
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1answer
63 views

Price of anarchy for selfish routing games with polynomial latency functions

I have a question regarding selfish routing games. For the case where we have affine latency functions I was able to calculate a worst case price of anarchy (PoA) of $4/3$. However, now assume $L_d$ ...
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2answers
59 views

On 2- player game.

Consider the following 2-player game: you start with n tokens on a table, in a single pile. Players alternate turns. On a player's turn, they must choose one pile of their choice, and split it into ...
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0answers
28 views

Mixed strategies as LP problem

A row player is playing against a column player and his yield table is -, C1, C2, C3 R1, -3, 2, -1 R2, 0, -2, 1 R3, -1, 3, -5 Is it then correct to ...
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1answer
64 views

Game of chicken payoff matrix for dominant strategy and nash equilibrium

Consider the payoff matrix for a game of chicken: ...
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2answers
47 views

Nash Equilibria in simultaneous game with four players

Four parliamentary parties are working on a necessary but highly unpopular law. Each party decides whether to put forward the law on its own behalf. If $n$ parties will put forward the law on its own ...
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4answers
436 views

Big List of examples of recreational finite unbounded games

What are some examples of mathematical games that can take an unbounded amount of time (a.k.a. there are starting positions such that for any number $n$, there is a line of play taking $>n$ times) ...
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1answer
45 views

Circular list from the 2nd element of the result of repeatedly perfect shuffling a magnitude ordered list of natural numbers less than an even number.

Start with a magnitude ordered list of the natural numbers that are less than a chosen even number greater than 0. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} Repeatedly 'Perfect Shuffle' this list, ...
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1answer
50 views

Restrictions on the rules of a game theory model

I am to model a problem and I want to employ game theory. The players are network's agents P = $\{1,\cdots,N\}$, the strategies S = $\{Red,Green\}$. The rules are: at the beginning of the game, ...
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1answer
115 views

Game Theory question about a financial pyramid scheme

Salut, fellow game theorists. I have to solve 6 Game Theory problems and fell almost hopeless. Would appreciate any guidance with this one. A company Zest is actively promoting its services. ...
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22 views

Game Theory question about a financial pyramid scheme. [duplicate]

I have to solve 6 Game Theory problems and feel almost hopeless. Would appreciate any guidance. A company Zest is actively promoting its services. Everyone who invests in Zest will receive their ...
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0answers
20 views

estimation of the parameters of generative process modelling second-price-auction

The generative process: There are 2 entities (A,B) entity A - is the exchange performing second-price-auction entity B - is somebody who is trying to understand the distribution-of-the-value people ...
4
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0answers
31 views

Nash Equilibria for the Effort Level Game

Player $i$ chooses an effort level, $e_i \in [0, 10]$. Let player $i$ have the following payoff function: $90 -e_i$ if $e_i > e_j$ and $80 -e_i$ if $e_i \leq e_j$. What is the Nash Equilibrium (NE) ...