The study of competitive and non-competitive games, equilibrium concepts such as Nash equilibrium, and related subjects. Combinatorial games such as Nim are under (combinatorial-game-theory), and algorithmic aspects (e.g. auctions) are under (algorithmic-game-theory).

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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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13 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
4 views

Zero-Sum Games in Characteristic Form for Cooperative N-Player Games

I want to show that if a game is zero-sum in its normal form, then it's zero-sum in its characteristic form too. This was an exercise in Peter Morris's book, 'Introduction to Game Theory.' I'm ...
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0answers
16 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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27 views

Is CHESS a-game of courtroom interest or conflict technique? [on hold]

That is how chess is thought of by me. This is a-game of warfare that begins by controlling or occupying situations for the most rapid improvement/implementation of your items produce the possibility ...
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1answer
66 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
15 views

Compute the number of directed graphs on four vertices. [on hold]

For $3$ vertices, the number of directed graph is $2^{6}=64$. I don't understand how we get $64$ either.
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1answer
22 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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17 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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21 views

prove why expected utility better than expected value in terms of unlimited value of expected

Why expected utility is better than expected value? i was asked by my supervisor to prove that expected utility is needed in mixed strategy and i need to prove it's better than expected value. i have ...
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9 views

N(N-1) Dyadic Games with Incomplete Info (and Bayesian)

I am attempting to learn about Bruce B. Mesquita's (new) approach on determining outcomes of bargaining games, partially outlined here. I am new to Game Theory and I would appreciate if anyone knows a ...
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56 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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17 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
21 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
14 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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0answers
30 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
31 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
24 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
23 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
56 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
51 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
24 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
75 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
66 views

Alice and Bob grid game

Given a $N$ x $N$ matrix with some black and white cells. Now Alice and Bob start playing a game alternatively. Alice moves first. Game proceed as follow : When a player makes a move, he/she needs ...
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22 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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0answers
30 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
50 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
38 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
36 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 ...
4
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0answers
89 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
35 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
21 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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0answers
51 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
47 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
23 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
31 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
41 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
350 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
44 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
41 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, ...
0
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1answer
98 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 ...
0
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0answers
18 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
29 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) ...
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1answer
80 views

Gamblers ruin formula

Hello , I have been reading about gamblers ruin and I found this formula can anyone confirm its accuracy ? I assume they only bet one chip a time
2
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1answer
40 views

Strategy for 2-player game, drawing uniform variables and optionally redrawing

Player 1 and Player 2 secretly and separately draw uniform random variables in [0,1]. They may (secretly) elect to redraw once and replace their value. Highest value wins. What is the optimal ...
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2answers
75 views

Graph theory and game theory

are there any areas of game theory which are studied by graph theoy? Do you know some good source on that?
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1answer
74 views

Given domain and range of a monotone function, what is the maximum slope?

I'm looking for a reference in answer to one of the following questions: Is there a general result out there that will give the maximum possible slope of a monotone function, given its domain and ...
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1answer
38 views

How can you calculate someones location?

Suppose there are 10 people who live in different cities. And I want to know who lives where. Each time I can ask two of them 'who of you lives closer to X?' Where X is myself or another person of the ...