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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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Is there a better concept than expectation for one time play?

Given a simple lottery game like Guess the right (random generated) number $\in [0,1000]$. Stake = 1€ Win= 2001€ the expected outcome is $\frac{1}{1001}\cdot2001 + \frac{1000}{1001}\cdot(-1) = 1$. ...
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2 player zero-sum-game rock paper scissors expected loss

For the Rock-Paper-Scissors game, I am trying to determine the expected loss for P1. The following matrix displays how much P1 has lost: A: | 0 1 -1 | | -1 0 1 | | 1 -1 0 | I am trying to find ...
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Reference concerning modeling of wargames by manifolds

I'm a student at algebraic topology. I've studied manifold theory by W. Boothby's book and have a little information about game theory. My question is that: Is there any reference which explains ...
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Is Game Theory Prescriptive or Descriptive?

I am trying to more clearly understand the objective of game theory. I started off by reading papers in economics, where the main focus seems to be on finding equilibria under various behaviorial ...
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A question on repeated game theory

I recently have come across a business problem which could be convereted into a game problem as follows: Imagine an infinitely repeated game between two players in which the firts player (leader) ...
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Help understanding the most valuable statistic in this RPG word problem

Assume that each playable character is assigned a static stat value total of 100, split between Attack and HP. For example, one character has 30 Attack and 70 HP while another has 60 Attack and 40 HP. ...
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Game theory - a shooter problem

I just met an interesting question but did not know how to approach it... Suppose two gunmen (A and B) are moving in a straight line towards each other in a fixed speed. Each of them only have one ...
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Show that the first child can not win

Three children have 10 pieces numbered from 0 to 9 on both sides. They play the following game: -The first child chooses a piece, so a number, preserves it and passes the number on a sheet -The ...
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Cournot duopoly market equation

What does '$a$' represent in this equation? I know what the rest means but cannot think what '$a$' represents? Consider a Cournot duopoly market with demand curve $𝑃 =a −𝑄$,where $𝑄 = 𝑞_1 +𝑞_2$...
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Comprehensive List of Characteristics of Payoffs of Games

Axelrod and Hamilton (1981) write that there are two characteristics to the payoff structure of the prisoner's dilemma: $T>R>P>S$ and $R>(S+T)/2$ Has someone published a comprehensive ...
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Help calculating probability of dice rolls in a board game

What is the probability of rolling a 6 symbol combination using 8 identical 6-sided dice (each dice having one duplicate symbol ie. d={A,A,B,C,D,E}), where the player is allowed discard one dice in ...
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Identifying Proper Sub Games

Does this game have one or two proper games? I think FB definitely is, but is UD?Extensive form game
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Pure strategies that are Evolutionary Stable?

I am currently struggling with this symmetric game with finding all pure stategies that are evolutionary stable. I know that strategy "A" or "a" is evolutionary stable since it is a strict NE. How do ...
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Creeper's Dilemma [closed]

I was watching a TV show (Cold Case) where a math teacher had an affair with a school nurse, there were some students involved too. Being a teacher myself, my mind wandered off to an interesting ...
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Notation of Payoff functions in the Selten game

The pictures are from Narahari's textbook, Game theory and Mechanism Design. Could anyone explain to me the last line (the definition of payoff functions)? I haven't seen this notation ever before ...
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Bandwidth Sharing Game example

This example is from Narahari's textbook on Game theory. I am not sure I understand the last part: the set of $n$ simultaneous equations has the unique solution: $$x_i^*=1/(1+n).$$ Basically, I don'...
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Game Theory - 2 Players choose between 0 and 1, if sum exceeds 1, utility for both is 0

Two players must choose a number simultaneously between 0 and 1. If x+y≤1 they both get utility equal to the numbers that they have chosen. Otherwise both get 0 utility. I think that the best ...
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Is there something I'm missing when computing the equilizing strategy for this non-cooperative bimatrix game?

Given the following non-cooperative bimatrix game: \begin{bmatrix} & (3,4) & (2,3) & (3,2) \\ & (6,1) & (0,2) & (3,3) \\ & (4,6) & (3,4) & (4,5) \\ \end{bmatrix} a) ...
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Conditional expectation in flipping coin. How much will I be willing to pay to see the first toss?

The subjected utility maximizer player revises her beliefs according to the Bayes' Rule. She has the opportunity to gamble on the toss of a coin: she can not participate, or she can say ...
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What is the optimal way to take $16$ question true/false test with four attempts?

Question: Suppose a student is taking a $16$-question true/false test with four attempts. They must keep the store that they obtain after the fourth trial. He or she does not know the answer to any ...
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Bayesian Stackelberg game

Can anybody provide me a little example of bayesian stackelberg game with the solution. I know how to solve Stackelberg game using backward induction but have no idea about bayesian.
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Memoization Confusion

Imagine the following game: There is a bank of numbers, and a target number. Players take turns selecting (and thereby removing) a number from the bank, and subtracting it from the target. The ...
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Prove that this card game between 2 people always ends in a finite amount of moves.

Update: Bram28 and Barry Cipra have given very good answers! I've also fixed a lot of my examples because of the better solutions. Also, as per Barry Cipra suggestion, I've created a follow-up ...
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why do extensive games with perfect information have at least one nash equilibrium?

I would argue that every finite extensive game with perfect information has a subgame perfect equilibrium [1] and every subgame perfect equilibrium is also a nash equilibrium, thus every finite ...
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Random Game Using Real Numbers

The original question: Alice and Bob play a game. To win the game, Alice needs $a$ points, and Bob needs $1$ point ($a$ is fixed for each game). In each round of the game, Alice picks a real number ...
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What are the Nash equilibria of this network?

Braess's Paradox provides an explanation for why traffic can worsen after new roads are added. For example, consider traveling from A to B in the following network: Cars dividing equally between the ...
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game theory: application to simulataneous and numerous auctions

Simple example before generalisation: 5 people have each 100$ (that they are bound to be bet on 3 different objects). The first is worth 2 points, the second 3 points and the last 4 points. The ...
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The complexity of finding pure Nash equilibrium in exact Potential games

Fabrikant., et al., in the paper "The complexity of pure Nash equilibria" (http://kunaltalwar.org/papers/purenash.pdf) show that finding a pure Nash equilibrium (PNE) in a Congestion game is a PLS-...
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How to solve this Yes/No query problem where we need to find the number of sets satisfying the given condition?

So let's say we have 2 people playing a game. Let the first person be $A$ and the second person be $B$. So $A$ guesses a number between $1$ and $n$ ( say $x$) and $B$ gives queries to $A$ in form of $(...
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How do I adjust action outputs when accounting for volume at which said actions are played?

I apologize for the vague and potentially misleading title, I am very new to statistics and do not yet have a handle on the jargon. Essentially, I have the table below: ...
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Finding Nash Equilibrium for 2x3 game *with no Pure NE*

There's no pure NE nor dominated strategies and I am struggling to solve for the MSNE when 2x3 matrix like this... $$\begin{array}{|c|c|c|c|}\hline & C & D & E \\ \hline A & 0,10 &...
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Nash equilibrium with calculus

I have to compute Nash equilibrium according to their payoff function and when the strategy space for the players are S1=S2=[0;1], which are the following: Payoff function of the first player: $f(x;y)...
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Some baseball game theory. You lose one game so that your odds of winning more games increases. Is there a math concept which represents this idea?

I never really liked baseball as I always thought it was too slow, but in an effort to make playoff pushes and being that baseball is a numbers game, I had this idea. Usually teams have their best ...
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Example on Bayesian Games

This is an example from the book "Game Theory and Mechanism Design", by Y. Narahari. The buyer 1's problem becomes $$\max_{b_1\in[0,\alpha_2]}(\theta_1-b_1)\frac{b_1}{\alpha_2}.$$ How do we compute ...
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Throwing Poker Chips Close to Wall Game

I just had an interview question involving a two-player game of throwing poker chips closest to the wall. Players take turns throwing chips (of which you start with zero, but chips can be "borrowed"), ...
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Game Theory Reccomendation, Mean Field Theory

I'm about to do a sort of reading course with a mathematics professor wherein I read and teach him about Game Theory. He claims not to know Game Theory. After that, we aim to read about Mean Field ...
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Game Theory number of ways to win in a sequential game

two players start with a and b points. In each set of the game, they can score a point from -k to k (both including). if s set are played, the number of ways the first player can win the game. So in ...
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Calculating expected payoffs by viewing actions as random variables

Let us suppose we have two players (X and Y) with X choosing action $x\in\{0,1\}$ and Y choosing action $y\in\{0,1\}$. If the payoff to player X is given by $\pi_X(x,y)=bx-dy(1-x)$, then we would ...
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What are great way for modelling business competitions between two companies in a computer program?

I am going to do project in game theory in which i will study different situations in business involving two or more companies.Any hint or suggestion how do i model this in a computer program ?
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What is the general approach for finding the equilibrium of a min-max problem?

I asked this question because I have trouble for taking a straight forward approach to find the equilibrium of a min-max problem. For example, consider the unconstrained optimization problem: $$ \...
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What kind of mathematics is this?

Little backstory, I basically taught myself Algebra I and II and some trigonometry using textbook self-study and some YouTube resources. But I'm trying to get into some more advanced stuff related to ...
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understanding pure and mixed Evolutionary stable strategies

I am trying to understand ESS-pure and mixed. Here is what I know of two strategies $A$ and $B$ and their fitness: ...
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Auctions - Placing Points to get into Classes

At my university there are not enough places in every class to accommodate every student. The scheme the university set up to solve this problem is as follows: Each student gets $1000$ points per ...
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Computation of an utility related to a geometric law

Let $X$ be a random variable such that $P(X=n)=p(1-p)^{n-1}$ ($1\leq p \leq 1$, $n\geq 0$). Let $d,a \in \mathbb{N}^*$, with $a<d$, $u>0$, and $$ U_a(X) = -u(d-a-X)1_{\{X<d-a\}}-2u(X-d+a)1_{\...
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How to do backwards induction for this problem?

This is the tree: https://imgur.com/a/MJ9mmBN I solved for the normal form equilibria: (SS, SS), (SS, SC), (SC, SS), (SC, SC), and (CC, CC) However, I am not sure how to go about backwards induction....
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Fairness on point distribution for problems

I'm running a contest, where each team that solves a problem gets a point value. The first team that solves a problem gets 5 points, second team gets 3 points, third team 2 points, all other 1 points. ...
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Optimal decision rules given a set of bimodal values

Some patients have two possible illnesses ; to determine which illness a patient has, we make a test (only once) that will result in one of five outcomes, which have the following conditional ...
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Is following conversion from extensive games to normal form correct?

I studied converson from extensive form games to normal form games from following pdf - http://www.sfu.ca/~shihenl/302/Strategies%20Memo.pdf So i tried to convert following game(source credit - ...
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Game Theory Legislative Bargaining

I'm very stuck - any help would be appreciated :) Consider a 3 person legislature with a closed rule with 3 rounds dividing a dollar, but unanimous agreement is required. Proposers are randomly ...
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What is the payoff function for games with more than two players?

For two player games, with payoff matrices $(A,B)$, let $x \in \Delta_x$ denote the mixed strategy of player $1$, and $y \in \Delta_y$ denote the mixed strategy of player $2$. Then the payoff ...