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].
2,141 questions
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Nash equilibrium in second price sealed-bid auction
I'm trying to understand the basics of game theory and the topic of auctions has arisen. I understand the basic concepts of auctions but I'm struggling with second price sealed-bid auctions.
I ...
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1answer
35 views
Duel question, why shoot when $P_1 (s)+P_2 (s)=1$
There are two duelists with one shot each, their probability to hit from a distance $x$ is given by two functions $P_1 (x)$, $P_2 (x)$ that are both continuously and strictly decreasing from $P(0)=1, ...
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1answer
26 views
Equilibrium in a Lottery
We have the following game with 1700 participants: Each participant can buy a lottery ticket for 1\$ (when a participant buys a ticket, he does not know how many other participants are buying tickets) ...
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0answers
18 views
Defining a cooperative game heavily dependent on edges
i'm trying to create a cooperative game based on graph $g = (N,E)$ where the value of the coalition $S$ must equal the weight ($w_i$) of the nodes in the set $\mathcal{V}$ which have at least 1 (one) ...
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8 views
Computing the Shapley value for a super-additive game
I have a specific problem I have been set, I'm asking here because I can't really find an answer anywhere else.
Consider the scenario where a company offers some service to its users. The company has ...
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0answers
10 views
Is this simple demand-based prices game a submodular game?
I have this simple market game:
$I=\{1,2...,n\}$ players
$S_i$ strategy space of each player $i\in I$
$u_i(s_i,s_{-i})=R_i(s_i)-C(s_i,s_{-i})$
There's only one type of resource. The resource is ...
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1answer
20 views
Probability distributions in Bayesian games
In a Bayesian game, each player $i$ learns his own type, $\theta_i$, which is his private information, and then uses his prior $\phi_i$ to form posterior beliefs over the other types of players, using ...
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24 views
proving if player 1 has a pure optimal strategy, player 2 should as well
Problem:
Prove that if in a matrix game 2x2 if the player 1 has a pure optimal strategy, so has player 2
Attempt:
Given:
We know that player 1 has pure optimal strategy, meaning:
$$P(x, \overline{...
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1answer
40 views
relation between inquisitive logic and logic as games?
In the very intriguing thesis "Questions in Logic" Ivano A. Ciardelli shows how to build a semantics of questions that reduces to Truth Conditional logic for factual statements where ¬¬p = p, but has ...
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20 views
Finding a solution using backward induction for the game shown in tree
there is a exercise in Game Theory(Decisions, Interaction and Evolution) by James N Webb (Exercise 5.1), the question is "Finding a solution using backward induction for the game shown in Figure 5.2?" ...
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1answer
49 views
+100
Proving that the Wardrop/Nash equilibirum flow on a graph is “stable”?
Let $[0, 1] \subset \mathbb{R}$ be denoted $\mathbb{R}_{[0, 1]}$. Let $[0, \infty) \subset \mathbb{R}$ be denoted $\mathbb{R}_{\geq 0}$.
Let $G$ be a finite, connected graph. Associate with each edge ...
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1answer
74 views
How to find Nash equilibrium in pure and mixed strategies? Problem.
A two player game.
Players choose a number from a segment $[0;1]$.
A payoff function of the first player $f_1(x,y)=|x-y|,$
where $x$ and $y$ - the numbers chosen by the first and the second players ...
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0answers
13 views
Why does finding the partial derivative solve this payoff matrix?
So I'm taking this math course and I decided to do all the homework the first day of class, and as I was pulling an all-nighter doing it, I got to the topic of game theory and payoff matrices. I never ...
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0answers
11 views
Modeling multi-stage games as extensive form games
Consider a finitely repeated prisoner's dilemma game. In each of $T<\infty$ stages, two players play a prisoner's dilemma game. At the end of each stage, each incurs a payoff dictated by the played ...
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0answers
15 views
Expected Cost in the Second Price Auction
I am going through this paper https://arxiv.org/pdf/1803.02194.pdf on Bidding Machine. In the section 3.1 Problem definition, I got the part about finding the probability of winning at bidding price $...
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21 views
game theory-Are second priced bids always a nash equilibrium?
I'm trying to understand the basics of game theory and the topic of auctions have come up. What I want to know is second priced bids always a nash equilibrium?
Suppose we have this question.
We ...
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0answers
11 views
When the set of correlated equilibria is a singleton?
Is there any case where I can say that the set of correlated equilibria is a singleton? I know the set of correlated equilibria includes the set of Nash equilibria, but in which cases they coincide? ...
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25 views
What's the chance of the next person leaving a joint venture when a person before leaves? [closed]
A quite interesting practical question came to my mind today. I don't know whether it's solvable and I'll try to put everything as clearly as I can.
Question: Say you have 9 friends and you are ...
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0answers
20 views
How to check if mixed strategy leads to Nash equilibirum?
I have a simple payoff matrix defined here:
matrix
My question is: If both players play all 4 strategies with 1/4 probability, does that lead to Nash equilibrium?
I can't quite figure this out. I ...
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0answers
12 views
How to start these questions from an epistemic game theory problem?
Upon reading an Epistmeic Game Theory book, I came upon a practical problem. However, as it is completely different than the examples in the book, I do not know how to approach it. Could somebody ...
2
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1answer
39 views
How do you solve the following differential equation (Proof of Lemma 3 of Hermalin, 1998)?
$(e(\theta) - s \theta)e'(\theta) = s(1-s)\theta$
The solution to the differential equation is given by:
$e(\theta)=\frac{1}{2}(s+\sqrt{4s-3s^2})\theta$
Here, the dependent variable is $e(\theta)$, ...
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0answers
63 views
Game Theory - Mixed strategy ESS
I have a payoff matrix of a symmetric game like this:
$ \begin{matrix}
& A & B \\
A & (3, 3) & (1, 2) \\
B & (2, 1) & (5, 5)
\end{matrix} $
I found that $(A, A)$ and $(B, ...
2
votes
1answer
33 views
Bounds and/or closed form for the “swerve numbers”?
You've probably experienced this: You're walking down a hallway when you notice you're on a collision course with somebody. Both of you swerve in one direction. Then you both swerve in the opposite ...
3
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2answers
45 views
Imbalance due to ELO rating
I want to use some rating system in my application. It will look like this:
$TotalRating = rating_1*significanceCoefficient_1 + rating_2*significanceCoefficient_2 + ... + rating_n*...
2
votes
2answers
37 views
Does the von Neumann-Morgenstern utility theorem work for infinite outcomes?
The von Neumann-Morgenstern utility theorem is easy to prove for a finite number of outcomes. Is it still true for an infinite number of outcomes?
With infinite outcomes, a lottery can now be any ...
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2answers
42 views
A game of nim determine value of X,Y [closed]
Alex and Bob plays a game
A box contains numbers from 1 to 1024
Alex goes first
Alex removes 512 numbers
Bob removes 256 numbers
Alex removes 128 numbers
Bob removes 64 numbers
Alex removes 32 ...
4
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0answers
41 views
final coalgebra of the 𝓟${_{<κ}}$(A×X) endo-functor in $Set^*$?
In the paper Coalgebraic Games and Strategies F. Honsell, M. Lenisa, and R. Redamalla use the functor $F_A$(X) = ${\mathscr{P}_{<κ}}$(A×X) to define games coalgebraically. This is a functor from ...
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0answers
28 views
Nash Equilibrium and Mixed NE Problem
Does the game have a pure Nash equilibrium?
Find all the mixed equilibria (note, there is at least one)
I'm having some problems solving this exercise about the game between player 1 and 2 in the ...
0
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1answer
15 views
Nash Equilibrium for this sequential game
Player one (P1) picks a number between 100 and 0 inclusive. Let's call this number X. Whatever the X P1 has picked, it is subtracted from 100 and now is in front of P1. So P1 has 100 - X in front of ...
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0answers
6 views
Existence of Pure Nash Equilibrium in Global Connection Game?
I have a query in the proof of the following result:
Result: A global connection game (GCG) always has a pure Nash equilibrium (PNE).
This result is proved by showing that a global connection game ...
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0answers
26 views
calculation of probabilities in correlated equilibrium
I'm struggling to understand how to calculate the probability of each cell in a 3x3 matrics when trying to find the correlated equilibrium that maximizes the sum of players utilities?
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0answers
17 views
Primary source for definitions re partitions, coarsest common refinement, join/meet etc.?
As much as I do appreciate the contributions on m.se, I need to be able to cite a primary source for definitions related to partitions, e.g., what a refinement/coarsening is, coarsest common ...
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1answer
23 views
Subgame Perfect Equilibria in a one-stage game
Consider the following one stage game, with two players A and B.
There is a pie which is to be divided between the two players. A can offer B any fraction of the cake, which B can accept or reject. ...
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1answer
44 views
What is the winning strategy for this problem?
Before the game starts, there are a few "points" on the desktop, and then the two players take turns to do the following operations until the operation can not be completed:
Starting from a "point" ...
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0answers
32 views
Finding Nash Equilibrium using Linear Program with strategy constraints
Finding the Nash Equilibrium p in mixed strategies of a 2-player, symmetric zero-sum game with 3 pure strategies can be done by solving LP:
max $(0, 0, 0, 1)^{T}(p_1, \ p_2,\ p_3,\ \epsilon)$
s....
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0answers
33 views
Simple continuous game or not?
Two players simultaneously pick a number from [0, 1]. Payoff of the first player (equal to the loss of the second) is the distance between those numbers.
Does there exist pure-strategy Nash ...
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0answers
13 views
Bayesian Games: Belief Functions
One way to formulate the Bayesian game in Game theory is to define the set of type combinations as $T:=\times_{j=1}^{n}T_j$ and say that the type combination $t=(t_1,\ldots,t_n)\in T$ is supposed to ...
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2answers
54 views
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1answer
38 views
Pure Nash equilibrium in Zero sum [closed]
Do zero sum games have a pure Nash equilibrium and if so how do I find the pure Nash equilibrium
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1answer
47 views
Finding the winning strategy of a variation of the Nim game
Here is a variant of the Nim game which I could not find out the winning strategy, the game rule is like this:
The games starts with 16 stones arranged as follow:
o (first pile)
ooo (second pile)
...
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0answers
26 views
Subgame Perfect Nash Equilibrium in Cournot oligopoly
I have some questions about how I'm supposed to find the SPNE in this particular Cournot oligopoly:
Consider the following market game: An incumbent firm, called firm 3, is already in an industry. ...
2
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0answers
34 views
Probability of winning a board game by chance
What is the chance of winning a board game like Connect4 by chance? The player who makes the first turn could theoretically win in a perfect game all the time. How can I calculate the probability that ...
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0answers
25 views
How to create probability and scoring formulas?
I have seen questions regarding building scoring systems but the answers given apply only to the specific problem.
I am trying to understand how people can come up with equations that express the ...
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1answer
36 views
Bet on the sum of two dices
There are two players and each one has a dice with six sides from 1 to 6. The probability of each side is equal. Now two players roll their dice, and they only know the number of their own dice. They ...
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30 views
Game Theory: Finding the nash Equilibirums of 2x3 bimatrix by graphically representing the best replies
I am having troubles understanding the graphical method for solving a 2 x 3 bimatrix and I turn to all of you for help:
To give an overview of my doubt, consider a 2 x 3 bimatrix game, (A,B)
...
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75 views
King of the Centre - Is this an existing game?
Consider an $n$-player infinitely repeated game.
First stage nature chooses for each player, $i$, a radius $r_{i}$.
For each later stage $t$ each player $i$:
The payer chooses a "target" $p_{i, t}$...
2
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1answer
32 views
Finding the Bayes-Nash Equilibrium for First-Price Auction with 2 bidders
Let $\sigma_i$ be the strategy profile for bidder $i$ that indicates how they should bid based on their value. As we know, if there are 2 bidders both with their values $v_1,v_2$ on $U[0,1]$ in a ...
2
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1answer
50 views
number guessing game [duplicate]
Someone gets to choose a number between $1$ and $100$. I than have to try and guess by guessing a number and being told if the number is higher lower or equal. If I get the number on my first try I ...
0
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0answers
11 views
Game Theory Nash Equilibrium - Iterative Closed Bag Exchange Donation Game
I am making up a game for a Holiday party and became interested in checking if the game is somehow broken or if there is an optimal solution, which would make it less enjoyable. A Nash equilibrium may ...
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0answers
19 views
Cake cutting when some players don't like cake
I am beginning to acquaint myself with the fair division literature. So far, I've always encountered the assumption that the value functions $V_i$ are normalized, such that $V_i([0,1])=1$.
But it ...
