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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2answers
66 views
Is equilibrium selection in zero sum game trivial?
Does a zero sum game always has a unique payoff, whatever the nash equilibrium selected is ? even with mixed strategies ?
If so, what is the proof ?
5
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2answers
385 views
Do Symmetric Games with Nash Equilibria always have a symmetric Equilbrium?
Define a game with S players to be Symmetric if all players have the same set of options and the payoff of a player depends only on the player's choice and the set of choices of all players.
...
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1answer
48 views
How do we prove that e = RPC, in game theory?
Here e is the expected value of the game for the row player, P is the payoff matrix from the perspective of the row player, R is the row matrix containing the probabilities for each of the row ...
2
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0answers
89 views
proof using (fixed point theorem)
I am seeking to solve for a Nash equilibrium in pure strategies $(d_2,d_2)$ involving two players, $1$ and $2$. Given that $h'(.)$ is s strictly decreasing and continuous function, $\Phi(d_1-d_2)$ ...
4
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2answers
142 views
Two players and two coins
Two players are playing a game. The first player has unlimited gold coins of 2 types, $C_1=2\$$ and $C_2=5\$$. Each turn he chooses one of these coins and hides it in his hand. If the second player ...
7
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3answers
110 views
Seemingly similar but different probability games
Burger King is currently running its "family food" game in which each piece can be modeled as a scratch off game where exactly one of three slots is a winner and you may only scratch one slot as your ...
1
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1answer
435 views
Finding subgame-perfect Nash equilibrium in the Trust game
I am facing a game theory problem which is as follows:
An experiment was designed to study individuals' propensity to be trusting and to be trustworthy in a task called the investment game. In this ...
5
votes
2answers
94 views
Question regarding technicalities in the paper Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent
For people on this board I have a probably pretty modest question, but since I'm not a mathematician (just an economist), I'm having trouble.
The full pdf can be found here: ...
4
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3answers
125 views
Consider a card game-parity
Consider a card game where the deck consists of 63 distinct cards. The deck is created in the following manner: each card consists of some number of symbols, where no two symbols are the same. There ...
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2answers
92 views
Reasonable strategy for simple game
I have a very simple probabilistic process which I have to deal with in the software project I'm involved in, yet I can't figure how to do it. I can describe the situation as a money game (in reality ...
0
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2answers
406 views
Subgame Perfect Nash Equilibrium
My homework question is summarized below:
There are 7 players (say P1,P2,...,P7) trying to split 100 dollars. The game starts with P1 proposing an allocation of the 100 dollars to each ...
1
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0answers
79 views
Shifted Young tableaux & Hook numbers & Bulgarian Solitaire
I would like to find articles or documentation regarding this process:
Starting from what ever integer partition, e.g. 5,2 for the number 7. Construct his Young tableaux and then fill it with Hook ...
9
votes
1answer
214 views
Strategy for a game of breaking sticks
Two persons have 2 uniform sticks with equal length which can be cut at any point. Each person will cut the stick into $n$ parts ($n$ is an odd number). And each person's $n$ parts will be permuted ...
2
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2answers
630 views
Winning strategy for a matchstick game
There are $N$ matchsticks at the table. Two players play the game.
Rules:
(i) A player in his or her turn can pick $a$ or $b$ match sticks.
(ii) The player who picks the last matchstick loses the ...
4
votes
1answer
250 views
Iterated prisoners dilemma with discount rate and infinite game averages
Suppose we have two players who are perfectly rational (with their perfect rationality common knowledge) playing a game. On round one both players play in a prisoners dilemma type game. With payoffs ...
5
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0answers
179 views
Olympic Badminton, or How to Design a Tournament
Hearing the recent news about disqualified Badminton players in the ongoing 2012 London Olympics got me wondering about how best to design tournaments to avoid situations where players are ...
6
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2answers
282 views
Simple dice game: Optimal strategy?
Here's the description of a dice game which puzzles me since quite some time (the game comes from a book which offered a quite unsatisfactory solution — but then, its focus was on programming, so this ...
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1answer
243 views
Finding Nash Equilibria with Calculus
The problem is summarized as:
There are two players. Player 1's strategy is h. Player 2's strategy is w. Both of their ...
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1answer
118 views
How does this game work? (Number game: subtract prime)
Problem
Alice and Bob play the following game.They choose a number N to play
with.The runs are as follows :
1.Bob plays first and the two players alternate.
2.In his/her turn ,a ...
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1answer
90 views
Submodular and supermodular games
Can someone please explain to me (with concrete examples) what are submodular and supermodular games, and their related concepts of games of strategic substitutes and strategic complements.
An ...
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1answer
298 views
Unable to find Nash equilibria in mixed strategies
Here is the strategic form game:
Player 2
Left Middle Right
Top 2,2 0,0 1,3
Player 1 Middle 1,3 3,0 1,0
...
0
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0answers
56 views
what exactly does symmetric game and symmetric equilibrium mean?
I am confused about the ideas of a symmetric game and symmetric equilibrium of a game under the following conditions.
1) pure strategy Nash equilibrium
2) Nash bargaining game where players set a ...
1
vote
2answers
270 views
Is there a winning strategy for Scrabble?
I am sure many of us are addicted to the popular Facebook app: Words with Friends, which is basically an online version of Scrabble. In Playing Games with Algorithms:Algorithmic Combinatorial Game ...
6
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1answer
351 views
Game theory problem: Poker with bluffing
Hope someone can help me with this one. The problem I am talking about can be found in the book titled "Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction" by ...
2
votes
1answer
88 views
Winning strategy
Is there a winning strategy for player one or two in the following scenario:
The game begins with the number
2012. In one turn, a player can subtract from the current number any natural number
less ...
1
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2answers
127 views
Finding the fixed point of a function
Let $p:A \times B \to \mathbb{R}$ be a nonnegative real-valued function on $A \times B$,
where $A$ and $B$ are arbitrary set.
Assume $f:A \to B$ and $g:B \to A$ are such that
\begin{align*}
f(a) ...
1
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0answers
95 views
Is Bingo Games Solved?
So we have numbers 5 rows by 5 columns. Different players have the same table. The numbers on each cell of the tables are different. Different players choose which numbers will be marked.
We select a ...
0
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1answer
72 views
Solution for assigning independent tasks to independent individuals
I have $n$ tasks that I wish to delegate to $m$ independent individuals, where $m$ is a factor or divisor of $n$. Each of the tasks $T_{1} ... T_{n}$ is independent. From the following two extremes, ...
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2answers
77 views
value of this possibly Monty Hall-related 2-person zero-sum game?
Player A tosses a fair coin. He knows how it lands; Player B does not. A can now play move 1 or move 2. If he plays move 1, he pays B £1. If he plays move 2, then B can either play move X or move Y. ...
0
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1answer
27 views
pure-poa is bigger that mixed-pos?
generally it's true that Pure price of anarchy is >= mixed price of stability.
but I just find cases where they are equal and I can't think of a case of strict inequality.
can you help me please?
...
6
votes
1answer
468 views
Number Game: 31 - Winning Strategy?
My Maths teacher taught us how to play a game called 31 on Friday. Not once did my Maths teacher lose. I want to know why.
I'll explain the game...
31 is a game between two people.
Let's say you've ...
0
votes
1answer
156 views
Given a victory condition and a set strategy, what are the chances of winning on a given turn in a game of Magic: The Gathering?
Tl;DR: You have winning cards. To win, you must be able to play those cards, and have them in your hand. Your hand is randomly drawn. When might you win? How could find the answer to this (very ...
5
votes
1answer
128 views
Stone games again
Two players are playing a stone-picking game.
There are some piles of stones. The number of stones in each pile is given.
Every player takes action in turns as following rules:
The one in his turn ...
0
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1answer
846 views
Mixed-strategy Nash equilibria
I didn't find in books, so I'm asking - Mixed-strategy Nash equilibria is always only one or doesn't exist for the one certain game? And I know that there can be several(and can not be at all) pure ...
2
votes
1answer
209 views
(Game Theory) Incomplete Information extension of the 'Centipede' Game
This question is an extension of the Centipede Game.
My prof. posed this to me in class and I can't figure out how to approach this problem.
Imagine in this game, there is an alternative ...
1
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1answer
114 views
Game Theory- Second-Price Sealed Auction- 2 Players
Assume Player 1 has valuation 400. Player 2 has valuation on the interval [0, 100]. What would the equlibrium be? Assume Player 2 knows Player 1's valuation, but Player 1 knows only the probability ...
0
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1answer
159 views
Find the Nash Equilibrium for a Cournot Game
Consider a Cournot game with $2$ firms. Firm $i$ has constanct marginal cost $C_i$, where $C_1 \lt C_2$. Inverse demand is linear: $p(q)=A-q$ (where $A \gt 2C_2 - C_1$). Find the Nash Equilibrium.
2
votes
1answer
74 views
Name for a certain “product game”
Let $G,H$ be two (combinatorial impartial) games. Consider the following new game $P$: The positions are the pairs of positions of $G$ and $H$. A move in $P$ is a move in $G$, or a move in $H$, or a ...
0
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1answer
206 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 ...
1
vote
2answers
175 views
summation notation for general sets
I'm working through an academic game theory paper and stumbled upon this summation notation in a proof and I'm not quite sure what it means:
$$\sum\limits_{j \in M \backslash\ \{i\}}$$
There is a ...
6
votes
1answer
145 views
Sunk cost auction modeling.
Consider the following auction concept. I call it a "SUNK COST AUCTION" Each person bids, but you pay all of the money that you bid for every bid you make. So, if you bid \$1 that \$1 is gone, even if ...
0
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2answers
72 views
minmax optimal strategies
consider we have game between adversary and player. Player can make some actions, let' call $w$ and adversary can make actions $\ell$. Then player get loss function $L(w, \ell)$. Adversary trying ...
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1answer
235 views
Is there a winning strategy for this game?
Andy and Bob play a game using a long straight row of squares, alternating turns. When it’s Andy’s turn, he writes an A in one of the blank squares. When Bob takes a turn, he writes a B in some blank ...
5
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1answer
153 views
Motivation for the Sprague-Grundy theorem
The Sprague-Grundy theorem states that every impartial combinatorial game under the normal play convention is equivalent to a (unique) nimber.
What does the equivalence relation thus defined tells us ...
0
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1answer
269 views
Simple Nim game with equal-sized piles.
Consider the standard Nim game, i.e. you can take as many coins as you want from a single pile, you should take at least one coin and you can't take coins from two or more different piles at the same ...
1
vote
2answers
274 views
Game Theory Nash Equilibria Question
I am stuck on this question from a practice microeconomic theory exam I am working on.
Consider the payoff matrix below, where $x>0$. For what values of x do both players have a dominant ...
0
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1answer
131 views
Wise decision using game theory?
There are 2 persons and two bags of oranges present in system.A bag is assigned to person.Each bag contains some oranges in range 1-10.After opening each person has been asked if they want to trade or ...
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1answer
84 views
Perfect-information game in extensive form definition
I'm writing a paper and I need to define what a perfect-information game in extensive form is. My paper includes material from Game Theory and Reinforcement Learning. Since the notation of both fields ...
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3answers
182 views
Nash equilibria - Why can we calculate a player's strategy without reference to their payoffs?
Consider the following calculation of Nash equilibria from Wikipedia:
...
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2answers
107 views
Finding a closed formula for some SG function
Consider the following sequence, defined by recursion:
$g(0)=g(1)=0$. If $n>1$, let $g(n)$ be the mex of the $g(k)$ with $\frac{n}{2} \leq k < n$.
The first values of $g(n)$ with $0 \leq n ...
