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5answers
86 views

Some examples of applications of Game Theory

I'm approaching my junior year of HS now, and I'm looking for a good science fair project to do. I love mathematics, so I decided to a category of mathematics that can help base logical conclusions to ...
2
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1answer
36 views

Game theory: Mixed Strategies and Nash Equilibrium

So I've recently become interested in game theory, and I've visited this site to help me understand what exactly game theory is and the applications of it. In the lesson, they use an example of ...
0
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0answers
15 views

Can we prove constructively that $\epsilon$-equilibrium converges to (mixed strategy) Nash equilibrium?

We know that by using standard classical mathematics, $\epsilon$-equilibrium does converge to exact (mixed strategy) Nash equilibrium as $\epsilon$ becomes smaller. My question is, can we prove this ...
2
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1answer
74 views

A game with numbers from MEMO $2013$

The expression $$\displaystyle \pm \Box \pm \Box \pm \Box \pm \Box \pm \Box \pm \Box $$ is written on the blackboard. Tow players, $ A $ and $ B $, play a game, taking turns. Player $ A $ takes the ...
11
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4answers
160 views

How do you create a nonlinear game that the player can always win?

I thought a lot about this question — and initially, I intended to ask this on gamedev.stackexchange.com — but due to its rather theoretical aspects, I think it might be more appropriate to address a ...
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2answers
84 views

Hex game winning strategy

I was teaching myself how to play a hex board game by reading some books a couple days ago. I learned how to do $2$ x $2$ and $3$ x $3$ hex games by starting at the principal diagonal. I wanted to ...
0
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1answer
32 views

The potential function of Prisoner's Dilemma

As in the famous example of "Prisoner's Dilemma" like this If the potential function is defined as: (V(q,q), V(q,c), V(c,q), V(c,c)) q = quiet, c = confess, V is the potential. So should the order ...
0
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0answers
19 views

de Bono's L-game modification

I am trying to find out if a simple modification od de Bono's L-game is still infinite if two players are perfect. Modified rule is that there no neutral pieces but, there is one piece for each player ...
1
vote
1answer
94 views

Optimal strategy for dominoes game

Here is the basic principle of the game I'm trying to find an optimal strategy for: Two players (say P and Q) are given a 2x3 grid and a domino. Then P chooses one way of positioning the domino on ...
0
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1answer
27 views

Optimal Algorithm for Pursuit-Evasion Scenario

Consider a "game" in which there are two players, A and B. A's goal is to avoid B, while B's goal is to capture A. A and B take turns making single steps over edges from one node to another on a ...
4
votes
1answer
60 views

A game problem- double or increment by 1

Its a two player game. Initially $P=1$, and there is some fixed integer $Q>1$. A valid move consists of either increasing $P$ by $1$ or doubling it iff on doing so $P$ does NOT exceed $Q$.The ...
0
votes
1answer
101 views

Game Theory - trying to find game name by description

My hobby AI research have led me to a thorethical game of particular design. As design is pretty simple, I'm almost sure that such game has well-known name and tons of research already done around it. ...
1
vote
1answer
96 views

Game Theory - Nash equilibrium question

Consider a game in which 2 players transmit packets in a network with a selected power $x ∈ [1, A]$ and $y∈ [1, A]$, respectively. The utility of the players can be expressed as: $$u_{i} (x,y) = ...
13
votes
4answers
186 views

perfect play in 1-dimensional Minesweeper

In 1-dimensional Minesweeper with a known number of mines (that are distributed uniformly), is there a known somewhat-simple strategy for perfect play? When there are n cells and [0 or n-1 ...
4
votes
1answer
128 views

A game of Chess - Ideal Solution

I am a student of physics. I have learnt some basic group theory, and I am wondering if there is any ideal solution for a given Chess game (like solving Rubik's cube). I know the no. of permutations ...
2
votes
1answer
144 views

Largest white rectangle on board

Given a string rectangular board which is divided into unit cells. Each cell is initially painted black or white. The character board[i][j] represents the cell with coordinates (i, j). Each of those ...
2
votes
1answer
55 views

What's the most efficient algorithm to determine the relative ordering of an unknown set of values?

This comes from a question on Arqade. The background is, there's a mall level. Vlad the organized crime boss wants $50,000 worth of mall property destroyed. Your task is to shoot and blow ...
4
votes
1answer
76 views

How to design a cost sharing auction format for collective bidding?

Problem goes like this: There's one resource which can only be utilized by a single set of agents $A_i$ (at any one time) out of $n$ predefined (disjoint) sets of agents. Each agent wants to use the ...
2
votes
1answer
73 views

the proof of Arrow's Theorem

I read Philip J. Reny's paper (Arrow’s Theorem and the Gibbard-Satterthwaite Theorem: A Unified Approach) What I cannot understand is step 5 of the proof of arrow's theorem. I think figure 4 is a ...
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2answers
225 views

A Nim-like game with conditions and strategies

The game: Given $S = \{ a_1,..., a_n \}$ of positive integers ($n \ge 2$). The game is played by two people. At each of their turns, the player chooses two different non-zero numbers and subtracts ...
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2answers
55 views

extensive and strategic game

definitions of extensive and strategic (normal) games are very different. Here is the question, what would you call a game which is extensive but in each step strategic. For instance at each step ...
1
vote
1answer
42 views

Segment crossing algorithm

I need an ideea of an algorithm to solve a puzzle 'game'. The game is : is given N number of line segments by coordinates [(X1n,Y1n),(X2n,Y2n)] some of segments have the same ends We've got ...
5
votes
1answer
95 views

Flip all to zero

I have a square grid of size $N$, with rows numbered from $0$ to $N - 1$ starting from the top and columns numbered from $0$ to $N - 1$ starting from the left. A cell $(u, v)$ refers to the cell that ...
0
votes
1answer
63 views

Prize distribution system based on quantity/priority per day

I'm trying to figure out a way to "fairly" distribute a pool of prizes on a daily basis depending on the time the contest will run, the priority and max items per day/week. For a better explanation, ...
1
vote
0answers
20 views

Are there any good resources to learn mathematical analysis of single player games and puzzles?

What are the best resources to understand the mathematical analysis of single player games like Solitaire, Free Cell, Sudoku, Rubik's Cube, etc.? Most game theory books I browsed in the local book ...
2
votes
1answer
278 views

questions on information set definition

The definition of "information set" is An information set is a set of decision nodes, all belonging to the same player, over which that player cannot distinguish. ...
1
vote
2answers
141 views

How do I grade the complexity of the below math puzzle game?

The game (I built it, and it is currently live on mobile) involves solving a pascal's triangle like grid of numbers with operators between the numbers - an example with 3 rows is: ...
0
votes
1answer
80 views

Partisan/Partial Game Theory

There are enough resources available on the internet regarding "impartial" game theory. But I cannot seem to find much information regarding "partial" game theory. Can someone name some such resources ...
2
votes
1answer
107 views

Sort objects into groups based on group size preference

I have a research question that involves human subjects being sorted into groups before playing a social game. Before sorting, each person decides on their preferred group size, from 1 to n; where n ...
2
votes
1answer
512 views

Finding Pareto optimal solution set in $O(n \log n)$ time

http://cs-people.bu.edu/kvodski/teaching/spring10/lab7.html says: For two points in 2-dimensional space, point ($x_i$, $y_i$) dominates ($x_j$, $y_j$) if $x_i > x_j$ and $y_i > y_j$. Given a ...
3
votes
5answers
354 views

Provide an algorithm $O (n ^ 3 \log n)$, any example?

Provide an algorithm computing performance $O (n^3 \log n)$. Your algorithm should contain only simple operations. Any idea of how to approach this problem?...I am studying for the computer science ...
0
votes
1answer
62 views

Simulating Mixed Nash Equilibria

I have a $N$ person game where each person has a set of $M$ discrete strategies. I know from the theory that at least one mixed strategy Nash Equilibrium exists. Can someone please tell me how do I ...
1
vote
1answer
141 views

Require help in writing the algorithm for my cricket simulation game

I am trying to write the algorithm for a cricket simulation game which generates runs on each ball between 0 to 6. The run rate or runs generated changes when these factors come into play like Skill ...
0
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0answers
30 views

What algorithms do you know for beltway reconstruction?

I've faced the beltway reconstruction problem and I've developed a simple backtrack algorithm, what algorithms do you know for this problem? Beltway Reconstruction Problem: Assume there is a set of ...
42
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2answers
2k views

A non-losing strategy for tic-tac-toe $\times$ tic-tac-toe

Consider a 9 by 9 matrix that consists of 9 block matrices of 3 by 3. Let each 3 by 3 block be a game of tic-tac-toe. For each game, label the 9 cells of the game from 1-9 with order from left to ...
1
vote
1answer
98 views

Two Player Game Useless Strategy

Let's consider the variant of dominated strategy which is the pure strategy that is not a best response to any mixed strategy of the opponent (two player game). Intuitively it sounds like more ...
2
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0answers
281 views

Is quantum game theory reducible to classical game theory? [closed]

Modnote: This question was manually migrated (closed and crossposted) to MathOverflow by request of the OP. Quantum game theory is an extension of classical game theory to the quantum domain. It ...
1
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0answers
99 views

Stable Matching Optimal Strategy Existence

There is a famous stable marriage problem. It's well known that the standard algorithm for stable marriage problem proposed by Shapley and Gale is man-optimal, men get a best according to their ...
3
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0answers
98 views

Unexpected hanging paradox maxmin strategies

I have a question about strategies of the players of Unexpected hanging paradox (I am very sorry for a long topic, topic exist already for a while, during this time I try to develop idea how to solve ...
3
votes
1answer
322 views

Converting a game in extensive form to normal form

I have some difficulties in representing the following game in the standard form. Game: two players game is represented as a game tree (in extensive form), a game tree is a full binary tree, both ...
5
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0answers
226 views

“Infinito”, a combinatorial game with infinite width game-tree

I recently designed a combinatorial game (sequential game of perfect information) with an infinite branching factor, that is it has a game-tree of infinite width. I'm wondering how is it possible to ...
2
votes
1answer
125 views

Games for which the Lemke-Howson algorithm provides incomplete results

I am exploring a large number of 2-player games. The Lemke-Howson algorithm is computationally very reasonable, and is able to find many equilibria. On the other hand, I know that there are equilibria ...
4
votes
0answers
86 views

Understanding Blackwell's Approachability Theorem

I'm not super solid on my linear algebra, so I am getting lost in the discussions of halfspaces. Can someone give me an intuitive explanation (possibly with a concrete toy problem) of Blackwell's ...
0
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0answers
307 views

Solutions to Nisan's Algorithmic Game Theory Exercises?

I am reading Nisan's "Algorithmic Game Theory". Does anybody know if you can find (part of) the solutions to the exercises online? I would like to double-check my answers. Thanks in advance!
5
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2answers
495 views

Game theory Computing pure Nash equilibrium probability

We have a $2$-player game and each player has $n$ strategies. The payoffs for each player are in range $\left[0,1\right]$ and are selected at random. Show that the probability that this random game ...
0
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0answers
45 views

Algorithm for precedence related job allocation

Suppose we have a set of jobs. Some jobs are related to others for example Job (a) has to finish for Job(b) to begin. Some other jobs are not related, that means can run in parallel. We have a ...
4
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1answer
727 views

Analytically solving (calculating Nash equilibrium for) 3-player extensive form games

Let's say we extend the popular half-street Kuhn poker variant to 3 players. The rules would be as follows: ...
0
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0answers
25 views

complexity of games with tokens and only-pay-once toll roads

I was reading http://arxiv.org/abs/1201.4995, and thought back to a game I used to play, which is close to being covered by part (c) of "Metatheorem 2" on page 4 of that paper. (The difference is ...
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2answers
323 views

Prime one heap Nim

I have been working on an interesting problem my lecturer mentioned recently. Prime Nim is a variant of the Nim game where you have a single pile with an arbitrary number $n\in \Bbb N+\{0\}$ of ...
1
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1answer
51 views

Game theory multiple cooperative adversaries

Are there any papers talking about games with multiple cooperative adversaries? I do research in computer science, and I am interested in this type of game. I am really not that knowledgeable in game ...