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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1answer
24 views

for the following values what will be the shapley value for each customer ? 32,27,19,56,12,8,13,26,50,8,12,25,35,45,42,3 [on hold]

is there any online calculator for finding shapley value ??From the theory of shapley value i am getting problem for finding shapley value .Please help me. for the following values what will be the ...
0
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1answer
26 views

Can a game with a pure strategy Nash equilibrium also have mixed strategy equilibria? [on hold]

I have questions: If zero-sum game has pure strategy Nash equilibrium (saddle point), can it have also mixed strategy equilibria? What if game is not zero-sum?
3
votes
3answers
91 views

Playing Odd-Even Cricket, is there a perfect strategy

This is a simple two-player game. One if the people is picked to 'bat'. Both players simultaneous choose a number from 1 to 6. (When playing against a person, you use your hands to show the number). ...
2
votes
1answer
49 views

When is the “Taxman Game” winnable?

I recently came across the "Taxman Game" the rules are in the link, but I'll repeat them here: We start with a pile of integers, from 1 to some number that you choose [$n$]. You take one, and I ...
0
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2answers
40 views

Mixed Strategy Nash Equilibrium in this game?

L (q) R (1-q) l (p) [(2, 1), (0, 1)] r (1-p) [(-1, 0), (1,7)] I'm having a lot of trouble understanding what the mixed strategy nash equilibrium is ...
3
votes
1answer
46 views

An inequality relating to moves to P-positions in Nim

I have been researching this variant of Nim. I have been unable to prove the following claim. What is annoying is that I feel I am missing something really obvious. Does anyone have any ideas on how ...
0
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1answer
47 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 ...
2
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1answer
23 views

What is the difference between mixed strategy and behavioral strategy games?

I a beginner in Game theory and reading the book "Non Cooperative Game Theory" by Tamer Basar. I am not able to comprehend the difference between behavioral strategy and mixed strategy. I saw this ...
3
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1answer
1k views

Mixed Strategy Nash Equilibrium of Rock Paper Scissors with 3 players?

It seems like most game theory tutorials focus on 2-player games and often algorithms for finding Nash equilibria break down with 3+ players. So here is a simple question: Is ...
0
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4answers
259 views

Recommended math background for game theory

I recently got interested in some game theory applications to poker. I want to try some of them out programmatically, but a lot of the math is a bit confusing. I learn math on my own fairly quick and ...
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2answers
94 views

Is it possible for a strategy game like paper, scissor rock to exist? [closed]

Is there a 2-player strategy game in which 3 (or more) programs don't form a clear dominance structure. That is, program A beats B, B beats C, but C beats A. I'd be more impressed if it was also the ...
0
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0answers
54 views

Is there a perfect game where there can be no draw and no chance is involved

Is there a game which is perfect, that is: always provides a decisive victor, and involves no component of luck Possible games which would be perfect or near-perfect might involve the pie rule. ...
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1answer
3k 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 ...
0
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1answer
38 views

“Guess the 2/3 of average” game

Let us consider the game "Guess the 2/3 of average" (description: https://en.wikipedia.org/wiki/Guess_2/3_of_the_average) I know, the strategy profile where all players play $0$ is a Nash ...
0
votes
1answer
24 views

Is 2nd-price with a discount auction truth-telling?

I know that 2nd-price auction is truth-telling, but 3rd-price auction is not. What If I run the regular 2nd-price auction, in the end, the winner is charged at the 2nd bidding price with a discount, ...
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0answers
109 views

Find measure such that…

I've a very concrete problem I can't solve. Consider the following function $k: [0,1]^2 \to \mathbb{R}:$ $$ k(x,y)=\begin{cases} 1 &\text{if } y > x \\ -1 &\text{if } x- \frac{1}{2} < ...
4
votes
1answer
102 views

What background is needed to study quantum game theory?

Currently I am learning ( a beginner ) about Bell inequalities and device independent outlook on quantum mechanics. I come across some papers using these concept in quantum game theory. Most of the ...
1
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2answers
236 views

Third and average price auction

Third price auction: the winner is the highest bidder but this time instead of paying the second highest bid, he would pay the third highest bid. -assume there are at least 3 bidders. - Average price ...
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0answers
57 views

Determine the optimal strategies

Player 1 and player 2 is playing a game where player 1 chooses 2 of the following numbers (not the same) 1,2 and 4. Player 2 chooses 1 number also among 1,2 and 4. Neither of the players know what the ...
2
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1answer
42 views

Can mixed strategies outperform pure strategies?

Let $G$ denote a game with a finite number $n$ of players in which each player $i$ can choose a mixed strategy $\sigma_i$ over a finite set of pure strategies $\Sigma$. Pure strategies can be seen as ...
4
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1answer
850 views

The Notion Of Degenerate Two Player Game

I try to get the intuitive understanding of the notion "degenerate two player game". Definition. A two-player game is called non degenerate if no mixed strategy of support size $k$ has more than $k$ ...
6
votes
2answers
226 views

Which mathematical game or puzzle did you invent?

A couple of weeks ago, a friend of mine showed me a extension of a game we are all familiar with that he was working on. The game we know is called Tic-Tac-Toe, and he was working on his own version ...
0
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0answers
78 views

Undestranding Basic Game Theory

Lately I'm studying game theory for an exam. I'm having troubles in understanding some theorems since notes I'm studying on are very brief and concise about sense of definition. In this question I'll ...
7
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1answer
76 views

Diagonal-free Sudoku grid

I have a Sudoku grid with the property that diagonally adjacent elements are distinct (it is also a torus under the same property). The grid offers new and exciting logical possibilites. My question ...
3
votes
1answer
96 views

Optimal strategy for 2 players Lights Out game variation

Consider a turn-based game for 2 players. They're both playing on the same board. The board is 8x8, randomly generated and each cell has 0 or 1 (with equal probabilities), for example: ...
0
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1answer
50 views

Poisson Application--Initial Survivors of an Attack

Phages kill bacteria. One or more phages can attack one bacterium, in which case the bacterium dies, and the phage(s) with it. Thus each phage can attack only one bacterium. Collectively and over the ...
4
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0answers
113 views

Is there a closed-form expression for Shapley value of glove game?

Suppose we have a coalition game with transferable utilities, with $m$ players having a right-handed glove and $n$ players having a left-handed glove. The value of a coalition is equal to the number ...
0
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0answers
31 views

Solving a Recurrence for a Mathematical Game

The problem is: Two players take turns removing coins from a pile. There are initially $n$ coins, and on each turn, a player can remove $a_1, a_2, \dotsc, a_k$ coins. The player who cannot remove ...
0
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1answer
35 views

Game Theory: Prisoners Dilemma

In $n=2$ person (say $A$ & $B$) prisoner's dilemma, the possible outcomes are $AB, CC,CD,DC,DD$ and the payoffs are $(1,1), (0,3), (3,0), (2,2)$ where $C$ is "cooperation" and $D$ is "defection". ...
2
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1answer
132 views

Strategy/Proof behind the Perfect solution of a Multiplication Game

So the below is the question Question: Jacob and Vicky play the fun game of multiplication by multiplying an integer p by one of the numbers 2 to 9. Jacob always starts with p = 1, does his ...
0
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0answers
13 views

How does the additivity axiom in the characterisations of the Banzhaf and Shapley-Shubik power indices work?

I am struggling to grasp in what sense some power indices - such as the Banzhaf and Shapley-Shubik indices - rely on a linear notion of power. Particularly, why do they satisfy the respective ...
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1answer
59 views

Python Integer Game

Jacob and Vicky play the fun game of multiplication by multiplying an integer p by one of the numbers 2 to 9. Jacob always starts with p = 1, does his multiplication, then Vicky multiplies the number, ...
3
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1answer
206 views

Perfect solution for a multiplication game

So I have encountered a question that I am struggling to figure out, what exactly would be considered a perfect way to play a game, especially when this game consists of two players. Its part of ...
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0answers
35 views

What is the connection between game theory and (modal) logic?

I'm interested in dynamic epistemic logic lately (reasoning about information and change in multi-agent systems). I also like game theory. I'm looking for some good resources about the connection ...
1
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1answer
304 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 ...
2
votes
2answers
41 views

Can this probability mechanic be used in a simulated gambling scenario?

This question is a bit complicated, so please bear with me. I realized this question after watching this video from the popular Youtube channel Numberphile. This video claims that when two random ...
1
vote
2answers
350 views

Dominant Strategy in Table Games

I have some basic background in game theory, but still there are exist simple questions that I cannot answer for sure. Whether Tic-Tac-Toe game has a dominant strategy? May be only one of the ...
2
votes
2answers
47 views

Limitation of Shapley value?

Accept my apology in advance if my question sounds stupid as i am early phase of exploration. Can someone give answer or point out the literature that gives answer of my two questions related to ...
5
votes
4answers
337 views

How to formally model the “hesitation” in the hat-guessing puzzle?

Hua Luogeng (in Chinese, 华罗庚) took a hat-guessing puzzle as an illustration in a booklet focusing on mathematical induction. The following description is a literal translation from Chinese. ...
1
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1answer
79 views

What is the relative strength of each of the players in this game?

This is a real life problem. A group of people meet once a week to play a game between two teams. Each round 2 people are randomly appointed captains. Each captain takes turns picking people to be on ...
2
votes
0answers
31 views

Expected Value in modified Let-it-Ride

Let-it-Ride is a casino table game which you can read about here: http://wizardofodds.com/games/let-it-ride/ This page also has expected values done for the normal game! In my modified version, ...
2
votes
1answer
35 views

Waiting for two buses

Coming back from work today I had the option to take one of two buses arriving one after another, both of the same line (i.e., going to the same place). The stop where I get on is relatively early on ...
4
votes
1answer
545 views

Calculating the Shapley value in a weighted voting game.

Given a special case of WVG (Weighted Voting Game) of $a$ 1s and $b$ 2s and a quota q, $ [q:1,1,1,1..1,2,2,..2] $. I need help with calculating the Shapley value of a player with a weight of $2$ and a ...
0
votes
1answer
530 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
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0answers
22 views

How to find an optimal solution for a missing player in a double-elimination tournament

Say that you have a double elimination tournament consisting of four teams with 2 players. Each of those teams of partners could be: (A,B), (C,D), (E,F), and (G,H), where A is B's partner, C is D's ...
6
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3answers
149 views

How do I calculate the odds of a given set of dice results occurring before another given set?

Dice odds seem simple at first glance, but I've never taken a Calculus based statistics course or game theory, and I think I may need to in order to solve some of the things I'm trying to solve. I can ...
0
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1answer
220 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. ...
5
votes
3answers
97 views

100-Sided Dice “Blackjack” Game

I am attempting to determine two variables in this game: The optimum strategy: (What number the bettor should stay at) The expected value given perfect play: (The percent return on a bet when using ...
109
votes
1answer
4k views

Identification of a curious function

During computation of some Shapley values (details below), I encountered the following function: $$ f\left(\sum_{k \geq 0} 2^{-p_k}\right) = \sum_{k \geq 0} \frac{1}{(p_k+1)\binom{p_k}{k}}, $$ where ...
0
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0answers
31 views

Support lemma - Game theory

Let α be $a$ mixed strategy profile, $a_i ∈ supp(\alpha _i), a_i \notin B_i(\alpha _{−i}), a_i' ∈ B_i(\alpha _{−i})$ and $a_i'$ defined by $\alpha_i'(a_i)=0$, $\alpha_i'(a_i')=\alpha _i ...