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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18 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
votes
1answer
24 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
87 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). ...
3
votes
1answer
45 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 ...
1
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1answer
22 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 ...
0
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1answer
37 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 ...
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votes
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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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} < ...
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, ...
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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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
votes
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 ...
0
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0answers
77 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 ...
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 ...
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 ...
3
votes
1answer
93 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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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 ...
0
votes
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". ...
1
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1answer
58 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, ...
4
votes
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 ...
1
vote
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 ...
2
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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 ...
2
votes
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 ...
3
votes
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 ...
2
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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 ...
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 ...
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 ...
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 ...
6
votes
3answers
148 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 ...
6
votes
0answers
42 views

Undetermined game of length $\omega_1+\omega$, without choice

On the following page, Taranovsky is talking about his "Determinacy Maximum" axiom: http://web.mit.edu/dmytro/www/DeterminacyMaximum.htm He also justifies the choice of the name, by pointing out that ...
0
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1answer
23 views

Calculating Shapley Value on voting game

I am facing a problem to understand the calculation of shapley value on the below example: Question: The parliament of Micronesia is made up of four political parties, $A$, $B$, $C$, and $D$, which ...
0
votes
1answer
40 views

Question about Game theory, matrix games.

Lets say you have a matrix game, where the matrix $A$ is the matrix, the column player can choose a column, the row player a row, and the row player pays the column player $A_{i,j}$. Assume we want ...
0
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0answers
24 views

Signaling game : response to zero-probability message

We have this signaling game : sender type $t$ is uniformly distributed among $[0, 1]$. She takes action A if $t < \phi$, B if $t > \phi$ if receiver takes action A' when seeing A and B' when ...
5
votes
1answer
62 views

Optimal strategy in a bidding game

Note: I do not expect a clean closed-form solution to this, and would be very surprised if one existed, but I figured I'd ask to see what ideas other people had. There is a \$100 bill up for auction. ...
0
votes
1answer
39 views

Dynamic game of incomplete information

Consider a 2-player game: You and a robber. The robber tells You to give him all your money, otherwise he will kill You. However, the robber could be a 'Good' person (i.e. he would not kill You ...
0
votes
1answer
31 views

Dynamic programming approach for multidimensional problem

I use a dynamic programming approach to optimize the behaviour of individuals playing a game.I have one strategy matrix that describes the behaviour of individuals in situation 1, which depends on ...
4
votes
1answer
87 views

Knight movement on chess field

I had this task in programming competition: There are two knights, which are $(p_1,q_1)$ and $(p_2, q_2)$. $(p,q)$ knight is figure, with p(q)-length first step, and q(p)-length second step in ...
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 ...
2
votes
1answer
42 views

Is my answer correct? (Devious auction game)

(Taken from here) The question was A man is auctioning a real $20\$$ bill. There are a vast number of bidders. A person may make as many bids as he wants. The starting bid is $5\$$. No $2$ ...
1
vote
2answers
34 views

Game Theory: Can someone explain the notation used in the definition of “best response”

I am reading a paper which states that that the best response correspondence of a player is mapping: $B_i(s_{-i}): S_{-i} \Rightarrow S_i$ such that $B_i(s_{-i}) \in arg\ max_{s_i \in S_i} ...
1
vote
1answer
36 views

Nash equlibrium game theory

Given the following game: Find nash equilibrium (NE) Find subgame perfect nash equilibrium. Main problem i have is with converting this to normal form of the game (because this is i think ...
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votes
1answer
46 views

Mixed strategy nash equilbrium

In a mixed strategy Nash equilibrium it is always the case that: a) for each player, each pure strategy that is played with negative probability yields the same expected payoff as the equilibrium ...
0
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0answers
15 views

How to calculate effect of different variables/parameters on a quantity?

I am developing a game for iOS. In the game I have around eight different parameters that directly affect the score of the player. We can say that these eight variables decide the difficulty of the ...
7
votes
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 ...
0
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0answers
11 views

Prove that a directed tree does not have a path from a descendant to its parent

Prove: Let T = (V, E) be a directed tree. If v is a vertex of V and u is a descendant of v, then there is no path from u to v. My idea is that if u is a descendant of v, then there exist a path from ...
1
vote
1answer
48 views

What is the name of this kind of games?

In game theory, suppose we have a set of players $\mathcal{N}=\{1, 2, \ldots, n\}$, a set of actions $\mathcal{A}_i$ of player $i\in\mathcal{N}$, and a payoff function $u_i$ of player ...
0
votes
1answer
47 views

binomial distributions and their transforming (6.37-6.39)

I'm lost and frustrated. I don't know how the author (Karl Sigmund; The Calculus of Selfishness) transforms 6.37 in the book pages imaged below: $$ P_y = \sigma w^{N-1} + ...
0
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1answer
46 views

Game with matches. Very interesting mathematical problem.

Suppose you have a set of matches. You arrange them in 9 rows such that the first row has one match the second two matches the third three and so on until the ninth row which has nine matches. There ...