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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0answers
39 views

A Game theory problem about two killers and two citizens? [on hold]

Two killers and two citizens, killers know the identities of others, citizens don't know the identities of others. Each guy will vote for a guy to be the killer in order (randomly predefined). If all ...
4
votes
1answer
909 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 $k$ ...
4
votes
1answer
51 views

Optimal Strategy Game of Communicating without Overlap

Today, I had a conversation which proceeded very poorly; indeed, I had this conversation with $n$ people, including myself, and everyone had something to say. Problem was that, for an unreasonably ...
0
votes
1answer
13 views

imperfect information in extensive form

Hi I'm trying to understand how to convert into extensive form this imperfect information game. consider the second graph of this example taken from example of imperfect information game in extensive ...
1
vote
1answer
37 views

Is my cake split envy-free (and coalition-resistant)?

I once read that splitting a cake in 4 parts envy-free is notoriouse difficult. Not to mention splitting it with 5 or more people. Methods involve arbitrarily long recursions and cake split onto ...
8
votes
1answer
143 views

Wizard against two dwarfs: guess the whole function

An evil wizard plays the following game with two dwarfs $A$ and $B$: he thinks of a function $f:\mathbb{R}\to\mathbb{R}$ (which is not required to have any regularity properties, such as ...
7
votes
1answer
95 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 ...
7
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4answers
372 views

Can Nash Equilibrium be more than two?

In the Prisoner's Dilemma example, we know that there is only one Nash Equilibrium. That is both of them confess. Is it possible that there are two Nash equilibrium in one example? Can you roughly ...
0
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0answers
42 views

Math Extended Essay Topics [on hold]

I am doing an IB Extended Essay in Math and need some help finding a viable topic. It needs to be 4000 words and high school level (calculus). I'm interested in game theory and triangulation, but ...
5
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1answer
37 views

Nash Equilibria for the Effort Level Game

Player $i$ chooses an effort level, $e_i \in [0, 10]$. Let player $i$ have the following payoff function: $90 -e_i$ if $e_i > e_j$ and $80 -e_i$ if $e_i \leq e_j$. What is the Nash Equilibrium (NE) ...
5
votes
1answer
149 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 ...
4
votes
1answer
556 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 ...
1
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1answer
57 views

Expected Utility Method and a Repeated Game Solution

I am trying to replicate Bruce B. de Mesquita's (BDM) results on political game theory for prediction. Based on where actors stand on issues, their capabilities, salience, BDM's method attempts to ...
0
votes
1answer
48 views

Facing problem to compute ShapleyValues [closed]

I am facing problem to compute the ShapleyValues. Suppose there are 5 people in a city. First person has 10 dollars, 2nd person has 6 dollars, 3rd person has 11 dollars, 4th person has 12 dollars and ...
1
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0answers
21 views

Example of infinite game without any Nash equiblibria

I have to find an example of a game that does not admit (mixed strategy) Nash equilibria. Consider a game in normal form. Let $N=\{1,2\}$ be set of players and $S_i=\mathbb{R}$ a set of possible ...
1
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2answers
362 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 ...
1
vote
1answer
33 views

Dual Core in Cooperative Game Theory

I'm a bit confused over if the dual core of a game is the same as the core of the original game. Definition of dual game: $$ v^*(S) = v(N) - v( N \setminus S ), \forall~ S \subseteq N.\, $$ I then ...
1
vote
1answer
321 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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2answers
4k views

Pure vs mixed strategy Nash Equilibria

Just learning about Nash Equilibria. The pure strategy one is explained as an outcome where both/all players feel like they couldn't have done better given what the others were doing. Mixed strategy ...
2
votes
1answer
931 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 ...
2
votes
2answers
37 views

A game with no pure or mixed strategy equilibrium?

I'm trying to find any and all pure or mixed strategy Nash equilibria for the game $$\begin{array}{|c|c|c|c|}\hline & L & C & R \\ \hline T & (6,2) & (0,6) & (4,4) \\ \hline ...
3
votes
1answer
30 views

Proof that $\min_{b\in B} u(a,b)\leq \min_{b\in B}\max_{a\in A}u(a,b)$

So I have two finite sets $A,B$ and $u:A\times B\rightarrow \mathbb{R}$ a utility function. I am asked to give a certain proof but I don't need help with the whole thing, I just need help figuring ...
1
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1answer
25 views

Game Theory (continuous utility, pure strategy)

I have a game in which two players, 1 and 2, choose a non-negative real number level of effort $e_1,e_2$ respectively. Their cost for this choice is $ce_i$ for $i=1,2$ where $c>0$ is the same for ...
3
votes
0answers
48 views

Auction Design : Multiple lots, one win max per bidder, not regret

This is a real life game theory problem. I have to organize an auction. There is a finite number of lots, which are not equivalent. There is a finite number of bidders; the number of bidders is ...
1
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1answer
46 views

Can a transitive relation be represented by a utility function?

I am currently studying for my Game Theory exam and came across a question that seems pretty basic but somehow can't wrap my head around. So if you could share some insight with me, that would be ...
0
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1answer
537 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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1answer
422 views

Reduce the payoff matrix using (weakly) dominated strategies

Below is the payoff matrix of a game. Use the principle of elimination of (weakly) dominated strategies to simplify the payoff matrix. What is the optimal solution of the game for the row player? ...
4
votes
1answer
93 views

Have I Found an Error in “Game Theory” by Hans Peters?

I am reading the book Game Theory: A Multileveled Approach Second Edition by Hans Peters. It appears to be the most recent copy. I've search here and on Google for a list of known errors in the book, ...
0
votes
1answer
31 views

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

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
100 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
55 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
votes
2answers
41 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
49 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
votes
1answer
49 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
votes
1answer
30 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
votes
4answers
262 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 ...
-1
votes
2answers
100 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
57 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. ...
1
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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
votes
1answer
44 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
27 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, ...
-1
votes
0answers
113 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
105 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
243 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 ...
0
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0answers
65 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
47 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 ...
7
votes
2answers
235 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
83 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 ...
3
votes
1answer
132 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: ...