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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3
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1answer
60 views

Stock market trading / Casino betting / Multi-player fun competition possible with the following input?

I would like to program some kind of online betting system for fun. Just for the fun factor, I would like the Twitch chat to be the random input (seed). As can be seen here, you can see one possible ...
9
votes
2answers
393 views

Prime Numbers and a Two-Player Game

In this question, $\mathbb{N}_0$ is the set of all nonnegative integers. The notation $\mathbb{N}$ is reserved for the set of all positive integers. Alex and Beth are playing the following game. ...
1
vote
0answers
24 views

Expectation of a continuous function

Can someone help with the following? I have a continuous function $g: A_i \times A_{-i} \to \mathbb{R}^k$, and a probability measure $\mu \in \Delta(A_{-i})$. We can let $A_i=\mathbb{R}^n$ and ...
0
votes
0answers
56 views

Is this a game theory problem or optimization problem?

Consider a problem that looks for a $x$ that can make the following problem into some equilibrium state (similar to an equilibrium solution to a min-max problem in game theory) $$ \max_x f(x)$$ $$ ...
-6
votes
0answers
42 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 ...
0
votes
1answer
14 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
38 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 ...
0
votes
0answers
43 views

Math Extended Essay Topics [closed]

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 ...
1
vote
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
votes
1answer
49 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
vote
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 ...
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 ...
1
vote
1answer
34 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 ...
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
vote
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
49 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
vote
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 ...
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
32 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
103 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
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 ...
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 ...
0
votes
1answer
45 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 ...
-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
votes
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
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} < ...
0
votes
1answer
30 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, ...
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
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 ...
0
votes
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 ...
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 ...
0
votes
0answers
35 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
134 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
votes
0answers
14 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
38 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
vote
1answer
66 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
123 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
40 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
votes
2answers
43 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
135 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
211 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
votes
0answers
34 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
37 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
vote
0answers
24 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
101 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
51 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
173 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
44 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
votes
1answer
29 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 ...