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].

learn more… | top users | synonyms

2
votes
1answer
146 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
254 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
37 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
42 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
25 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
votes
4answers
179 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
116 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
405 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
56 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
75 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
65 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
votes
0answers
30 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
98 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
62 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
89 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
130 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
votes
0answers
50 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 ...
1
vote
2answers
68 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
47 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 ...
-1
votes
1answer
83 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
votes
0answers
42 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 ...
8
votes
1answer
158 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 ...
1
vote
1answer
54 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
52 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
votes
1answer
79 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 ...
3
votes
1answer
188 views

Subgame perfect Nash equilibrium & perfect Bayesian Nash equilibrium - Game theory

For a week or so I have been struggling with the topics around the concept of subgame perfect Nash equilibrium (SPNE) and the perfect Bayesian Nash equilibrium (BNE). Namely: Is it possible to apply ...
2
votes
1answer
86 views

move a cuboid from start to destination

Consider the field with infinitely many boxes, "S" means start, "D" destination, and I already found a way to move a $1\times 2\times 4$-cuboid (as you can see on the right at this picture) from the ...
0
votes
1answer
191 views

Gambling to pay off debt?

Someone told me something interesting today. They said they were going to take their bonus check from work, to the casino because they have "better odds" of paying off more debt then if they would ...
0
votes
0answers
29 views

A minimum settlement for a bargaining problem

Question: Alpha and Beta are 2 companies. Now Alpha thinks that Beta has violated Alpha's trademark. Beta denies that. Now, Alpha is threatening to go to the court and claim 5,000,000 EUR from Beta ...
1
vote
1answer
85 views

Brouwer's fixed point continuous function

Can anyone point me out the continuous functions without brouwer fixed point's for the following sets $$A = \{x \in \mathbb{R}^2 | x_1,x_2 \geq 0 \text{ and }x_1^2+x_2^2 = 1 \}$$ $$B = \{x \in ...
0
votes
1answer
66 views

Game theory question- no idea how to proceed

A monopolist sells two products, X and Y . There are three consumers with asymmetric preferences. Each consumer buys either one unit of a product or does not buy the product at all. The per-unit ...
0
votes
2answers
61 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 ...
1
vote
1answer
26 views

Algorithms for computing Nash equilibria

Excuse me, since I am modeling a situation into a nonzero-sum n-player non-cooperative game. I wonder if there is any algorithm for computing its Nash equilibria?
0
votes
1answer
104 views

Game theory question- boxes

There are two players 1 and 2, and the game begins with player 1 selecting one of the boxes marked 1 to 16. Following such a selection, the selected box, as well as all boxes in the square of which ...
1
vote
1answer
40 views

How much is it worth to participate in a second price auction?

You have a valuation for an object (say $v_a$), which you don't know yet but you know is distributed U[0,1]. You will be competing in a second price auction against a completely identical guy as you, ...
0
votes
1answer
155 views

What is a two person constant sum game?

I read that a two-person constant-sum game is a two-player game in which, for any choice of both players strategies, the row player's reward and the column player's reward add up to a constant value ...
1
vote
3answers
114 views

Looking for the function of x for a line that approaches, but never reaches 100

I'm looking for the function of x for a line that intersects at (0,0) and (100,80), and as x goes off into infinity, the line approaches, but never touches 100. See image attached. I am writing a ...
1
vote
1answer
92 views

A proof related to diameter of a simplex S

Question: Prove that the diameter $\mathcal p(S)$ of a simplex $\mathcal S$ equals the greatest Eucledian distance between two vectors in the simplex. My opinion: We all know what every vector in the ...
0
votes
1answer
47 views

Mixed strategy Nash Equilibrium

How do I solve this problem by using mixed strategy Nash equilibrium? \begin{pmatrix} (2,0)& (1,1)&(4,2)\\ (3,4)&(1,2)&(2,3)\\ (1,3)&(0,2)&(3,0) \end{pmatrix} I tried to ...
2
votes
0answers
129 views

Cournot competition: profit maximizer vs. market share maximizer

Today during an informal conversation with an established business researcher, I learned such a fact: In the classical Cournot competition model, if one player is a profit-maximizer, the other ...
5
votes
2answers
188 views

Do you need true randomness to beat the two-envelope game?

A well-known (non-)paradox in probability involves a two-envelope game played between two players, $A$ and $B$: $A$ selects two distinct (real) numbers, $x$ and $y$, writing each one down on a card ...
1
vote
1answer
43 views

Probability of number of drawing cards in a scenario being equal to that in another scenario

I came across the following question in a book:- $Q.$ Cards are drawn one by one at random from a well shuffled pack of $52$ cards. $(a)$Find the probability that exactly $n$ cards are drawn before ...
2
votes
0answers
96 views

Finding the core of a coalition game

I need to find the core of a 3-player coalition game graphically, given that $v(\phi)=0$, $v(1) = 9, v(2)=8, v(3) = 9, v({1,2}) = 14, v({1,3})=15, v({2,3}) = 13, v({1,2,3}) = 21$ So I'm following the ...
8
votes
1answer
161 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 ...
0
votes
0answers
29 views

Unfair coin tossing game,target,optimal fixed investment,

Suppose the player has capital 1\$. He chooses a number $f\in[0,1]$.He tosses an unfair coin repeatedly, which wins for him, with probability $p$, a gain $q\times f \times$ current capital \$,where ...
0
votes
0answers
47 views

Finding the expected revenue of a first price auction

I'm currently trying to solve for the expected revenue of a first price auction involving n players who draw their values v independently from F with support $[\underline{v}, \bar{v} ]$ and positive ...
0
votes
1answer
44 views

Example of a matrix which is copositive plus but not PSD.

This came up in our game theory course. While doing the Lemke's algorithm for solving LP, it was said that the process terminates when the matrix $M$ is copositive plus. Now copositive plus has a ...
1
vote
1answer
52 views

game theory question

For a non-cooperative bimatrix game the feasible set is $$\{(u,v)=(\mathbf{p}^TA \mathbf{q},\mathbf{p}^TB \mathbf{q}):p \in X^*, q \in Y^*\}$$ graph the non-cooperative feasible set for the Battle ...
1
vote
0answers
45 views

Forming a differential equation from game

I was wondering if someone could help me form a differential equation from the following game: A population consists of two types of diets, fish and veg. People play a with every other person and the ...
1
vote
1answer
43 views

show no equilibrium pairs exist in a non cooperative game using pay-off set?

I am trying to understand the following exersice from the solutions of my professor and I really don't understand what she is doing. The exersice is the following: Suppose the matrix below is a pay ...