The study of competitive and non-competitive games, equilibrium concepts such as Nash equilibrium, and related subjects. Combinatorial games such as Nim are under (combinatorial-game-theory), and algorithmic aspects (e.g. auctions) are under (algorithmic-game-theory).

learn more… | top users | synonyms

2
votes
2answers
231 views

Mixed strategy nash equilibria in from $2\times N$ bimatrix form

I'm looking for a way of finding (manually!) mixed strategy Nash equilibria in a $2\times N$ game. Calling player 1 the player with two strategies and player 2 the one with $N$ strategies, I've ...
2
votes
1answer
149 views

Cournot game and Bertrand game: Are they classes of game?

Can we use the term "Cournot Game" to describe a competition with output quantity in general? Or, does "Cournot Game" only refer to the game studied by Cournot? For example, if we study a dynamic ...
16
votes
4answers
2k views

Is chess Turing-complete?

Is there a set of rules that translates any program into a configuration of finite pieces on an infinite board, such that if black and white plays only legal moves, the game ends in finite time iff ...
0
votes
1answer
833 views

Number of pure strategies for each player in a simple game

I've just started following a game theory course. I'm still getting used to the concepts so I hope I can get some comment on my thoughts. This is a homework exercise. Consider a four square board. ...
0
votes
2answers
115 views

Does selecting more boxes initially change the math of “Deal or no Deal”?

Apologies if this seems to duplicate questions 835 and 886, but I think it's a different question... In Deal or No Deal the contestant selects one of 26 boxes and then chooses boxes in groups of 6, ...
0
votes
1answer
229 views

Apply game theory/Nash equilibrium in computer security scenario

I want to apply the game theory to a scenario in security . where two ppl the optimal outcome of a game is one where no player has an incentive to deviate from his or her chosen strategy after ...
1
vote
1answer
145 views

Can this problem be approached with Game Theory?

Hallo all, I would like some insight on this one: There are two players A and B each having a countable set of naturals lets say Sa and Sb. Initially Sa has cardinality n and Sb has cardinality 0 ...
1
vote
1answer
175 views

Term for a fully connected balanced graph (Rock paper scissor)

Is there a mathematical, graph theory, game theory term for a graph that is fully connected and balanced evenly with each other node. I'm thinking in situations like Rock paper scissors where each ...
1
vote
1answer
118 views

Reducing an infinitely large matrix to a finite matrix using domination

I'd very much appreciate it if anyone with any familiarity of game theory could help out a newbie. I came across the following problem doing homework in an introductory game theory course: ...
7
votes
3answers
3k views

Secretary problem - why is the optimal solution optimal?

I have read about this problem: http://en.wikipedia.org/wiki/Secretary_problem But I want to see how it is proven that the "optimal" solution is indeed optimal. I understand how to prove that if the ...
15
votes
7answers
1k views

Game theory textbooks/lectures/etc

I looking for good books/lecture notes/etc to learn game theory. I do not fear the math, so I'm not looking for a "non-mathematical intro" or something like that. Any suggestions are welcome. Just put ...
1
vote
1answer
92 views

Nonhedonic coalitional game vs. hedonic coalitional game

What is the difference between nonhedonic and hedonic coalitional games?
7
votes
5answers
417 views

Good non-mathematician book on Game Theory

I'm looking for a good book on Game Theory. I run a software company and from the little I've heard about Game Theory, it seems interesting and potentially useful. I've looked on Amazon.com but ...
2
votes
2answers
636 views

How to calculate perceived value?

Is there a known formula to calculate perceived value? If I am auctioning some popular product that is worth $100 (shelf price), how much would people bid if they: Have a 1 in ...
0
votes
1answer
47 views

Standardize heuristic values

I'm currently writing a reversi AI. What it does is, it looks a few moves ahead and then evaluates the boards and gives them scores, depending on how good it is. I use a few methods for evaluating ...
2
votes
1answer
226 views

Nash equilibrium and common knowledge

If NE is a CK? It seems that yes since given all information about payoffs/strategies players can derive NE based on the procedures similar to that of in the common knowledge, but I'm not sure.
8
votes
1answer
343 views

Common knowledge as a fixed point

I read on a wikipedia page that from the modal logic formalization CK can be formulated as a fixed point. If it also holds for the set theory formalization? If it does, where I can find about it? ...
4
votes
3answers
362 views

Cooperative Game Theory specialized forum

I am looking for research-focused Game Theory forum, especially in Cooperative Game Theory. As it sometimes happen google provides links on either conferences (as opposed to online forums) or forums ...
2
votes
2answers
360 views

calculate dominant mixed strategy in two person game w/ finite strategies

For a two person game, player one has strategies A,B,C. Inspection reveals strategy B is strictly dominated by some mixture between A and C. How does one calculate the probabilities assigned to A ...
3
votes
1answer
555 views

Game about placing pennies on table

This problem is from The Art and Craft of problem solving book: Consider the following two player game. Each player takes turns placing a penny on the surface of a rectangular table. No penny can ...
18
votes
1answer
1k views

Number of moves to solve a flood-it/sock-dye game

[ Question based on the sock dye game ] [ Update: It appears that this game is better known as "Flood it" and is NP-hard. Also, "the number of moves required to flood the whole board is $\Omega(n)$ ...
4
votes
1answer
231 views

Meaning of a partial derivative here?

I am given a 'tariff' function for two countries, $i=1, 2$. Both players can select a tariff between 0 and 100. If player $i$ selects $x_i$ and player $j$ selects $x_j$, country $i$ gets a payoff of ...
5
votes
1answer
473 views

Finding Nash equilibrium aka finding where lines intersect

I am tagging this as multivariable calculus because it potentially involves taking partial derivatives. I am working on some mathematical treatment for Cournot duopoly models (not homework, just ...
5
votes
1answer
287 views

Algebraically finding a Nash equilibrium

Here's the problem that relates to a whole class of problems to which I am trying to figure out a general solution. Given two players 1 and 2 who can select a number from the interval $[0, 1]$, ...
3
votes
1answer
608 views

Set of rationalizable strategies

Consider a guessing game with ten players, numbered 1 through 10. Simultaneously and independently, the players select integers between 0 and 10. Thus player i's strategy space is $\mathbf{S}_i$ $=$ ...
9
votes
3answers
375 views

Is there experimental evidence that people ever play mixed Nash equilibrium in real games?

Have any studies been done that demonstrate people (not game theorists) actually using mixed Nash equilibrium as their strategy in a game?
1
vote
1answer
182 views

Nash equilibrium for 2 players' game

Consider a game with two players P1 and P2. For P1 the set of strategies is $x_1,...,x_m$ and $y_1,...,y_n$ for P2, gains are $f_1(x_i,y_j)$ for P1 and $f_2(x_i,y_j)$ for P2. Define mixed strategies ...
1
vote
1answer
204 views

Optimal strategy and equilibrium

Consider the following 2-players game: the set of actions for the player 1 (P1) is $U_1$, for the player 2 (P2) is $U_2$. Utility functions are $g_1(u_1,u_2)$ and $g_2(u_1,u_2)$. First, P1 decide ...
3
votes
2answers
498 views

Finding best response function with probabilities (BR) given a normal-matrix representation of the game

We are given players 1, 2 and their respective strategies (U, M, D for player 1, L, C, R for player 2) and the corresponding pay-offs through the following table: $\begin{matrix} 1|2 & L & C ...
2
votes
3answers
402 views

Game with a coin in the hand

The game is the following: player1 is hiding the coin in his hand and the player2 has to guess where is the coin. If he guesses that it is in the right hand of the player1, he obtains €2 (player1 ...
1
vote
0answers
173 views

Extension of lady and monster

A famous problem: a lady is in the center of the circle lake, the monster is on the boundary of the lake. The speed of the monster is $v_m$, of swimming lady - $v_l$. The goal of the lady is to come ...
13
votes
5answers
1k views

A lady and a monster

A famous problem: a lady is in the center of the circular lake and a monster is on the boundary of the lake. The speed of the monster is $v_m$, and the speed of the swimming lady is $v_l$. The goal of ...
0
votes
3answers
161 views

Is it possible to collude in a perfect information game?

Is it possible to collude in a perfect information game? Exercise 10-7 from book "Algorithms And Networking For Computer Games" - Jouni Smed, Harri Hakonen, p 225
1
vote
3answers
75 views

Payoffs question

Suppose players can pay 1 unit of payoff to pick what kind of person they meet (ie. football fan or opera fan). How do I calculate the proportion of football fans in the long run?
4
votes
2answers
2k views

Picking a number nearest two thirds the average

I am interested in the following game for $n$ players: Each of the $n$ players chooses a random integer from the interval [0,100] and the average of these numbers (call it $a$) is computed. If we ...
1
vote
2answers
257 views

Game on the tree, cutting branch

We have a forest of rooted trees. Two players makes alternating moves according to the following rule: one move is to cut vertex and all its children. Player which makes last move (no vertices remain) ...
1
vote
1answer
81 views

$N\setminus S$ is not $\beta$-effective for $A\setminus B$, and $S$ is not $\beta$-effective for $B$

Given a social choice function $F$, a subset $B\subset A$ of the candidates and a coalition $S\subset N$ of the voters, $\beta$-effectiveness of $S$ for $B$ is equivalent to $N\setminus S$ not being ...
7
votes
2answers
2k views

Difference between Minimax theorem and Nash Equilibrium existence

Von Neumann's Minimax theorem (quoted from Wikipedia): For every two-person, zero-sum game with finite strategies, there exists a value V and a mixed strategy for each player, such that (a) Given ...
1
vote
1answer
360 views

game theory hw. von Neumann-Morgenstern's expected utility theory

Tom prefers A over B and B over C. Also, Tom is indifferent between a lottery in which he gets C with probability p and A with probability 1-p and a lottery in which he gets B with a probability p and ...
5
votes
2answers
792 views

game theory models of bridge

Does anyone know if there exists any small-scale game-theoretical models of the game of contract bridge, similar to the many simplified versions of poker that have been analysed?
1
vote
0answers
116 views

Question on social choice functions

We showed in class that every strongly, exactly consistent s.c.f is strongly firm (I don't know if this is the right translation - we defined strong firmness as the equivalence of $*,\alpha,\beta$ ...
3
votes
1answer
95 views

Do the positions of the initial dots affect the game sprouts?

The Wikipedia article on sprouts, seems to suggest that it does not, although I can't see how to prove it.
12
votes
3answers
613 views

Best Strategy for a die game

You are allowed to roll a die up to six times. Anytime you stop, you get the dollar amount of the face value of your last roll. Question: What is the best strategy? According to my calculation, for ...
3
votes
2answers
421 views

Computing Bayesian Nash Equilibrium

I recently made a model to solve a conflict problem in sports. The model is based on Bayesian Games: a complete definition can be found here. The thing is that I am now looking to compute the ...
4
votes
2answers
253 views

Newspaper competition

A newspaper launches a competition. It said that readers should submit one number between 1 and 1000. A £2000 prize would be awarded to the person that got the closest to 2/3 of the mean of all the ...
14
votes
5answers
1k views

Probability of dice sum just greater than 100

Can someone please guide me to a way by which I can solve the following problem. There is a die and 2 players. Rolling stops as soon as some exceeds 100(not including 100 itself). Hence you have the ...
5
votes
1answer
229 views

Measure of value of resources in a competitive game

Let we have a competitive survival game in which a player has choice between different resources to earn. The question here is which resource should he prefer to maximize the chance of survival. I ...
2
votes
2answers
166 views

how do i theoretically find the expected length of the following game?

Given the following game, there is a hider and a seeker, each game consists of the hider randomly selecting one of two places to hide that is A with probability p and B with 1 - p, and the seeker ...
5
votes
2answers
495 views

Zero-Sum Game Theory

Me and a team of programmers are programming a robot to play a game in a competition. We did not create the hardware, and all teams will use the same type of robot. GAME DESCRIPTION The game has ...
10
votes
5answers
1k views

What is the probability of getting yahtzee?

What is the probability of getting yahtzee using N dices with X sides in Y throws in a single round? Which side of the dice one gets yahtzee with doesn't matter (e.g. it doesn't matter if it is ones ...