Tagged Questions

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).

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0
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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
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1answer
225 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
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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
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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
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2answers
355 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
541 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
459 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
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1answer
276 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
600 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
371 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
179 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
481 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
398 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
172 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
160 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
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vote
3answers
74 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
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2answers
784 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
94 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
610 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
413 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
252 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
164 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
487 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 ...
2
votes
1answer
1k views

Symmetric nash equilibrium

I was reading this paper on position auctions for web ads. Basically, there are N slots each with an expected number of clicks (in a particular time period) $x$. Each agent makes a bid $B_i$ of how ...
5
votes
8answers
8k views

Deal or no deal: does one switch (to avoid a goat)?/ Should deal or no deal be 10 minutes shorter?

Okay so this question reminded me of one my brother asked me a while back about the hit day-time novelty-worn-off-now snoozathon Deal or no deal. For the uninitiated: In playing deal or no deal, the ...
19
votes
3answers
8k views

How is prisoner's dilemma different from chicken?

Chicken is a famous game where two people drive on a collision course straight towards each other. Whoever swerves is considered a 'chicken' and loses, but if nobody swerves, they will both crash. So ...