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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Big Balloon Game

The problem In this game, you are given empty balloons one by one, and for each balloon you are to inflate it with air until you are satisfied. If it does not burst, you gain happiness points ...
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1answer
384 views

Nash equilibrium: Can I delete weakly dominated strategies in this case?

As far as I know, an equilibrium can involve a weakly dominated strategy, but cannot involve a strictly dominated strategy. Is there a general rule for when/if you can safely delete a weakly dominated ...
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1answer
24 views

On a possibility/impossibility of a certain twisted situation in a tournament

Recently I encountered the following puzzle: Consider a game for two players which can only result in a win of one of the players (no ties). Now $n$ players decided to play this game each with ...
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2answers
36 views

Prisoners' Dilema

I started to learn about game theory just now. I am confused about the prisoners' dilema, when 2 prisoners are given a choice whether to keep silent or rat out the other guy. From what I read, if one ...
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1answer
3k views

Number Game: 31 - Winning Strategy?

My Maths teacher taught us how to play a game called 31 on Friday. Not once did my Maths teacher lose. I want to know why. I'll explain the game... 31 is a game between two people. Let's say you've ...
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26 views

What is a good introductory book on Rational Choice Theory for a mathematician?

I'm interested in Rational Choice Theory as an approach to political science. Amongst other, related subjects, I'd like to know a thing or two about Arrow's impossibility theorem (and other aspects of ...
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374 views

Does introducing penalties for getting true/false questions incorrect result in higher skill penetration (less luck/variance)?

A student is asked to answer 50 true/false questions and he would get 35 right and 15 incorrect if he had to put his best guesses for each question down. Now, for each question he has a certain ...
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2answers
38 views

Useful analogy to interpret the notion of evolutionary stable strategy (ESS)

I am seeking a good analogy to understand the concept of evolutionary stable strategy (state) Let $\pi$ denote the fitness of a population, $\pi_{ij}$ is the fitness of strategy $i$ against strategy $...
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47 views

Can this game end in a draw?

We have this game: Clarifications: Pawns can move and take across sides. Pawns can't jump over other pieces when moving by two squares. "Forward" means from the middle of your side towards the ...
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1answer
650 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 ...
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2answers
59 views

Why players play nash equilibria?

I have to hold a talk about pure strategy normal form games. I will explain the Nash equilibrium. I think the definition is not that hard to understand as opposed to the idea why Nash received the ...
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1answer
25 views

In a game with imperfect information, can there be no subgame-perfect equilibrium?

In our Game Theory class, we learned that games can have multiple Nash equilibria and multiple subgame-perfect Nash equilibria ($SPNE$). In one of our example problems, however, we came across a game ...
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1answer
71 views

Strategy set in Tic-Tac-Toe [closed]

I read in a book that the cardinality of the strategy set of the first player in a game of Tic-Tac-Toe is approximately equal to $10^{126}$ but I cannot see how to arrive at this result. Disclaimer: ...
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32 views

Weighted War - Game of Mind and Probability

Weighted War is a game of bidding, where: Both players have cards valued from $1$ to $11$ in their hands There is a third pile of cards from $1$ to $11$ face down on the table and shuffled,...
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1answer
50 views

The Thirty-one Game: Winning Strategy for the First Player

I am going through UCLA's Game Theory, Part I. Below is an exercise on page 6: The Thirty-one Game. (Geoffrey Mott-Smith (1954)) From a deck of cards, take the Ace, 2,3,4,5, and 6 of each suit. ...
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2answers
44 views

Iterated Best Response to find Pure Nash Equilibria

The context of this question is Game Theory. I've been trying to apply a simplified (?) version of the Iterated Best Response (IBR) technique to find Pure Nash Equilibria (PNE) in games generated by ...
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1answer
27 views

How do you seed a “non-binary” tournament?

In a typical tournament, seeding is arranged to provide proportionate advantage to competitors based on their perceived relative ability. (Good teams get to play bad teams, bad teams have to play good ...
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1answer
623 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 ...
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1answer
436 views

Finding values such that the game is strictly determinable

Please help me to solve these two problems. Q1)Find the range of values of p and q that will make the entry (2,2) a saddle point of the game. $$ \begin{pmatrix} &player B\\ ...
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3answers
48 views

Decision theory references for advanced undergrad/early grad students?

I'm studying measure theoretic stochastic calculus, and I was hoping to pick up some knowledge of decision theory along the way. I'm very happy with Rudin or Karatzas in level of rigor, and I was ...
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4answers
2k views

Adding digits to make a number prime or composite

Players A and B alternate writing one digit to make a six-figure number. That means A writes digit $a$, B writes digit $b$, ... to make a number $\overline{abcdef}$. $a,b,c,d,e,f$ are distinct, $a\...
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1answer
42 views

Economics: Nash equilibrium

Two firms, firm 1 and 2 , are competing in prices in two differentiated product markets. The demand for respective firms products are given by the following demand functions; $$ q_1(p_1, p_2)=a-p_1+...
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1answer
59 views

Economics : Game-theory (Nash equilibrium)

This is a homework question, but resources online are exceedingly complicated, so I was hoping there was a fast, efficient way to solving following question. Question: Six students are going on a ...
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2answers
806 views

Nash equilibrium in first price auction

I'm trying to understand Exercise 18.2 from Martin J. Osborne and Ariel Rubinstein A Course in Game Theory about finding pure Nash equilibria in a first-price auction. There are $n$ players, named ...
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1answer
38 views

Prove that forcing A is superior to offering opponent a choice between A and B

In a game of Magic earlier today my opponent played Coercive Portal, which led to a situation in which he could either: force me to choose A; or allow me to choose A or B. I was surprised when my ...
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1answer
408 views

Game Theory - trying to find game name by description

My hobby AI research have led me to a thorethical game of particular design. As design is pretty simple, I'm almost sure that such game has well-known name and tons of research already done around it. ...
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1answer
65 views

Sharing and odd pizza

Here is a classical problem, which every mathematician will have seen at least onece in their life: Anne and Ben are sharing a pizza. The pizza is divided into an even number of pieces of unequal ...
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25answers
58k views

Splitting a sandwich and not feeling deceived

This is a problem that has haunted me for more than a decade. Not all the time - but from time to time, and always on windy or rainy days, it suddenly reappears in my mind, stares at me for half an ...
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1answer
30 views

Second price auction when number of items and bidders are the same

For an advertising slot bidding problem, let's say there are two slots and two bidders. If bidder A bids \$10 and bidder B bids \$8, bidder A will win the first slot and pays \$8. How about bidder B? ...
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1answer
36 views

Generalized First Price Auction or Generalized Second Price?

Sorry if I ask the same question again but in the other post I'm not able to edit my question because I wasn't using an account. By the way, the question: I'm running some tests to decide which type ...
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1answer
31 views

Game Theory: (basic) minmax linear function help

Background I am looking for some help with the reasoning here for a few things in my game theory book (my math expertise is quite weak - below is from the text): From Text Book \begin{eqnarray} min ...
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65 views

(Infinite hat)-guessing problem

$2$ men are playing a game: they are wearing countably infinitely many hats on their heads. The hats are either black or white with probability $\frac 12$. They see the other's man hats but cannot see ...
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1answer
35 views

simplex method tableau

If I have the matrix: x1 x2 s1 s2 s3 z 1 4 1 0 0 0 | 12 2 5 0 1 0 0 | 2 1 3 0 0 0 1 | 4 ---------------- -2 -1 0 0 0 1 | 0 Then, where x1 is the row of 1, 2, 1....x2 is the row of 4, 5, 4.......
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1answer
18 views

How to create a fair dynamic scoring system? [closed]

I am currently in the process of creating a game consisting of a fixed set of tasks of varying difficulty. Each player gets the same set of tasks to choose from and is awarded a certain number of ...
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1answer
2k 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 $k$ ...
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1answer
41 views

what is the fairest ratio of k to n for this game

Here is a description of a two player game with players plr1 and plr2 that is played on a n by n grid. Players take turns filling cells in the grid. plr1 goes first and wins by completing a straight (...
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1answer
821 views

I can't find the Nash equilibrium of this 3x2 game.

Sorry for my English, I am French but i couldn't find help on the French website (so I am here). I have a question about this two-player game: $$ \begin{array}{c|cc} & y_1 & y_2 \\ \hline ...
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1answer
619 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? ...
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2answers
29 views

Expected value and variance of a random variable, defined as the largest of $6$ randomly drawn numbers

Let each of the numbers from $1$ up to $49$ be written on a ball, and let all these balls be contained in a box. From this box, we randomly draw exactly $6$ numbers (without putting them back, so we ...
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0answers
37 views

Game theory: how is law of large number applied here?

This is a claim rephrased and lifted from from Herbert Gintis' book "Game Theory Evolving" Pg187 Consider an evolutionary game with $n$ pure strategies $i = \{1, \ldots, n\}$, and time periods $t ...
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1answer
34 views

A question about interval operation result in a game

A state is:$A_{q}=(A_{q}^{0},...,A_{q}^{E})$ where $A_{i}^{j}$ is interval, $q$ and $E$ are positive integer The initial state is $A_{m}=((0,1),\emptyset...,\emptyset)$ , $m>E$ Procedure: Every ...
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1answer
430 views

Odds of winning a two part drawing

There is a local drawing that involves being selected out of an estimated 6000 entries, and then correctly selecting 1 of 3 numbers in order to win. The numbers have are actually cards in a deck that ...
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2answers
386 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 ...
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0answers
14 views

About those equivalences in games, is it posible to…

I've heard about some games which can be reduced to TicTacToe, i guess in general there should be some simplier games and other complex games could be reduced to them. I've been wondering, is it ...
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14 views

Which type of games can I model this problem

I'm dealing with Smart grid retailers and I'm dealing with retailer's price decision , there are multiple retailers which sell electricity to users and they are competing in Price with capacity ...
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1k views

Splitting the dollar Nash equilibrium

I'm working on a game theory problem I can't seem to figure out. Players 1 and 2 are bargaining over how to split $\$10$. Each player names an amount $s_i$, between 0 and 10 for herself. These ...
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19 views

Compute the set of subgame perfect equilibria for this game (mixed strategies help)

In the above game there are 2 proper subgames (not including the whole game itself). I know there's 9 sub-game perfect equilibrium i have to figure out. I've managed to work out 4 of those, the ...
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1answer
58 views

How exactly is the St Petersburg Paradox giving bounded payoff in average-of-N-trials?

I understand why the expected value of the St Petersburg Paradox is algebraically infinite, but intuition tells me that in practice any given round of the game will not go on multiplying the pot for ...
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1answer
16 views

Incentive compatible revenue maximizing multiunit auction

The Vickrey-Clarke-Groves Auction is an example of incentive compatible (truthful reporting) multiunit auction, but it is only maximizing social utility, not the seller's utility. If my ...
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0answers
38 views

Optimal strategy in an idealized dating scenario

The question I have is in some ways a variation on the stable marriage problem adapted to the situation of dating. Suppose there are $n$ boys and $n$ girls, where every boy ranks the girls from $1$ ...