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

-1
votes
1answer
21 views

Good books to learn Combinatorial Game Theory?

I am currently doing my IB Diploma and we are supposed to make an extended essay on a subject of our choice- and i chose math. my research question is- "how to derive a perfect strategy to always win ...
3
votes
1answer
1k views

Mixed Strategy Nash Equilibrium of Rock Paper Scissors with 3 players?

It seems like most game theory tutorials focus on 2-player games and often algorithms for finding Nash equilibria break down with 3+ players. So here is a simple question: Is ...
1
vote
1answer
28 views

Game theory: solutions concepts if each player has different utility

Assuming, I have a network game (where the players are e.g. users in a network), how is it possible to model user-specific a-priori information (which results in different utility functions for each ...
0
votes
1answer
24 views

What is the quickest way to find Nash equilibria in two player bimatrix game?

Suppose the cost/penalty matrix of a game is given as: $$M = \begin{bmatrix} (-5,-5) & (0,0) \\ (0,0) & (-3,-3) \end{bmatrix}$$ Then the game as two equilibria $(u_{11},u_{21})$ and ...
1
vote
1answer
19 views

Question about usage of $\leq$ in definition of Nash equilibrium

Quick definition: Given $g$, a strategy N-tuple $u^* = (u_1^*,...,u^*_N)$ is said to be a Nash equilibrium if: $$J_i(u_i^*, u^*_{-i}) \leq J_i(u_i, u^*_{-i}), i \in N$$ where $J$ is ...
0
votes
0answers
31 views

In what ways would a course on convex optimization be useful in game theory?

From talking to several other people in the past, and referencing Quora, it seems that convex optimization is really a tiny subset of game theory in that it only models the behavior of one single ...
1
vote
1answer
21 views

Can someone please help me understand what a “player set” is in extensive form game

my text defines player set as: In N-player game $g$, each non-terminating node is partitioned into $N+1$ sets $g^0, ... g^N$. These are player sets. However it makes no attempt to identify ...
1
vote
1answer
24 views

Devising a method to arrive at a square only being able to move right and up

I was recently presented with a problem where I have a 10x10 grid and a marker that starts at position (1, 1). Two players are able to manipulate the marker by moving it as far right, or (exclusive) ...
0
votes
3answers
28 views

Reducing TIC-TAC TOE State Space by using Symmetry in Artificial Intelligence

Im learning Heuristics in AI.I see that for brute force search there are 9! states.But the textbook says that first 3 levels are reduced by symmetry.How does that work?
0
votes
1answer
11 views

A question in Osborne-Rubinstein A course in game theory,

I am having trouble with Rubinstein's electronic email game (proposition 83.1) in the textbook(first edition). My question: Line 7 starting from the "proof", "...player 2's expected payoff is at ...
4
votes
1answer
967 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 $k$ ...
3
votes
2answers
90 views

How many legal states of chess exists?

I have a fairly simple question. How many legal states of chess exists? "Legal" as in allowed by the rules and "state" as an unique configuration of the pieces. I'm not asking for the number of ...
1
vote
2answers
372 views

Dominant Strategy in Table Games

I have some basic background in game theory, but still there are exist simple questions that I cannot answer for sure. Whether Tic-Tac-Toe game has a dominant strategy? May be only one of the ...
0
votes
0answers
13 views

numerical solution for nash equillibrium

I have the following setup. $\pi_1=f_1(q,r)$ and $\pi_2=f_2(q,r)$ are the real valued payoff/profit functions of the two players. Player 1 gets to pick $q$ and player 2 gets to pick $r$. I also know ...
0
votes
0answers
32 views

Probabilities in this blackjack variation

Let's say I play blackjack (52 cards, figures count for 10, aces count for 1 or 11) and alone (no dealer). The cards I use for one particular game are always removed at the end of that game and won't ...
5
votes
5answers
357 views

How to formally model the “hesitation” in the hat-guessing puzzle?

Hua Luogeng (in Chinese, 华罗庚) took a hat-guessing puzzle as an illustration in a booklet focusing on mathematical induction. The following description is a literal translation from Chinese. ...
0
votes
0answers
39 views

“Composition” property in cooperative game theory?

I am trying to find a property which can help to analyse the composition of a cost/profit division and which allocation rules (e.g., Shapley value or nucleolus) would satisfy it. In short, the idea ...
6
votes
1answer
64 views

Tzaloa 2015 game problem (piles with $1,2,4 \dots 2^{19}$ coins each)

We have $20$ piles with $1,2,4,8\dots 2^{19}$ coins repectively and two players. In each turn a player must select five piles that have at least one coin and remove exactly one coin from each. Player ...
0
votes
1answer
39 views

Why does the 1st player in this subset take-away game always have a winning strategy?

This is a HW problem of mine that I cannot, for the life of me, figure out. There is a take-away game where there are a number of elements A, and the person that wins is that last person to remove a ...
1
vote
1answer
352 views

Optimal strategy for dominoes game

Here is the basic principle of the game I'm trying to find an optimal strategy for: Two players (say P and Q) are given a 2x3 grid and a domino. Then P chooses one way of positioning the domino on ...
0
votes
1answer
23 views

Nash equilibrium for two players game.

Consider a game for two players, say "Player A" and "Player B". The two sets of strategies are denoted by $A$ and $B$, available to the players. Consider a symmetric situation where the players have ...
0
votes
1answer
40 views

Find a Nash equilibrium solver

The solvers I know so far are designed only to allow payoffs as given numbers. But is there a solver allowing users to type payoffs as variables?
2
votes
0answers
72 views

Expected travel of random walk in arbitrary game with multiple payouts

As explained here, the average distance or 'travel' of a random walk with $N$ coin tosses approaches: $$\sqrt{\dfrac{2N}{\pi}}$$ What a beautiful result - who would've thought Pi was involved! ...
0
votes
1answer
23 views

When solving a system of equations for a game theory question, can the solutions be negative?

I have a homework question on solving a game matrix geometrically. $m =$ $\begin{bmatrix}1 & 11\\7 & 2\end{bmatrix}$ (after adding the constant $k$ to ensure it's a positive matrix) The ...
0
votes
0answers
72 views

Finding Nash equilibrium in game with random event at event tree?

I have posted a question about finding the NE of sequential game with imperfect information. It is lucky that the game can solve could be dealt with could be dealt with by a simpler argument. Here is ...
1
vote
1answer
434 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? ...
2
votes
0answers
55 views

A fashion victim puzzle

Consider $n \in \mathbb{N}$ fashion-sensitive kids, each wearing a T-shirt; for simplicity, kid $i \in \{1, \ldots, n\}$ initially wears shirt $i$. Tastes over the shirts are summarized in an $n ...
10
votes
2answers
550 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. ...
-3
votes
1answer
48 views

How to find the Nash equilibrium or subgame perfect equilibirum in a sequential game with imperfect information? [closed]

I have a problem with the sequential game with random event at the event tree. The model of the game as follows: Player = $\{A,B\}$ Pure strategy of player $A: A1, A2, A3$ For each strategy of ...
0
votes
1answer
541 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 ...
0
votes
1answer
55 views

English translation of von Neumann's “Zur Theorie der Gesellschaftsspiele”, 1928

Some colleagues and I are reading various classic papers. We would like to read von Neumann's "Zur Theorie der Gesellschaftsspiele", 1928, but do not read German. Do you know of an English ...
5
votes
2answers
135 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 ...
0
votes
1answer
27 views

IESDS and Nash Equilibrium - same solution [closed]

Applying the Iterated Elimination of Strictly Dominated Strategies (IESDS) to a game resulted with the same solution of the Nash Equilibrium. What does this imply? Actually that specific "quadrant" ...
3
votes
2answers
64 views

System of Differential Equations- Asymmetric First-Price Auction

I am working on a problem in my Auction Theory textbook regarding a two-player asymmetric first price auction. Assume the bidders are risk neutral. The problem statement is as follows: ...
6
votes
0answers
160 views

Cutting a Banach-Tarski Cake

I was reading a cake-cutting problem here (not really related, so I won't link to it), and for some reason, this variation occurred to me. I have no idea whether this problem is even well-formed: ...
0
votes
1answer
61 views

Game Theory - Contributing to a public good

I have attempted to answer the question but I think I am trying to answer it in a very difficult way as the algebra gets messy and confusing. If anyone could help me out it would be greatly ...
0
votes
1answer
61 views

Who's winning this coin drawing game?

There are 2 piles of coins, each containing 2010 pieces. Two players A and B play a game taking turns (A plays first). In each turn the player on play has to take 1 or more coins from 1 pile or ...
1
vote
1answer
47 views

What is the mixed strategy equilibrium bid, if any, for complete information auction games with minimum bid?

Consider the following complete-information, auction game. There are two players $i=1,2$. Each bids simultaneously a value $b_i\in[0,\infty)$. The payoff function is symmetric: $$ \pi_i ...
3
votes
1answer
58 views

A deadly game of two werewolves and two townsfolk

This question was closed due to lack of own effort shown. Because I like the game of werewolf (a.k.a. Mafia) and thought it was a nice idea to pose a simplified version of it as a game-theoretic ...
2
votes
1answer
70 views

How can I find the Nash equilibrium for this 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 ...
0
votes
1answer
65 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) $$ \max_x f(x)$$ $$ ...
2
votes
1answer
50 views

Mixed strategy problem - game theory

I have a basic doubt in a question of game theory. Assume that in a $2$ player game the mixed strategy profile $((a,b,0),(c,d,0))$ is a mixed strategy NE. Does the indifference condition in a mixed ...
1
vote
0answers
79 views

Putnam game theory question

There are $n\ge1$ boxes in a line where $n$ is an odd integer. Two players, Connor and Andrew, are playing a game. On a turn, you can place a stone in a box OR take a stone out of a box and place a ...
0
votes
0answers
18 views

super-additive, sub-additive, and shapely value limitations?

I am working on the coalition formation. Most of the scientist used concept of shapely value for distributing the utility among the members of coalition. Up to my understanding, shapely value is good ...
1
vote
0answers
31 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 ...
4
votes
1answer
53 views

Optimal Strategy Game of Communicating without Overlap

Today, I had a conversation which proceeded very poorly; indeed, I had this conversation with $n$ people, including myself, and everyone had something to say. Problem was that, for an unreasonably ...
0
votes
1answer
16 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
41 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 ...
8
votes
1answer
153 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 ...
7
votes
1answer
106 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 ...