# Questions tagged [game-theory]

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### JUSTICE & INJUSTICE — two 2-player finite games

There is a non-empty finite set $\ K,\$ say, of plates. Initially, there are $\ p_0(k)\$ stones on the $k$-th plate, where $\ p_0(k)\in\mathbb Z_{_{\ge0}}\$ for each $\ k\in K.$ So far, it is like ...
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### Two-player item picking game

Two players $A$ and $B$ play this game: There are $n$ items, where the $i$th item is of value $a_i$ to player $A$ and is of value $b_i$ to player $B$. Two players take turns picking items, and each ...
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### Can you escape from two lions in a closed arena?

You're at the center of a circular arena. A pair of lions are at the border, planning to catch you. One of them moves as fast as you, but the other moves slower than you. The three of you are confined ...
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### What is a good formalization of this classic math puzzle? [closed]

Here is a classic math olympiad problem (but this is NOT my question!): Each of the girls A and B tells the teacher a positive integer but neither of them knows the other's number. The teacher writes ...
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### Surprising applications of the theory of games?

I am currently studying the applications of games in quantum information theory and related fields and I am aware of its uses in places like model theory and set theory. So I was curious, what are ...
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Let $(X,d)$ be a compact ultrametric space. Hartig and de Vink considered the following ultrametric on the set $P(X)$ of probability on $X$: $$\hat d(\mu,\nu)=\inf\{r>0:\forall x\in X\;\;\mu(B_r(x))... • 4,525 1 vote 0 answers 107 views ### Game with Turing machines Introduction The following game is quite nice: Alice has, in secret, constructed a polynomial P \in \mathbb{Z}[x]. On day n=1,2,3,..., she secretly writes down P(n) on a piece of paper. Each day,... • 15.7k 0 votes 0 answers 111 views ### Game on a square grid (part II) Related to this question, where there the solution was unexpected for us. Let n,m be positive integers, n \le m \le n^2/2. The board is n \times n square grid. Phase 1: Two players, A,B make ... • 24.7k 1 vote 2 answers 269 views ### Do restricted Nim-like games have winning strategies? Considering a Nim-like game to be: There are three piles A,B,C, and the amount of their elements are |A|=2, |B|=5, |C|=6; There are 2 players. Each time a player can either take x (1\leq x \leq ... 3 votes 1 answer 272 views ### Game theory approach to Trans Europa The other day I was playing a game called Trans Europa (or Trans America) which is quite graph theoretic in flavour. The game takes place on a triangular lattice graph with certain distinguished ... • 5,030 -1 votes 1 answer 143 views ### Why do two potentials of a game only differ by a constant? [closed] Can someone explain to me the proof on page 7/20 of the original paper about potential games (https://www.cs.tau.ac.il/~mansour/sem-game-02-03/monderer-potential-96.pdf)? It is about why two ... • 101 28 votes 7 answers 6k views ### Why is game theory formulated in terms of equilibrium instead of winning strategies? Game theory, on the outset, seems to invite the questions, "what can I do to win" or "how do I beat my opponent?" So many people who are not familiar with game theory look to game ... • 479 8 votes 1 answer 227 views ### Name of a game : Remove two chips from a vertex or one chip from both ends of an edge Consider a finite graph \Gamma with a positive number n_v\geq 0 of chips stacked at each vertex v of \Gamma. Two players play in turn with moves consisting either of removing two chips from a ... • 17.6k 4 votes 1 answer 1k views ### Who wins this two player game of making squares? Two players take turns coloring edges on an n-by-n grid. Both players use the same color. Every time a player surrounds a square of the grid, they mark that square with their name and go again. ... 5 votes 1 answer 535 views ### Can we determine the game-theoretically best first move by White in chess without solving chess? In turn-based board games with high branching factor (such as chess) are there any arguments that could ascertain the ideal first move but not solve the entire game? I am asking because solving chess ... • 59 6 votes 1 answer 330 views ### Do random asymmetric games have more complicated strategies than random symmetric games? Let \Delta \subset \mathbb R^n be the locus of vectors whose entries are nonnegative and sum to 1. For M an n\times n matrix over \mathbb R, let x_M \in \Delta be the vector x that ... • 141k 1 vote 1 answer 281 views ### Is there an equilibrium for this non-zero-sum game? The game G(N,M) is played: N (N\geq 2) is the number of players, labeled 1~N. In the beginning they have a pot with some chips in it. Players move alternatively in the order from 1 to N.... • 2,601 5 votes 2 answers 287 views ### Is there a dominant strategy for this game? Alice and Bob have N_A and N_B warriors under their command, numbered 1~N_A and 1~N_B respectively. Alice has 1 fighting power at her disposal, and Bob has b (b\gt 0). Before the ... • 2,601 2 votes 0 answers 122 views ### Existence and uniqueness of solution of a nonlinear system I need a proof of the following result to calculate a Nash equilibrium in the Showcase Showdown game. For all n>1, the system of equations$$\left\{ \begin{aligned} (1+e^{x}(-1+x))^{n-2}&=\...
The fugitive is at the origin. They move at a speed of $1$. There's a guard at $(i,j)$ for all $i,j\in \mathbb{Z}$ except the origin. A guard's speed is $\frac{1}{100}$. The fugitive and the guards ...