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Questions tagged [gt.game-theory]

Theoretical question related to Computer Science and Game Theory

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Sequential Two-player Game related to "Bandit Detection"

Alice and Bob play a game over $n$ rounds. At each round, Alice picks a number $x_t \in [0,1]$ and Bob simultaneously chooses whether to "peek" at the number $x_t$ which is represented by a ...
Amaryllis 's user avatar
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0 answers
62 views

Undecidability of games with limited hidden state

Surprisingly, approximate win probability for one-player games with randomness and 3 bits of hidden state (in addition to non-hidden state; rational transition probabilities) is uncomputable. Question:...
Dmytro Taranovsky's user avatar
1 vote
0 answers
87 views

Do game semantics for logic have Curry-Howard-like correspondence with game semantics for programming languages?

Both for logic and PLs do have notion of game semantics. Both are defined by two-player dialogue game, but players are different. In first case it is game between Verifyer and Falsifyer and in second ...
uhbif19's user avatar
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4 votes
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Which variant of the ellipsoid method was used for the Santa Claus problem?

As one of the steps in the article The Santa Claus problem (Bansal and Sviridenko, 2006) the following linear problem was considered (at the end of the second page, as the dual): \begin{align*} &\...
eden hartman's user avatar
2 votes
1 answer
120 views

Approximating the utilitarian welfare minus a constant

Assume we have $n$ agents and $m$ indivisible goods that need to be allocated among the agents such that their sum of utilities is maximized. Denote the set of allocations by $\mathcal{A}$ and the ...
eden hartman's user avatar
3 votes
1 answer
213 views

Which 1-player games are EXPTIME-complete? Also, are there any known games that are EXPSPACE-complete?

I noticed a lot of 1-player games have been shown to be NP-Hard, like Pac-Man, The World's Hardest Game, Tetris, etc. For PSPACE-Complete, I noticed that Wikipedia listed these 1-player games: It is ...
edit's user avatar
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1 answer
225 views

What Complexity Class is this? Is this already known?

Let's call this the Path Game. For this example, lets imagine a 16x16 grid: Some of the squares in this grid are "deadly." If you step on it, you must restart and try to go over again. We ...
Bapcap's user avatar
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2 votes
2 answers
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Trying to understand the intuition behind Yao's Minimax Principle

$\newcommand{\A}{\mathcal{A}}\newcommand{\I}{\mathcal{I}}\newcommand{\E}{\mathbb{E}}\newcommand{\C}[2]{C(I_{#1},A_{#2})}$The question that I am wondering in this post is if there is any intuition to ...
DenLilleMand's user avatar
3 votes
0 answers
51 views

Online assignment lower bound results

I am reading the following paper which presents a $(1-\epsilon)$-competitive online algorithm for the MaxMin (similar to the makespan) problem, defined as follows: a set of requests are arriving in an ...
Doc Stories's user avatar
1 vote
1 answer
174 views

Can theoretical computer science be combined with mechanism and information design and applications in financial markets

I am considering to take a position as a phd student in a computer science department. I am a mathematician with a master degree in finance and my research interests are mainly focused in game theory. ...
Phd student's user avatar
-1 votes
1 answer
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Algorithm for finding traffic equilibrium

I watched a youtube video about a certain interesting property of springs and road networks. It made me think: if we represent a network of roads as a graph where edges are roads described by a ...
Ace shinigami's user avatar
9 votes
0 answers
160 views

"Looking for help understanding a proof by Gossner (1998)."

Although there is no use of cryptographic protocols in Gossner (1998), the author refers to protocols of communication and he has a main result that I struggle to prove, because he does not use a ...
Nav89's user avatar
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1 vote
0 answers
74 views

Algorithmic game theory with decentralized mechanism of exchanging information

An interesting topic that I want to understand has to do with the decentralized exchange of information among a network of agents, however there is not a specific theory to make such a mathematical ...
Nav89's user avatar
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1 vote
1 answer
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How do we evalute the difference between a predicted value $\hat{v}$ and the true nash equlibrium value $v$

Consider a bimatrix game problem with matrix $A$ and $B$. The definition of the value $v = [v_1, v_2]$ of the Nash equilibrium $(x, y)$ are as follows, $$v_1 = x^TAy,$$ $$v_2 = x^TBy.$$ The situation ...
dawen's user avatar
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135 views

Is this "choose and switch" game just 2SAT in disguise?

Suppose you have $n$ switches lined up on a wall, labeled left to right from $1$ to $n$. The switches are either on or off. You get a list of $q$ choices that must be made. A choice consist of two ...
Marc Grec's user avatar
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3 votes
1 answer
193 views

Algorithm to find $n$ player nash equilibrium

This is the question asked 10 years before. Most of the algorithm and software mentioned are out of date. I am wondering is there new approchs for this problem in the last 10 years? The game dealing ...
dawen's user avatar
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1 answer
171 views

Application of Yao's Minmax Principle for Adaptive Randomized Algorithms

Reference Request: I am interested in references where Yao's Minimax Principle is applied for adaptive randomized algorithms if any. More generally, I am interested in minimax lower bound results for ...
Soumya Basu's user avatar
10 votes
0 answers
192 views

Is 4-in-a-row PSPACE-complete?

This paper by Laurens Kuiper shows that axis-parallel k-in-a-row is PSPACE-complete in complexity for k ≥ 5, but leaves the question open for k = 4. Has there been any research progress on this ...
user76284's user avatar
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11 votes
1 answer
608 views

The theoretical complexity of Go - The state of the art

What are the latest advances in theoretical complexity of Go? I know some early works about the complexity of Go: "Go is polynomial-space hard" proved that Go is PSPACE-hard. "Ladders are PSPACE-...
Blanco's user avatar
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13 votes
3 answers
1k views

A game on several graphs

Consider the following game on a directed weighted graph $G$ with a chip at some node. All nodes of $G$ are marked by A or B. There are two players Alice and Bob. The goal of Alice (Bob) is to ...
Alexey Milovanov's user avatar
8 votes
1 answer
367 views

Winning strategy in the game of triplets

The game of triplets is defined by a finite set of elements $X$, and a finite multi-set $T$ containing triplets of elements. Two players take turns picking elements from $X$ until all elements are ...
Erel Segal-Halevi's user avatar
10 votes
1 answer
505 views

What is the complexity of this game?

This is a generalization of my previous question. Let $M$ be a polynomial-time deterministic machine that can ask questions to some oracle $A$. Initially $A$ is empty but this is can be changed after ...
Alexey Milovanov's user avatar
5 votes
0 answers
774 views

Games on Turing machines that are AH-hard

I'm interested in proving that finding optimal play in a particular two-player game is harder than the arithmetic hierarchy. I suspect this to be true, because even carrying out a deterministic end-...
Stella Biderman's user avatar
10 votes
1 answer
411 views

Is this game EXPSPACE-complete?

Let $M$ be a polynomial-time deterministic machine that can ask questions to some oracle $A$. Initially $A$ is empty but this is can be changed after a game that will be described below. Let $x$ be ...
Alexey Milovanov's user avatar
1 vote
0 answers
87 views

Nim-game variant - weird ending condition

the game is structured like this: two players the players alternate moves 4 heaps $h_1,h_2,h_3,h_4$ with sizes $n_1,n_2,n_3,n_4$ at each move, the player can either remove one or two elements from ...
Simone Procaccia's user avatar
10 votes
1 answer
274 views

Equilibrium in a Halting Game

Consider the following 2-player game: Nature randomly picks a program Each player plays a number in [0, infinity] inclusive in response to nature's move Take the minimum of the players’ numbers, and ...
John Wentworth's user avatar
3 votes
0 answers
54 views

Correlated random models of game trees

Say we want to understand a game tree search algorithm in a theoretical context. Thus, we want a parameterized family of problem instances, separate from actual games such as a chess, so that ...
Geoffrey Irving's user avatar
3 votes
2 answers
727 views

Can generalized twenty questions be solved by a greedy algorithm?

The game of twenty questions can be generalized in the following way. Let $\Omega$ be a finite set and $\mathcal Q$ a collection of subsets of $\Omega$, called the questions. A point $x\in\Omega$ is ...
Jack M's user avatar
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1 vote
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Circuit games in extensive form with imperfect information

Consider $l,m,n,N \in \mathbb{N}$ and circuits $C: \{0,1\}^{l+m} \rightarrow \{0,1\}^l$, $D: \{0,1\}^{l+n} \rightarrow \{0,1\}^l$. Consider the following zero-sum two-layer extensive-form game with ...
Vanessa's user avatar
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2 votes
0 answers
201 views

Two-player zero-sum games in extensive form represented as directed acyclic graphs

The following is a way to represent two-player zero-sum games in extensive form. Consider a directed acyclic graph $G$ where each non-terminal vertex is one of 3 types: player 1 vertex, player 2 ...
Vanessa's user avatar
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2 votes
1 answer
175 views

Maximum stable matching/allocation

I checked some papers on two-side stable allocation/matching (marriage, worker/company, doctor/hospital), but has not found any literature on the following problem. Can someone point out if I missed ...
user2789928's user avatar
1 vote
1 answer
181 views

The logic in derivation of virtual welfare

I am learning algorithmic game theory with the lecture notes posted by Tim Roughgarden. In lecture 5 it is proved that the problem of revenue (or profit) maximization in single-parameter environment ...
xyguo's user avatar
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6 votes
1 answer
203 views

On bandwidth of graphs

I am trying to find references on algorithms for graphs of bounded bandwidth, in the same way as it is done with treewidth for instance. I could only find research related to computing the bandwidth, ...
Denis's user avatar
  • 8,903
1 vote
1 answer
694 views

Minmax vs Maxmin

I'm reading this paper about building a combat simulator for 8 unit vs 8 unit mini combats in StarCraft: Brood War. The basic idea is to build a search tree simulating these small combats in order to ...
xdhmoore's user avatar
  • 113
-4 votes
1 answer
158 views

Understanding Prisoner's dilemma [closed]

Imagine two prisoners held in separate cells, interrogated simultaneously, and offered deals (lighter jail sentences) for betraying their fellow criminal. They can "cooperate" (with the other prisoner)...
Atinesh's user avatar
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16 votes
0 answers
541 views

Quantum Hardness of Finding Nash Equilibria

This question is inspired by the recent, beautiful work On the Cryptographic Hardness of Finding a Nash Equilibrium by Bitansky, Paneth, and Rosen. Their main result is that the existence of ...
Daniel Apon's user avatar
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7 votes
3 answers
2k views

What is the application of combinatorial game theory

I find Combinatorial Game Theory very interesting as my primary interest is mathematics. My question is why do Computer Scientists (who tend to have a more practical approach) study it as well? Are ...
Halbort's user avatar
  • 153
0 votes
0 answers
299 views

Finding an equivalent NP-complete instance for this game-theory problem

I apologize if this question is not a good fit for CSTheory. I'm a PhD student who has just started out and I'm working on a game-theory problem in one of my classes. Although my professor hasn't ...
Vivin Paliath's user avatar
4 votes
1 answer
200 views

Stackelberg solution to $n$-player Hotelling's game on a segment

Suppose that several agents need to place points (one per agent) on the interval $[0,1]$. An agent's goal is to maximize the volume of the Voronoi cell that contains his point. When $n$ agents must ...
Aryeh's user avatar
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5 votes
0 answers
207 views

Applications of Combinatorial Games in Computational Biology

I'm looking for general references in the literature about applications of games algorithmics in computational biology. Q1. What are the notable cases of computational-biology or bioinformatics ...
XORwell's user avatar
  • 650
2 votes
0 answers
103 views

What mathematical models can analyze and optimize such message passing system?

I look for a mathematical model that can accommodate, analyze and suggest optimizations for a system that can be humanly described as message passing black box programs to which where optimal message ...
DuckQueen's user avatar
  • 121
3 votes
1 answer
861 views

Is there a tool for finding Nash equilibria in parametric games?

There are a few tools, either online or offline, that could solve (find equilibrium) in a game explicitly given as a real-valued matrix. Such tools are Game Theory Explorer and Gambit. However, as ...
R B's user avatar
  • 9,458
14 votes
1 answer
252 views

Computationally bounded version of Nash equilibrium?

I'm wondering if there is a computationally bounded version of the Nash equilibrium concept, something along the following lines. Imagine some kind of two-player perfect information game which is ...
Timothy Chow's user avatar
  • 7,560
2 votes
1 answer
461 views

How to prove the existence of a pure Nash equilibrium?

I have a game as given by the table below. I would like to prove that the game has always at least one pure Nash equilibrium (NE). I used a computer program and in fact the game has a pure NE. So, I ...
Chiba's user avatar
  • 23
11 votes
3 answers
927 views

Implementation of surreal numbers for games

There is a very nice construction by Conway of surreal numbers. They are "numbers" that contain both real numbers and ordinals, are totally ordered, and have all the properties of a field (except they ...
Denis's user avatar
  • 8,903
-2 votes
1 answer
340 views

Iterated Prisoner's Dilemma Algorithms

While reading a post on Scott Aaronson's blog about Eigenmorality, I ran across the idea of the iterated prisoner's dilemma tournament. I've studied some TCS on my own, but had never really thought ...
user avatar
1 vote
1 answer
125 views

Generalized Secretary Optimization Problem

In the standard Secretary Problem, the goal is to hire the best secretary from a list of candidates. I've recently witnessed a failed hiring attempt for a needed position and it inspired a similar ...
bbejot's user avatar
  • 1,099
9 votes
1 answer
317 views

Secretary hiring game

This is an extension of the classical secretary problem. In the hiring game you have a set of candidates $\mathcal C=\{c_1,\ldots,c_N\}$, and order on how skilled each worker is. W.l.o.g, we assume ...
R B's user avatar
  • 9,458
32 votes
3 answers
2k views

Is this variation of TQBF still PSPACE-complete?

Deciding if a quantified boolean formula such as $\forall x_1 \exists x_2 \forall x_3\cdots \exists x_n \varphi(x_1, x_2,\ldots , x_n),$ always evaluates to true is a classical PSPACE-complete ...
JWM's user avatar
  • 752
6 votes
1 answer
1k views

Why is computing pure Nash equilibria NP-complete?

In this paper, it is claimed that computing pure-strategy Nash equilibria of games in standard normal form is NP-complete. This confuses me, because I do not understand why it is hard to guess the ...
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