Theory of dynamic processes with several competing actors that try to achieve some goal in a strategic way.

learn more… | top users | synonyms

3
votes
1answer
38 views

Evaluation functions of Minimax algorithm

Let's say we have the following relationship between $f_1$ and $f_2$: $$f_2(s) = \sqrt{1 + f_1(s)}$$ And $f_1$ returns a positive value. Why is it that minimax search using $f_2$ is guaranteed to ...
4
votes
2answers
92 views

Number of winning combination in Nim

I am studying game theory and I am wondering how many winning combinations are possible for Nim game? Suppose, stones = 500 and piles = 5. With these number, there are many initial game positions are ...
0
votes
1answer
22 views

Computing losing positions in modified Wythoff's game efficiently

Wythoff's game is as follows: there are two players $A$ and $B$ ( $A$ being the first player ) and there are $2$ piles of stones. When his turn a player can remove one or more stones from anyone pile ...
2
votes
1answer
68 views

Reccurrence for the game of pile of stones

I am trying to solve this question from Project Euler for past few days: Divisor game. The problem is as follows: Two players are playing a game. There are $k$ piles of stones. When it is his turn ...
3
votes
1answer
27 views

In Minimax, how should we handle draws?

A player playing the Minimax strategy should choose moves which minimise their maximum loss. What should happen when draws can happen? Should we class the draw as a win because we aren't losing? Or ...
3
votes
1answer
36 views

Winning strategy of Nim game when picking from multiple piles is allowed

I am studying with Game theory right now. In Nim game, in any turn, a player can move any number of stones from any one pile. I am wondering what might be the winning strategy of first player if in ...
3
votes
0answers
35 views

How are benchmarks created?

Computing equilibria in games and the complexity thereof is imho still quite a young field in which a lot of work still is to be done (especially the former). GAMUT (2004) is a very nice "suite of ...
1
vote
1answer
60 views

Metaheuristic for NP-complete problem without exact algorithms other than brute-force

Computing Pure Nash Equilibria (PNE) is a Game Theory related problem. Deciding if there exists PNE in a given game has been shown to be NP-Complete (Gottlob et al.). I want to design a metaheuristic ...
0
votes
0answers
50 views

A 9 token game of Nim tree construction

Trying to construct the full tree for a 9 game token of Nim and am slightly confused. I don't understand how two players, min and max, will make their pick. For example, max picks first and can only ...
3
votes
1answer
78 views

Complexity of solving LP with a non-linear growth in variables/constraints

It has been shown that any Linear Program (LP) can be solved in a polynomial number of steps. An example of such algorithm is the ellipsoid method. To solve a problem which has $k$ variables and ...
2
votes
0answers
40 views

What are the theoretical and practical contributions of Multiagent Systems to science?

Speaking about multiagent systems (MAS) is about as fuzzy as talking about artificial intelligence systems (AI). They are in essence the distributed counterpart of AI. While there are no so-called "...
2
votes
1answer
56 views

Induction proof of alpha-beta search

Is there a functional specification of alpha-beta search that makes it easy to prove by induction that the algorithm works? My first thought is that the algorithm introduces an $[\alpha,\beta]$ ...
1
vote
0answers
22 views

Voronoi game in discrete space

Here i want to discuss about Linear Voronoi game. The game consists of two players, and a finite set of users placed along a line. Each player has 2m facilities, where m>0 is a fixed integer. The ...
2
votes
1answer
59 views

that there would be no perfect strategy for poker

In my opinion, every imperfect information game where there is the possibility of bluffing lacks a perfect (or winning) strategy, for the simple reason that knowing your opponent's strategy will let ...
1
vote
0answers
39 views

Why is Game Theory used to explain implementations of 3GPP D2D communication?

My question is about D2D as it relates to 3GPP (release 13+, I believe). All I have read on the subject uses Game Theory as a mechanism to explain usage. Why would authors use Game Theory for ...
3
votes
1answer
87 views

Why isn't chess an impartial game?

In Combinatorial Game Theory, a major distinction is drawn between impartial games and partisan games. To be impartial, a game must satisfy these conditions: (1) The game is finite; i.e. there is a ...
0
votes
0answers
46 views

Is $AM = AM[2]$?

Any $k$ round AM can be reduced just two rounds whereby Arthus just does the $k$ coin tosses and passes on the information to Merlin. Merlin sees all the coin toss results and computes everything ...
2
votes
1answer
46 views

Adversarial Monte Carlo Tree Search Assymetry

Monte Carlo Tree Search with UCT is praised for it's assymetric tree growth, growing promising subtrees more than non-promising ones. But in a 2-player adversarial game, when a win at one node is a ...
1
vote
0answers
46 views

Stable matching of producers, consumers and objects

Has the following version of the stable matching problem been studied? There are $k$ types of objects. There are $n$ producers, each of whom can produce a single object of any type, and has a ...
-1
votes
1answer
32 views

Is it possible to make excluded search with for loop in Java? [closed]

I am trying to calculate all pure strategy Nash equilibrium in a mxn game. It requires to check all pure strategy pairs (m.n pairs). Suppose player 1 has m strategies. Algorithm should start with the ...
2
votes
1answer
465 views

How to implement the regret matching algorithm?

My question is the following: How to calculate the regret in practice? I am trying to implement the regret matching algorithm but I do not understand how to do it. First, I have $n$ players with ...
-1
votes
1answer
683 views

Where is the recursion, in the minimax-decision algorithm?

The below is from an article titled: Minimax: Recursive Implementation To be a recursive function, you need to call yourself. What part of this pseudo code is calling itself? How does depth-...
1
vote
1answer
79 views

How do I compute this non terminal positions evaluation, for tic-tac-toe?

Looking at this solution on page 3 but having trouble understanding the evaluation function specifically. For non terminal positions, we use a linear evaluation function defined as Eval (...
2
votes
1answer
230 views

Optimizing resource management game (similar to Farmville) [closed]

Given a fully deterministic single player resource management game with a pre-known finite number of turns and reasonably simple rules (eg, Farmville, if it were single player, deterministic, and ...
3
votes
2answers
188 views

Metagame Paradox: what is wrong with this explanation?

Today I've heard about fascinating metagame paradox. I tried to come up with an explanation via Turing Machines formalization (below). Do you know what is the solution to the paradox? (the post ...
1
vote
1answer
3k views

Mastermind (board game) - Five-guess algorithm

The algorithm (from here) - Create a set S of remaining possibilities (at this point there are 1296). The first guess is aabb. Remove all possibilities from S that would not give the same ...
1
vote
1answer
544 views

Dynamic subtraction game

I came across the following dynamic subtraction game: There is one pile of n chips. The first player to move may remove as many chips as desired, at least one chip but not the whole pile. ...
1
vote
0answers
305 views

Modification of Nim Game Winning Strategy

Here is the variation: We have some P piles of numbers,each having some pi numbers , and in each turn a player may choose a pile, and then a number from the chosen pile. All the numbers greater than ...
1
vote
0answers
604 views

Complexity of Alpha-Beta pruning with optimal move ordering

I originally read that Alpha-Beta pruning has time complexity of $O(b\ ^{m/2}\ )$ with perfect ordering (where b = branching factor, m = maximum ply depth) but have recently come across claims that ...
8
votes
1answer
240 views

High maths for game theory

I am a starting Ph.D. student in computer science, and I am trying to understand some classic game-theory papers, such as those by Nash, Kalai and Smorodinsky. But I find it hard to understand the ...
3
votes
1answer
95 views

Reference introductory books or articles to Game Semantics

Where can I find introductory books, articles, notes or slides on Game Semantics? I have searched a lot on the internet but I'm not satisfied by the material I found. It either is too informal, or it ...
6
votes
1answer
351 views

In what ways can we distinguish between a human and bot behavior?

Updated based on comments: In what ways can we distinguish a human being doing certain activities online and a bot programmed to do similar activities, say checking email, downloading some music ...
6
votes
1answer
1k views

Guessing the smallest unique positive integer

Let us consider the following game: there are some players and a computer. Each player inputs one positive integer and his name (player doesn't know another's numbers, just his own). When all the ...
1
vote
1answer
202 views

Nash Equilibrium of 2-players game

I have a rather interesting exercise in Game Theory. Assume there is a 2-players game, and player $i$ has $n_i$ pure strategies. The game is given by listing the payoffs for each player for each $n_1 ...
3
votes
0answers
63 views

Online algorithm for planning

Let S be a system whose state can be altered by performing actions. Each action has two possible outcomes, and each outcome brings to a specific system state. A ...
1
vote
1answer
141 views

$\epsilon$ - Nash Equilibrium exceeds Nash Equilibrium

I wonder if there exists a game in which $\epsilon$ - Nash equilibrium leads to a much higher payoff than any other Nash equilibrium. Show, for every $\epsilon$ > 0, a two player game where there is ...
2
votes
0answers
239 views

Nash equilibria in 3-player game with symmetry

Consider 3-player game. Players $x,y,z$, each player has two strategies. $x$: $x_1$ and $x_2$, $y$: $y_1$ and $y_2$, $z:z_1$ and $z_2$. The outcome of the game are represented by the labels of the ...
4
votes
1answer
435 views

Finding a winning strategy for toads and frogs

Recently I got interested in a game called Toads and Frogs and I'm trying my best to come up with some software which would be able to beat an average (i.e. not knowing the strategy) human though I'm ...
0
votes
0answers
57 views

Nash Equilibrium in Tree of Bounded Degree

I have an exercise which I can't solve. Exercise. Consider a game where the players have $2$ pure strategies each and assume that the graph $G$ is a tree with maximum degree $3$. Give a polynomial ...
5
votes
1answer
111 views

'Stones' game complexity

I'm trying to find complexity class of finding winning strategy for first player in following game: Intance of 'Stones' game is: finite set $X$ relation $R \subseteq X^3$ set $Y \subseteq X$ and ...
3
votes
1answer
311 views

Difference between Dominant strategy and Winning Strategy

I am a little bit confused by the definition of dominant strategy and winning strategy, what's the difference between them. Following are the definitions taken from wikipedia, below every definition ...
10
votes
2answers
342 views

Fair cake-cutting when players join late

The usual statement of the fair cake-cutting problem assumes that all $n$ players get their share at the same time. However, in many cases the players arrive incrementally. For example, we may divide ...
10
votes
2answers
151 views

Fair division of two-dimensional cake

I am interested in procedures for fair division of land (i.e. envy-free division, or at least proportional division). In contrast to the well-studied cake-division problem, land-division is two-...
3
votes
1answer
200 views

Poker with Bluffing (game theory)

I'm doing a self-study of Game Theory Evolving by Gintis, and am stuck on problem 4.16 "Poker with Bluffing". The first question asks "Show that Ollie has 64 pure strategies and Stan has 8 pure ...
1
vote
3answers
342 views

Is this NIM game tree correct?

I have an assignment to construct a game of Nim (a game in which two players must divide a pile of tokens into two unequal sizes; 6 can be divided into 2 & 4 but not 3 & 3). I was provided a ...
4
votes
1answer
69 views

Minimal-envy land division

There is a land divided to $D$ districts. There are $C$ citizens. We want to divide the land to the citizens, such that each citizen receives a single land-plot in a single district. Each citizen ...
13
votes
0answers
329 views

Complexity of deciding whether there is a winning strategy in the following game

The sum divider game for $n$ starts with the set $M_0 = \{1,\dots,n\}$. Player A chooses a number $m_1$ from $M_0 \setminus \{1\}$ and B has to choose a divider $m_2$ of $m_1$ from $M_1 = M_0 \...
4
votes
1answer
61 views

Congestion Game with Varying Price

I molded my problem as the following game (it is a congestion game with varying price): $N$ players share resources $E$, $S_i$ is the strategy space of player $i$ which is in $2^E$ (where $2^E$ is ...
7
votes
2answers
190 views

Is it more effective to vote for a woman?

A certain political party wants to encourage women to participate in their primary elections, so they decide, that the 4th position is reserved for a woman. That is, if there is no woman in the top 4 ...
1
vote
1answer
5k views

Nim game tree + minimax

Problem : Two players have in front of them a single pile of objects, say a stack of 7 pennies. The first player divides the original stack into two stacks that must be unequal. Each player ...