Questions tagged [game-theory]

For questions regarding the use of the mathematical theory of games (Von Neumann, Morgenstern, Nash etc) in AI. For questions about the use of AI in game design and gaming, use [gaming].

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29 views

What are some strong algorithms for Perfect Information, Deterministic Multiplayer Games?

I have a series of games with the following properties: 3 or more players, but purely non-cooperative (i.e., no coalition forming); sequential moves; perfect information; deterministic state ...
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46 views

Computation of the counterfactual regret in CFR algorithm

I'm currently trying to understand the counterfactual regret minimization algorithm as presented in this document: http://modelai.gettysburg.edu/2013/cfr/cfr.pdf. I think I have a good understanding ...
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What is the size of 6-players no limit Texas holdem Poker?

What is the number of game states/information sets in 6-players, no limit, Texas Holdem? A year ago, Pularius reached a super-human level in 6-players no limit Holdem Poker. I am interested in the ...
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1answer
70 views

Find the expected reward in an expectimax-based dice rolling game?

I have this question that I'm kinda stuck on. It's a game scenario in which we set up an expectimax tree. In the game, you have 3 dice with sides 1-4 that you roll at the beginning. Then, depending on ...
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34 views

Are regret values in each block of MC external sampling stored in each node of the block we are traversing down (denoted by $\{Q_1,…, Q_n\}$)?

Everything I know about Monte Carlo counterfactual regret minimization (CFR) comes from the paper Monte Carlo Sampling for Regret Minimization in Extensive Games by Marc Lanctot et al. So, I will use ...
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1answer
118 views

How exactly is Monte Carlo counterfactual regret minimization with external sampling implemented?

I have read many papers, such as this or this, explaining how external sampling works, but I still don't understand how the algorithm works. I understand you divide $Q$, which is the set of all ...
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1answer
136 views

What is the state-space complexity of Spades?

AI reached super-human level in many complex games, including imperfect information games such as six-player no-limit Texas hold’em poker. However, it still did not reached that level in Trick-taking ...
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1answer
31 views

What is a good way of identifying volatile positions for a checkers game?

I am implementing an AI for a mobile checkers game, and have used alpha-beta pruning with Minimax. Now I have the problem of horizontal effect, and need to do Quiesence search to avoid that. Any ...
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28 views

Minimax algorithm with only partial visibility

I'm trying to implement the minimax algorithm with alpha beta pruning on a game that works like this: Player 1 plays (x1, y1). Player 2 can only see the x-value (x1) that Player 1 played (and not ...
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1answer
99 views

Optimal mixed strategy in two player zero sum games

I am currently studying game theory based on Peter Norvig's 3rd edition introduction to artificial intelligence book. In chapter 17.5, the two player zero sum game can be solved by using the $\textbf{...
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64 views

When is shallow pruning possible in alpha-beta pruning for multi-player games?

I have read up on some research papers that state that shallow pruning is possible when ...
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56 views

Is Monte Carlo tree search guaranteed to converge to the optimal solution in two player zero-sum stochastic games?

I'm aware that convergence proofs for Monte Carlo tree search exist in the case of deterministic zero sum games and Markov decision processes. I have come across research which applies MCTS to zero-...
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1answer
330 views

What's the optimal policy in the rock-paper-scissors game?

A deterministic policy in the rock-paper-scissors game can be easily exploited by the opponent - by doing just the right sequence of moves to defeat the agent. More often than not, I've heard that a ...
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1answer
29 views

Compressing text using AI by sending only prediction rank of next word

Is there any effort made to compress text (and maybe other media) using prediction of next word and thus sending only the order number of the word/token which will be predicted on the client side i.e ...
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43 views

Does Algorithmic Mechanism Design come under the field of AI?

I see many papers in AAMAS talk about artificial intelligence and mechanism design simultaneously. I was wondering, for the sake of being pedantic, is mechanism design could be classified under AI.
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78 views

How do you prove that minimax algorithm outputs a subgame-perfect Nash equilibrium?

At every node, MAX would always move to maximise the minimum payoff while MIN choose to minimise the maximum payoff, hence there is nash equilibrium. By using backwards induction, at every node, MAX ...
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1answer
97 views

Shouldn't the utility function of two-player zero-sum games be in the range $[-1, 1]$?

In Appendix B of MuZero, they say In two-player zero-sum games the value functions are assumed to be bounded within the $[0, 1]$ interval. I'm confused about the boundary: Shouldn't the value/...
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1answer
76 views

Why does our AI play worse at even levels of depth?

We are building an AI to play a board game. Leaving aside the implementation, we noticed that it plays worse when we set an even (2,4,6,...) level of depth. We use a minimax depth-first strategy. Do ...
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30 views

What should be a good playing strategy in this 2-player simultaneous game?

This is a bot making problem from here. I am detailing the problem. The picture above shows the initial configuration of the game. P1 represents player1 and P2 represents player2. A scotch bottle is ...
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1answer
48 views

How are the Bellman optimality equations and minimax related?

Is the philosophy between Bellman equations and minimax the same? Both the algorithms look at the full horizon and take into account potential gains (Bellman) and potential losses (minimax). ...
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29 views

Impact or applications of introducing attention in deep networks modelling multi-agent systems

I have been reading quite a lot about the research progress in the domain of self attention-based neural networks that were introduced by Google Inc. in their paper titled "Attention is all you ...
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26 views

Understanding the nature of psychological defense system by artificial intelligence

Do you think psychological defense system, for example, repression, regression, reaction, formation, isolation, undoing, projection, introjection, sublimation, etc., could be created by artificial ...
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1answer
122 views

Interesting examples of discrete stochastic games

SGs are a generalization of MDPs to multiple agents. Like this previous question on MDPs, are there any interesting examples of zero-sum, discrete SGs—preferably with small state and action spaces? I'...
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1answer
111 views

What is the difference between game theory and machine learning?

What is the difference between game theory and machine learning? I had gone through the papers Deep Learning for Predicting Human Strategic Behavior, by Jason Hartford et al., and When Machine ...
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2answers
143 views

What is the difference between genetic algorithms and evolutionary game theory algorithms?

What is the difference between genetic algorithms and evolutionary game theory algorithms?
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54 views

What is the difference between evolutionary game theory and meta-heuristics?

Here is a list of meta-heuristic algorithms Ant colony optimization, Ant lion optimizer, Artificial bee colony algorithm, Bat algorithm, Cat swarm optimization, Crow search algorithm, Cuckoo ...
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2answers
201 views

Are perfect and imperfect information games modelled as fully and partially observable environments, respectively?

In perfect information games, the agent can see all the moves performed in the past. Besides, it can observe the next action that will be put into practice by the opponent. In this case, can we say ...
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2answers
85 views

AI with conflicting objectives?

A recent question on AI and acting recalled me to the idea that in drama, there are not only conflicting motives between agents (characters), but a character may themselves have objectives that are in ...
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3answers
1k views

How to calculate the optimal placements for settlements in Catan without an ML algorithm?

Is it possible to calculate the best possible placements for settlements in Catan without using an ML algorithm? While it is trivial to simply add up the numbers surrounding the settlement (highest ...
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1answer
148 views

How can an AI play Flow Free?

The game "Flow Free" in which you connect coloured dots with lines is very popular. A human can learn techniques to play it. I was wondering how an AI might approach it. There are certain rules of ...
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0answers
238 views

What is the state of the art AI training technique for imperfect information 2 player turn based games?

As far as I can tell (correct me if I'm wrong), Alphazero (with MCTS and neural network heuristic function RL) is the state of the art training method for turn based, deterministic, perfect ...
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91 views

How does Friend-or-Foe Q-learning intuitively work?

I read about Q-Learning and was reading about multi-agent environments. I tried to read the paper Friend-or-Foe Q-learning, but could not understand anything, except for a very vague idea. What does ...
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3answers
159 views

What approaches are there to apply AI to global economic processes?

Today, AI is mainly driven by own-profit-oriented companies (e.g. Facebook, Amazon, Google). Admittedly, there's a lot of AI in the health sector (even in the public health sector) and there's a lot ...
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57 views

Negative counterfactual regret

I am reading the paper Regret Minimization in Games with Incomplete Information on CFR algorithm. On page 4, the paper defines $R^{T,+}_{i,\text{imm}}=\max\{R^{T}_{i,\text{imm}}, 0\}$ after equation (...
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47 views

How can/should I use AI to populate a game (in the game theory sense) from text input

I'm wanting to conduct game theoretic analyses of ongoing conflict situations (e.g. the US/North Korea negotiations; Syrian conflict; etc) as reported in the news media. I believe that AI may help me ...
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50 views

What to study for this simple poker game?

I'm a programmer with a background in mathematics, but I have no experience whatsoever with artificial intelligence/neural networks. I'd like to study it as a hobby, and my goal for now is to solve ...
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2answers
185 views

Can Alpha–Beta be used on symmetric zero sum games?

This question was asked in an AI exam. How would you answer such question?
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4answers
1k views

If two perfect chess AI's played each other, would it always be a stalemate or would white win for an inherent first-move advantage?

In the circumstances of two perfect AI's playing each other, will white have an inherent advantage? Or can black always play for a stalemate by countering every white strategy?
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2answers
277 views

What if there's a game where all the AI people actually lived? [closed]

Imagine the fictitious scenario in a role playing game (RPG) where the non-playing characters (NPCs) within the RPG are conscious of their own surrounding and consider the developer to be god. The ...
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44 views

Strong and Weak Dominance Table

I have this table, 2 agents and I want to find for each agent if any action is strongly or weakly dominated. This is the table: Now, i've found a solution but I'm not sure if it's correct. So for let'...
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1answer
173 views

Can minimax be used when both players want to increase their score?

If both the players want to increase their score (by selecting the highest or best cost path), can this be done using the minimax algorithm, or are there other algorithms for this purpose?
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1answer
98 views

Is there a way to predict points on a map?

I have a data set with historical information of some events (let's say event A and event B),these events describe the discovery of land mines, the coordinates of the event and the date of the event; ...
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52 views

Mini (local) NN for Mobile?

I'm working on architecture for a game AI where, due to the nature of the game, the classical approach seems likely be sufficient to beat most humans--the endgame is tractable and traditional game-...
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3answers
446 views

How to define or represent evil in logic

Is there any well defined method to define or represent evil in abstract logic, binary or AI form? Video games method of representing evil is relative to the player context (thus subjective, and not ...
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2answers
3k views

How to make minimax optimal?

By optimal I mean that: If max has a winning strategy then minimax will return the strategy for max with the fewest number of moves to win. If min has a winning strategy then minimax will return the ...
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1answer
167 views

Is there any flaw to this solution to the One shot prisoner's dilemma

I wrote a solution to the one shot Prisoner's dilemma:     Introduction My solution applies to a prisoner dilemma involving two people (I have neither sufficient knowledge of the prisoner'...
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3answers
2k views

Why spend so much time and money to build AIs to play games?

I was reading about John McCarthy and his orthodox vision of Artificial Intelligence. To me, it seems like he was not very much in favour of resources (like time and money) being used to make AIs play ...
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3answers
999 views

Perfect play in information incomplete games

As titled, is there such thing as perfect play (or at least "perfectly optimal") in a game with incomplete information? Or at least a proof as to show why there cannot? Naively (and seemingly ...
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71 views

Is there a measure of AI relative strength, modified by resources?

For instance Strength/Size*Speed, where size and speed refer to memory and processing. We now have very strong, narrow AI, but they tend to run on fast hardware without volume restrictions. To ...
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273 views

Are there any other machine learning models apart from Reinforcement Learning and Q Learning to play video games?

OpenAI's Universe utilises RL algorithms and I have heard of some game-training projects using Q learning, but are there any others which are used to master/win games? Can genetic algorithms be used ...