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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Question about definitions of "regret" and "no-regret learning rule" in "Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations"

let $\alpha^t$ be the average per-period reward the agent received up until time $t$, and let $\alpha^t(s_i)$ be the average per-period reward the agent would have received up until time $t$ had he ...
1 vote
2 answers
61 views

Why do iterative deepening search start from the root each iteration in the context of the minmax-algorithm?

Consider the graph below for an understanding on how IDS work. Now my question is: why do IDS start at the root every iteration, why not start at the previously searched depth in the context of minmax?...
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Utility function vs evaluation function vs heuristic function in terms of minmax + alphabeta

So i am trying to grasp the difference between a utility function, an evaluation function and an heuristic function in terms of the minmax algorithm with alphabeta on top. So far my understanding is ...
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the best case time complexity for the minimax algorithm with alpha-beta pruning

It is well-known that the node ordering plays an important factor in minimax algorithm \alpha-\beta pruning. Especially the worst case time complexity is O(b^m) ...
2 votes
0 answers
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When to model decision-making problem as single agent vs multi-agent problem?

I understand the goals and purposes of RL in the case of a single agent and the underlying model, i.e. MDPs, for RL problems (or sequential decision making with uncertainty in general). My question is ...
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51 views

Examples of rationalizable AI

The marvelous book Game Changer: AlphaZero's Groundbreaking Chess Strategies and the Promise of AI gave rise to this question. It is - in my opinion - a perfect example of rationalizing a piece of AI ...
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Are these two definitions of regret in RM algorithm equivalent?

(2.1c) on p.1130 of the original paper on regret matching states that $$ D_t^i(j,k) = \frac{1}{t} \sum_{\tau=1}^t \big[ u^i(k,s_\tau^{-j}) - u^i(s_\tau) \big] \;. $$ At the end of page 5 of this ...
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Would AlphaZero work just with a value network?

There is a nice post about the intuition why AlphaZero works. One of the advantages of using a policy network in the games where a perfect simulator is available (such as chess) is to save computation ...
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Book/course recommendation on game theory application to multi-agent system (reinforcement learning)

Is there any great game theory book or course that discusses the application of game theory to modern reinforcement learning or multi-agent systems? Or a classic reference book that can help me get a ...
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AI for games which involve social intelligence. Games like warewolf where players must persuade, charm, threaten etc

I'm looking for any introductory/accessible reading on AI that can play games which involve social intelligence. Games like poker, where you might bait someone into overcommiting their hand or ...
2 votes
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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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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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1 answer
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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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1 answer
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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 ...
4 votes
1 answer
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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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1 answer
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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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0 answers
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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 ...
1 vote
1 answer
402 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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1 vote
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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-...
5 votes
1 answer
641 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 ...
1 vote
1 answer
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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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1 answer
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Why is tic-tac-toe considered a non-deterministic environment?

I have been reading about deterministic and stochastic environments, when I came up with an article that states that tic-tac-toe is a non-deterministic environment. But why is that? An action will ...
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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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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 ...
1 vote
1 answer
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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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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 ...
1 vote
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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 ...
2 votes
1 answer
118 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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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 ...
2 votes
0 answers
47 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 ...
6 votes
1 answer
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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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2 answers
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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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4 votes
2 answers
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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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2 votes
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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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6 votes
2 answers
499 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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2 votes
2 answers
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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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3 votes
3 answers
3k 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 ...
4 votes
1 answer
285 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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3 votes
0 answers
318 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 ...
2 votes
0 answers
96 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 ...
1 vote
3 answers
163 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 ...
3 votes
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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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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 ...
1 vote
0 answers
58 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 ...
1 vote
2 answers
231 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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4 answers
2k 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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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'...
3 votes
1 answer
228 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?
3 votes
1 answer
142 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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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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