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How to win some simple iteration games [article]

Alessandro Andretta, John R. Steel
1993 arXiv   pre-print
For a countable M elementarily embeddable in some V_eta, we can show that II wins G(M,omega_1) and that I does not win the G+(M).  ...  We introduce two new iteration games: the game G, which is a strengthening of the weak iteration game, and the game G+, which is somewhat stronger than G but weaker than the full iteration game of length  ...  How not to lose Let M be a countable coarse premouse. We will consider the following iteration game on M, called G + (M).  ...

How to win some simple iteration games

Alessandro Andretta, John Steel
1997 Annals of Pure and Applied Logic
If P is illfounded then I wins, otherwise let M" 1 = P and we move to the next round a + 1.  ...  For a countable M elementarily embeddable in some V", with two players I and II, we can show that II wins Y(M,o,) and that I does not win Y'(M). A. AndreNa, J.  ...  He would like to thank the Mathematics Department of UCLA for its hospitality.  ...

The Fixpoint-Iteration Algorithm for Parity Games

Florian Bruse, Michael Falk, Martin Lange
2014 Electronic Proceedings in Theoretical Computer Science
Note that the Walukiewicz formulas only define winning regions; some additional work is needed in order to make this algorithm compute winning strategies.  ...  Second, fixpoint iteration does not compute positional winning strategies.  ...  The reason is the simple fact that iterations for some X j with an even j are greatest fixpoint iterations that gradually remove nodes from the winning sets.  ...

Investigating vanilla MCTS scaling on the GVG-AI game corpus

Mark J. Nelson
2016 2016 IEEE Conference on Computational Intelligence and Games (CIG)
However, I do ind that given enough computational budget, it manages to avoid explicitly losing on most games, despite failing to win them and ultimately losing as time expires, suggesting an asymmetry  ...  The General Video Game AI Competition (GVG-AI) invites submissions of controllers to play games speciied in the Video Game Description Language (VGDL), testing them against each other and several baselines  ...  Acknowledgment This work was supported in part by the European Union FP7 grant 621403 (ERA Chair: Games Research Opportunities). Thanks to the reviewers for helpful comments and suggestions.  ...

Games and winning strategies

R Back
1995 Information Processing Letters
ILvo-person games are modeled as specifications in a language with angelic and demonic nondeterminism, and methods of program verification and transformation are used to reason about games.  ...  That a given strategy is winning can be proved using a variant of the traditional loop correctness rule.  ...  Acknowledgments We would like to thank Roland Backhouse, David Gries and the anonymous referees for their helpful comments.  ...

Simple Fixpoint Iteration To Solve Parity Games

Tom van Dijk, Bob Rubbens
2019 Electronic Proceedings in Theoretical Computer Science
Furthermore, we modify our algorithm to only partially recompute deeper fixpoints after updating a higher set and show that this modification enables a simple method to obtain winning strategies.  ...  We show that the resulting algorithm is simple to implement and offers good performance on practical parity games.  ...  The challenge is thus to recognize early that some vertices are distractions and the key question to ask of these algorithms is how they accomplish this.  ...

Differential Game Logic

André Platzer
2015 ACM Transactions on Computational Logic
The logic dGL can be used to study the existence of winning strategies for such hybrid games, i.e. ways of resolving the player's choices in some way so that he wins by achieving his objective for all  ...  Hybrid games are determined, i.e. from each state, one player has a winning strategy, yet computing their winning regions may take transfinitely many steps.  ...  Least fixpoint ς α * (X) corresponds to some higher iterate ςλ α (X) of ςα(·) from winning condition X.  ...

New Algorithms for Solving Simple Stochastic Games

Rafał Somla
2005 Electronical Notes in Theoretical Computer Science
Many interesting problems, including parity games and hence also mu-calculus model checking, can be reduced to simple stochastic games.  ...  We show how one can proceed from one subregion to the other so that, eventually, a region containing the optinal payoffs will be found.  ...  Using this fact we show how to iterate through the subregions in such a way that eventually the subregion containing the optimal vector will be found.  ...

Algorithms for Parity Games [chapter]

Hartmut Klauck
2002 Lecture Notes in Computer Science
It is the aim of this chapter to review some of the algorithmic approaches to the problem of computing winning strategies (resp. of deciding if a player has a winning strategy from a given vertex) in parity  ...  We will explain why the problem of solving parity games lies in UP ∩ co-UP, explore its relations to some other games, and describe the theoretically most efficient algorithm for the problem known so far  ...  Then we show how to reduce these to discounted payoff games.  ...

Long Games and σ-Projective Sets [article]

Juan P. Aguilera, Sandra Müller, Philipp Schlicht
2021 arXiv   pre-print
Finally, we show how to generalize the proof to obtain proofs of the determinacy of σ-projective games of a given countable length and of games with payoff in the smallest σ-algebra containing the projective  ...  ., those belonging to the smallest pointclass containing the open sets and closed under complements, countable unions, and projections.  ...  set A ⊂ (ω ω ) n with the property that Player I wins G iff x ∈ A, no matter how the players continue playing the rest of G.  ...

Biasing MCTS with Features for General Games [article]

Dennis J. N. J. Soemers, Éric Piette, Cameron Browne
2019 arXiv   pre-print
The features are formulated in such a way that they are easily interpretable and applicable to a wide range of general games, and might encode simple local strategies.  ...  This paper proposes using a linear function approximator, rather than a deep neural network (DNN), to bias a Monte Carlo tree search (MCTS) player for general games.  ...  Learning curves for other games (in which a simple greedy player still has a win percentage close to 0% against UCT, as we would expect) are omitted to save space. C.  ...

Understanding Sampling Style Adversarial Search Methods [article]

Raghuram Ramanujan, Ashish Sabharwal, Bart Selman
2012 arXiv   pre-print
To provide further insights, we develop synthetic game tree instances and discuss interesting properties of UCT, both empirically and analytically.  ...  It has been particularly successful in the game of Go but the reasons for its success are not well understood and attempts to replicate its success in other domains such as Chess have failed.  ...  a state from which the opponent has a relatively simple winning strategy; such traps, even at surprisingly shallow depths, were found to be abundant even in grandmaster games of Chess.  ...

Extremal Coalitions for Influence Games Through Swarm Intelligence-Based Methods

Fabi醤 Riquelme, Rodrigo Olivares, Francisco Mu駉z, Xavier Molinero, Maria Serna
2022 Computers Materials & Continua
In this article, we apply some variations of this solution to find extreme winning and losing coalitions, and thus efficient approximate solutions for the length and the width of influence games.  ...  An influence game is a simple game represented over an influence graph (i.e., a labeled, weighted graph) on which the influence spread phenomenon is exerted.  ...  Simple games are cooperative games where the benefit obtained by the coalitions is always binary, i.e., coalitions can either win or lose [2] .  ...

Automatic Generation of Alternative Starting Positions for Simple Traditional Board Games [article]

Umair Z. Ahmed, Krishnendu Chatterjee, Sumit Gulwani
2014 arXiv   pre-print
1 to win, and the expertise levels of the two players.  ...  Our approach leverages symbolic methods and iterative simulation to efficiently search the extremely large state space.  ...  The research was partly supported by Austrian Science Fund (FWF) Grant No P23499-N23, FWF NFN Grant No S11407-N23 (RiSE), ERC Start grant (279307: Graph Games), and Microsoft faculty fellows award.  ...

Bluffing as a Rational Strategy in a Simple Poker-Like Game Model

Andrea Guazzini, Daniele Vilone
2013 Journal of Complex Systems
We present a simple adaptive learning model of a poker-like game, by means of which we show how a bluffing strategy emerges very naturally and can also be rational and evolutionarily stable.  ...  Despite their very simple learning algorithms, agents learn to bluff, and the most bluffing player is usually the winner.  ...  The target of this paper is to show how bluffing strategies can arise naturally as a mathematical property of a very simple model, without any references to psychological assessments.  ...
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