Showing papers on "Game tree published in 2005"

Method and apparatus for conducting a game of chance

Abstract: A system and method are provided for playing a game of chance. The game of chance may include, for example, a lottery-type game. A result of the game of chance is revealed to a player in another medium. In one example, the result is revealed during multiple game instances of one or more online games. In one example, the online game is a reveal element game.

Evolution of iterated prisoner's dilemma game strategies in structured demes under random pairing in game playing

Abstract: We discuss the evolution of strategies in a spatial iterated prisoner's dilemma (IPD) game in which each player is located in a cell of a two-dimensional grid-world. Following the concept of structured demes, two neighborhood structures are used. One is for the interaction among players through the IPD game. A player in each cell plays against its neighbors defined by this neighborhood structure. The other is for mating strategies by genetic operations. A new strategy for a player is generated by genetic operations from a pair of parent strings, which are selected from its neighboring cells defined by the second neighborhood structure. After examining the effect of the two neighborhood structures on the evolution of cooperative behavior with standard pairing in game-playing, we introduce a random pairing scheme in which each player plays against a different randomly chosen neighbor at every round (i.e., every iteration) of the game. Through computer simulations, we demonstrate that small neighborhood structures facilitate the evolution of cooperative behavior under random pairing in game-playing.

Positional games on random graphs

Abstract: We introduce and study Maker/Breaker-type positional games on random graphs. Our main concern is to determine the threshold probability pF for the existence of Maker's strategy to claim a member of F in the unbiased game played on the edges of random graph G(n, p), for various target families F of winning sets. More generally, for each probability above this threshold we study the smallest bias b such that Maker wins the (1 : b) biased game. We investigate these functions for a number of basic games, like the connectivity game, the perfect matching game, the clique game and the Hamiltonian cycle game. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005

Method for representing a game as a unique number

Abstract: Methods and apparatus for representing game arrangements by a single number, typically an integer, are described. These game arrangements can be applied to most any game including essentially all games played on gaming machines. Conversions can be made between symbolic representations of game arrangements and numeric representations of game arrangements. These conversions can be made using “ordering factors” such as game symbols and positions of such game symbols.

Match game processing method, match game system, and storage medium thereof

Abstract: A match game processing method performs a match game having a plurality of stages by a plurality of players. By communicating among game apparatuses, a control unit controls to synchronize among the plays by the players in a virtual space, on a stage-by-stage basis. The game can be completed with a reduced waiting time of each player. Also, in a ghost match, the game proceeds in such a way that the control unit in the game apparatus performs a simple playback of a ghost data, according to the execution result obtained through the operation inputs from the player. Thus, in response to the execution result by the player, the ghost match is performed and the game time can be shortened.

Trees and Extensive Forms

Abstract: This paper addresses the question of what it takes to obtain a well-de?ned extensive form game. Without relying on simplifying ?niteness or discreteness assumptions, we characterize the class of game trees for which (a) extensive forms can be de?ned and (b) all pure strategy combinations induce unique outcomes. The generality of the set-up covers “exotic” cases, like stochastic games or decision problems in continuous time (di?erential games). We ?nd that the latter class ful?lls the ?rst, but not the second requirement.

Game-tree search with combinatorially large belief states

Abstract: In games such as kriegspiel chess (a chess variant where players have no direct knowledge of the opponent's pieces' locations) the belief state's sizes dwarf those of other partial information games like bridge, scrabble, and poker-and there is no easy way to generate states satisfying the given observations. We show that statistical sampling approaches can be developed to do well in such games. We show that it is not necessary for the random sample to consist only of game boards that satisfy each and every one of a player's observations. In fact, we win 24% more often by beginning with such completely consistent boards and gradually switching (as the game progressed) to boards that are merely consistent with the latest observation. This surprising result is explained by noting that as the game progresses, a board that is consistent with the last move becomes more and more likely to be consistent with the entire set of observations, even if we have no idea what sequence of moves might have actually generated this board.

Extensive-Form Argumentation Games.

Abstract: Two prevalent approaches to automated negotiation are the application of game-theoretic notions and the argumentation-based angle; these two schemes are frequently at odds. An elegant view of argumentation is Dung’s abstract argumentation theory [2], which cold-shoulders the internal structure of arguments in favor of the entire debate’s global structure. Dung’s theory is elaborated by work in dialectical argumentation theory, which focuses on dialogues between two players. In this paper, we enhance the abovementioned frameworks by considering two-agent settings where each of the agents is identified with a set of arguments. A binary attack relation between arguments is given, as well as (most importantly) a payoff function that assigns real values to every possible valid dialogue. Such game-based argumentation frameworks can be lucidly realized as games in extensive form (marrying, in a sense, the game-theoretic and argumentationbased approaches). We investigate specialized notions of “maximally-defendable” sets of arguments, and the correlation between the properties of the agents’ argument sets and the size of the associated game tree. Furthermore, algorithmic issues are considered: we present simplifications and efficient solutions for our argumentation games, and discuss a special case where the representation of the framework is logarithmic in the size of the associated game tree.

Asymmetric graph coloring games

Abstract: We introduce the (a,b)-coloring game, an asymmetric version of the coloring game played by two players Alice and Bob on a finite graph, which differs from the standard version in that, in each turn, Alice colors a vertices and Bob colors b vertices. We also introduce a related game, the (a,b)-marking game. We analyze these games and determine the (a,b)-chromatic numbers and (a,b)-coloring numbers for the class of forests and all values of a and b. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 169–185, 2005

Generalized amazons is PSPACE-complete

Abstract: Amazons is a perfect information board game with simple rules and large branching factors. Two players alternately move chess queen-like pieces and block squares on a 10×10 playing field. The player who makes the last move wins. Amazons endgames usually decompose into independent subgames. Therefore, the game is a natural testbed for combinatorial game theory. It was known that determining the winner of simple generalized Amazons endgames is NP-equivalent. This paper presents two proofs for the PSPACE-completeness of the generalized version of the full game.

Average reward timed games

Abstract: We consider real-time games where the goal consists, for each player, in maximizing the average reward he or she receives per time unit. We consider zero-sum rewards, so that a reward of +r to one player corresponds to a reward of - r to the other player. The games are played on discrete-time game structures which can be specified using a two-player version of timed automata whose locations are labeled by reward rates. Even though the rewards themselves are zero-sum, the games are not, due to the requirement that time must progress along a play of the game. Since we focus on control applications, we define the value of the game to a player to be the maximal average reward per time unit that the player can ensure. We show that, in general, the values to players 1 and 2 do not sum to zero. We provide algorithms for computing the value of the game for either player; the algorithms are based on the relationship between the original, infinite-round game, and a derived game that is played for only finitely many rounds. As memoryless optimal strategies exist for both players in both games, we show that the problem of computing the value of the game is in NP∩coNP.

Path or flow based bonus game

Abstract: The present invention is a player participatory bonus game intended for use in a gaming environment. After a primary game event triggers play of the bonus game, the player is presented with a game arena which shows start points, end points, and locations in between where game pieces may be placed. The game pieces are specially themed so that the player wins by created a path or flow from a start point to an end point, using selected bonus pieces and placing them on the indicated location points.

Chess-like game involving hidden information

Abstract: A chess-like game involves hidden information. The information provided to a player of the game includes positions and types of game pieces on a) squares that are occupied by game pieces belonging to the player and squares that are diagonally adjacent thereto, b) squares to which one or more of the game pieces belonging to the player can move according to their respective movement patterns and which are not occupied by an enemy game piece and squares that are diagonally adjacent thereto, and c) squares occupied by enemy game pieces that can be captured or put into check by one or more of the game pieces belonging to the player can move according to their respective movement patterns. The information excludes positions and types of game pieces on any other squares. The game may also involve non-alternating moves.

Bias and pathology in minimax search

Abstract: This article presents the results of experiments designed to gain insight into the effect of the minimax algorithm on the error of a heuristic evaluation function. Two types of effect of minimax are considered: (a) evaluation accuracy (Are the minimax backed-up values more accurate than the heuristic values themselves?), and (b) decision accuracy (Are moves played by deeper minimax search better than those by shallower search?). The experiments were performed in the King-Rook-King (KRK) chess endgame and in randomly generated game trees. The results show that, counter-intuitively, evaluation accuracy may decline with search depth, whereas at the same time decision accuracy improves with depth. In the article, this is explained by the fact that minimax in combination with a noisy evaluation function introduces a bias into the backed-up evaluations, which masks the evaluation effectiveness of minimax, but this bias still permits decision accuracy to improve with depth. This observed behaviour of minimax in the KRK endgame is discussed in the light of previous studies of pathology in minimax. It is shown that explaining the behaviour of minimax in an actual chess endgame in terms of previously known results requires special care.

Selecting evaluation functions in opponent-model search

Abstract: Opponent-Model search is a game-tree search method that explicitly uses knowledge of the opponent. There is some risk involved in using Opponent-Model search. For adequate forecasting, two conditions should be imposed. Both the prediction of the opponent's moves and the judgement of future positions should be of good quality. The two conditions heavily depend on the evaluation functions used.In the article we distinguish evaluation functions by type. Three fundamentally different types are introduced. Thorough analysis of a variety of characteristics leads to eight possible orderings. The role of the evaluation functions is studied by attempting to answer five research questions. Moreover, actual computer game-playing programs investigate the research questions by a series of experiments in which Opponent-Model search is performed. The game of Bao is our test bed, it was selected because of its relatively narrow game tree, which allowed for an appropriate search depth in the experiments. We restrict ourselves to five evaluation functions generated with the help of machine-learning techniques. A set of round-robin tournaments between these evaluation functions show that when the above conditions are met, Opponent-Model search can be applied successfully. Answers to the research questions are given in the conclusions.

Effective discovery of intrusion protection strategies

Abstract: Effectiveness of discovery of strategy knowledge is studied for problems where the space of hypothesis of solutions is specified by game trees and target solutions are discovered by methods capable of systematic acquisition of expert knowledge about them. A version of Botvinnik's Intermediate Goals At First algorithm is developed for strategy formation based on common knowledge planning and dynamic testing of the plans in the corresponding game tree. Applied to the intrusion protection problem the algorithm for a range of types of knowledge in form of goals and rules demonstrates strong tendency to increasing the efficiency of strategy formation with an increase in the amount of knowledge available to the system.

Why minimax works: an alternative explanation

Abstract: In game-playing programs relying on the minimax principle, deeper searches generally produce better evaluations. Theoretical analyses, however, suggest that in many cases minimaxing amplifies the noise introduced by the heuristic function used to evaluate the leaves of the game tree, leading to what is known as pathological behavior, where deeper searches produce worse evaluations. In most of the previous research, positions were evaluated as losses or wins. Dependence between the values of positions close to each other was identified as the property of realistic game trees that eliminates the pathology and explains why minimax is successful in practice. In this paper we present an alternative explanation that does not rely on value dependence. We show that if real numbers are used for position values, position values tend to be further apart at lower levels of the game tree, which leads to a larger proportion of more extreme positions, where error is less probable. Decreased probability of error in searches to greater depths is sufficient to eliminate the pathology and no additional properties of game trees are required.

A metalogic formalization of legal argumentation as game trees with defeasible reasoning

Abstract: We outline an approach to logical analysis and formalization of legal argumentation and dispute as game trees, wellknown in AI, using metalogic programming. The argument/counter-argument dialectic is facilitated through defeasible reasoning, and the applied principles are sought demonstrated by unravelling of a legal case within statutory law.

Equilibrium concepts in differential information economies

Abstract: We summarize here basic cooperative and noncooperative equilibrium concepts, in the context of differential information economies with a finite number of agents. These, on the one hand, game theoretic, and, on the other hand, Walrasian equilibrium type concepts are explained, and their relation is pointed out, in the context of specific economies with one or two goods and two or three agents. We analyze the incentive compatibility of several cooperative and noncooperative concepts, and also we discuss briefly the possible implementation of these concepts as perfect Bayesian equilibria through the construction of relevant game trees. This possibility is related to whether the allocation is incentive compatible. This depends on whether there is free disposal or not.

Interactive game system with computer-animated game pieces

Abstract: An interactive computer game system (10) for one or more players includes a game server (12) that generates a first game piece (19A) controlled by a first player, and a second game piece (19B). The first game piece (19A) has a first adjustable battle parameter that is adjustable by the first player and a first fixed battle parameter that is not adjustable by the first player. The second game piece (19B) can have a second adjustable battle parameter that is adjustable by the second player and a second fixed battle parameter that is not adjustable by the second player. The game pieces (19A, 19B) engage in a battle having an outcome determined by an algorithm that is based at least partly upon one or more of the adjustable battle parameters and/or one or more of the fixed battle parameters. In another embodiment, the game server (12) generates a pool of game pieces from which the players select activated first game pieces and second game pieces, respectively. The game pieces of each player engage in battles until only one player has at least one activated game piece remaining, and is thereby determined the winning player.

Checkers using a co-evolutionary on-line evolutionary algorithm

Abstract: The game of checkers has been well studied and many computer players exist. The vast majority of these 'software opponents' use a minimax strategy combined with an evaluation function to expand game tree for a number of moves ahead and estimate the quality of the pending moves. In this paper, an alternative approach is described where an on-line evolutionary algorithm is used to co-evolve move sets for both players in the game, playing the entire length of the game tree for each evaluation, thus avoiding the need for the minimax strategy or an evaluation function. The on-line evolutionary algorithm operates in essence as a 'directed' Monte-Carlo search process and although demonstrated on the game of checkers, could potentially be used to play games with a larger branching factor such as Go.

Methods and apparatus for solving mathematical problems for entertainment

Abstract: A game including a game board with a game travel path defined thereon, a game token moveably placeable on the game travel path, and a move generator associated with the game comprising numbers, mathematical operators, mathematical operations, variables, and variable values. A method of constructing a move includes forming the mathematical expression components into a mathematical expression to yield a movement value, and then moving the game token along the game travel path according to rules of the game for the movement value.

Polynomial space suffices for deciding nash equilibria properties for extensive games with large trees

Abstract: We study the computational complexity of deciding the existence of a Pure Nash Equilibrium or a subgame perfect Nash equilibrium with a given payoff and other related problems in finite multi-player extensive games with perfect information. We propose three ways of representing a game with different degrees of succinctness for the components of the game. We show that when the number of moves of each player is large and the player function and the utilities are represented succinctly the considered problems are PSPACE-complete. In contraposition, when the game is described extensively by means of its associated tree all the problems are decidable in polynomial time.

An optimal algorithm for querying priced information: monotone boolean functions and game trees

Abstract: We study competitive function evaluation in the context of computing with priced information A function f has to be evaluated for a fixed but unknown choice of the values of the variables Each variable x of f has an associated cost c(x), which has to be paid to read the value of x The problem is to design algorithms that compute the function querying the values of the variables sequentially while trying to minimize the total cost incurred The evaluation of the performance of the algorithms is made by employing competitive analysis We determine the best possible extremal competitive ratio for the classes of threshold trees, game trees, and monotone boolean functions with constrained minterms, by providing a polynomial-time algorithm whose competitiveness matches the known lower bounds

Design game with deductive component

Abstract: A game of deduction including game components (20) and rules for playing a game for a plurality of players, a goal of which may be for one player to deduce, through a question and answer process, an image on a game card chosen by another player. A game board (12), multiple game cards (20), and a set of image elements (38) with an accompanying game palette may be suitable for playing the game of deduction.

The online clique avoidance game on random graphs

Abstract: Consider the following one player game on an empty graph with n vertices. The edges are presented one by one to the player in a random order. One of two colors, red or blue, has to be assigned to each edge immediately. The player's object is to color as many edges as possible without creating a monochromatic clique Kl of some fixed size l. We prove a threshold phenomenon for the expected duration of this game. We show that there is a function N0 = N0(l, n) such that the player can asymptotically almost surely survive up to N(n) ≪ N0 edges by playing greedily and that this is best possible, i.e., there is no strategy such that the game would last for N(n) ≫ N0 edges.

Implementation of Adaptive Genetic Algorithm of Evaluation Function in Chinese Chess Computer Game System

Abstract: Adaptive Genetic Algorithm(AGA) is used to solve the problem of chinese chess game on computer.The game system is divided into four parts: searching engine,move generator,evaluation function,and opening book.Then,the AGA is brought into evaluation function to automatically adjust and optimize the parameters' combination of evaluation function by tournament algorithm.Based on the above methods,an off-time self-study system is designed.The experiment results show that the AGA improves the performance of the program developed.

Analyze and guess type of piece in the computer game intelligent system

Abstract: Siguo game is an interesting test-bed for artificial intelligent research. It is a game of imperfect information, where completing players must deal with possible knowledge, risk assessment, and possible deception and leaguing players have to deal with cooperation and information signal transmission. Since Siguo game is imperfect information game that the player doesn't know the type of piece and strategy that opponent moves, to exactly guess type of opponent' piece is a very important parameter to evaluate the capability of Siguo game program. In this paper, we first construct a fuzzy type table by analyzing more than one thousand different embattle lineups (i.e. chess manuals) of Siguo game, and then we present a algorithm that updates type table by using information from opponent during playing game. The updating type of pieces algorithm is designed by considering the two strategies, i.e. optimism and pessimism based on the fuzzy notion. At last we give a method to guess the type of piece by using fuzzy type proximity relation between two neighboring pieces.

Murder She Programmed: Dynamic Plot Generating Engine for Murder Mystery Games

Abstract: There is an increased demand for more interactive and dynamic single-player computer games. Most currently proposed solutions usually focus on multi-linear narrations. The problem with those solutions is that they do not actually create a dynamic game, they only increase player choices; the games themselves continue to follow a fairly strict storyline. In this article a new game engine is proposed that dynamically creates new game plots for a murder mystery based game. The game engine uses Bayesian networks to create a new plot based on a probability map of a typical murder mystery novel. To abstract plot elements for the construction of the Bayesian network a unique morphology similar to the morphology of the Russian structuralist Vladimir Propp is created. A directed graph, which is inferred from the resulting Bayesian network, is used as a knowledge base for a murder mystery game. This game sets up a complete and consistent murder mystery that is solvable with logical inference. Each new game generates a unique plot, a murder mystery with all the attributes that are needed for such a plot to be logically consistent, coherent, and complete, and make sense to the human perspective. This game engine is responsive to preset constraints rather than a pre-authored narration, which opens up numerous possibilities for integration in computer games where the constraints can be manipulated by interactions from game events and player interaction. 11.. 1. Introduction