Showing papers on "Game tree published in 2001"

Graphical models for game theory

Abstract: We introduce a compact graph-theoretic representation for multi-party game theory. Our main result is a provably correct and efficient algorithm for computing approximate Nash equilibria in one-stage games represented by trees or sparse graphs.

Game of chance with multiple paths on a virtual scratch ticket

Abstract: An online game of chance and methods of conducting and playing the game on a virtual instant ticket are disclosed. The game is based on a map having multiple branches and nodes, where a desired path is selected by clicking on the branch or node as play progresses between a starting point and multiple finishing points. Each available branch or node that is selected results in a prize value being increased, decreased, or a token being awarded for later use in the game. In a single player mode, a final prize is awarded to the player. In multiple player modes, the final prize is divided among the players according to predetermined criteria.

Game system and method for network player credit-wagering

Abstract: Game system for maintaining enthusiasm for and excitement of match-type games performed over a network. A central administrating device, game terminal devices 30 , terminal management devices 31 , and entry-processing devices 39 are connected over a network. Game execution credits are assigned by investing a certain amount of money into the entry-processing device 39 . When a players and spectator wagerer accesses a terminal management device, the central administrating device performs a game entry procedure, and subtracts game execution credits from the players and spectator wagerer's credits. Players and spectator wagerers can bet their credits against one another. The credits put at stake that are added/subtracted depending on the game result are specified via the terminal management device 31 , and players and spectator wagerer's credits are updated in accordance with the game result.

Online game of chance providing a multi-player extension of a single-player virtual scratch ticket game and a method of playing the game

Abstract: An online game of chance that produces a multi-player extension to an individual, instant lottery-type game and a method of playing the game are disclosed. The game comprises a first, individual phase of play using a virtual game substrate (10) and a second, group phase of play comprising a plurality of virtual game substrates from first phase of play that are arrayed in a matrix. The first, individual phase of play is based on in instant lottery version of the well-known game of tic-tac-toe; the object being to match a plurality of game pieces (16), e.g., three, in one of a contiguous row, column, and diagonal. The object of the second phase of play is to use the combination of virtual game substrates to produce a match with one or more predetermined winning array combinations. This provides each individual participant with a second chance of winning.

Network game method and network game system

Abstract: The present invention provides a second network game (for example, a betting game) using the results of a first network game (for example, a horse racing game), wherein third party users other than users running a first network game can participate. A greater number of users will thereby have interest in the first network game and the first network game will be built up. Also, a greater number of users can participate in a network game through the second network game.

On the computation of the nucleolus of a cooperative game

Abstract: We consider classes of cooperative games. We show that we can efficiently compute an allocation in the intersection of the prekernel and the least core of the game if we can efficiently compute the minimum excess for any given allocation. In the case where the prekernel of the game contains exactly one core vector, our algorithm computes the nucleolus of the game. This generalizes both a recent result by Kuipers on the computation of the nucleolus for convex games and a classical result by Megiddo on the nucleolus of standard tree games to classes of more general minimum cost spanning tree games. Our algorithm is based on the ellipsoid method and Maschler's scheme for approximating the prekernel.

Methods and systems for conducting lottery-type games with strategy elements

Abstract: The present invention provides methods and systems for interactively playing a lottery-type game among a number of players. In one embodiment, this is accomplished on a network of gaming terminals in communication with a central controller. An objective of the game is for a player to select the number closest to the randomly selected number that represents the winning number for the lottery game. This is a significant departure from the prior art, in that the game of the present invention does not require an exact match to produce a win and in that the game results in a win for every drawing. Thus, the lottery-type game of the present invention improves the gaming experience for the player, which will result in prolonged and more frequent play, thereby maximizing revenues for the operator of the game.

Game management device, game program and game system

Abstract: PROBLEM TO BE SOLVED: To allow the control of communication data quantity on the game terminal side to perform a comfortable game operation because the transmission frequency of partial game world data is varied depending on the size of a partial game, and a size change request is transmitted from the game terminal. SOLUTION: A game server 20 judges whether a moving character is present in the partial game world that is a part of a game world every movement of the moving character. When the partial character is present in the partial game world, the partial game world data is transmitted from the game server 20 to a portable communication terminal 30. In the portable communication terminal 30, the partial game world based on the transmitted partial game world data is reproduced. When a size change request is transmitted from the portable communication terminal 30 to the game server 20, the size of the partial game world is changed in response to this size change request. COPYRIGHT: (C)2002,JPO

Game system and game program to be used for the system

Abstract: PROBLEM TO BE SOLVED: To enable a player to really feel the movement of a game world when a character moves in the game world. SOLUTION: This game system displays the game world of a first game world of a first display means and displays the game world of a second game world different from the first game world on a second display means. Further, the system processes a game according to the operation of an operation means and when the result of processing satisfies a prescribed condition, the system moves a prescribed character between the first game world and the second game world. Further, the system judges which of the first game world and the second game world the character exists in, and displays the character on the first display means or the second display means.

Learning on Graphs in the Game of Go

Abstract: We consider the game of Go from the point of view of machine learning and as a well-defined domain for learning on graph representations. We discuss the representation of both board positions and candidate moves and introduce the common fate graph (CFG) as an adequate representation of board positions for learning. Single candidate moves are represented as feature vectors with features given by subgraphs relative to the given move in the CFG. Using this representation we train a support vector machine (SVM) and a kernel perceptron to discriminate good moves from bad moves on a collection of life-and-death problems and on 9 × 9 game records. We thus obtain kernel machines that solve Go problems and play 9 × 9 Go.

System and method for network game, and managing device, managing method, and managing program

Abstract: PROBLEM TO BE SOLVED: To change the contents of a network game according to position information of a game instrument in which the network game is performed. SOLUTION: A server and each player on a game site are connected via the Internet. The server respectively changes a background which is a pattern of a network game, configuration of the ground in the network game related to progress of the network game, the nature of a unit which is a movement nucleus in the network game or the effect of an item in the network game, or the like, according to position information received from each player.

Algorithmic Aspects of a Chip-Firing Game

Abstract: Algorithmic aspects of a chip-firing game on a graph introduced by Biggs are studied. This variant of the chip-firing game, called the dollar game, has the properties that every starting configuration leads to a so-called critical configuration. The set of critical configurations has many interesting properties. In this paper it is proved that the number of steps needed to reach a critical configuration is polynomial in the number of edges of the graph and the number of chips in the starting configuration, but not necessarily in the size of the input. An alternative algorithm is also described and analysed.

Lambda-search in game trees - with application to go

Abstract: This paper proposes a new method for searching two-valued (binary) game trees in games like chess or Go. Lambda-search uses null-moves together with different orders of threat-sequences (so-called lambda-trees), focusing the search on threats and threat-aversions, but still guaranteeing to find the minimax value (provided that the game-rules allow passing or zugzwang is not a motive). Using negligible working memory in itself, the method seems able to offer a large relative reduction in search space over standard alpha-beta comparable to the relative reduction in search space of alpha-beta over minimax, among other things depending upon how non-uniform the search tree is. Lambda-search is compared to other resembling approaches, such as null-move pruning and proof-number search, and it is explained how the concept and context of different orders of lambda-trees may ease and inspire the implementation of abstract game-specific knowledge. This is illustrated on open-space Go block tactics, distinguishing between different orders of ladders, and offering some possible grounding work regarding an abstract formalization of the concept of relevancy-zones (zones outside of which added stones of any colour cannot change the status of the given problem).

Game system, game device, game device control method and information storage medium

Abstract: To provide a game system allowing two players to enjoy a game together toward a common goal. In a cooperation requiring event area, a giant rock blocks a path to be followed by a player character. The giant rock cannot be moved by the player character alone. Then, the game device of the player character is made connected for communication to other game device so that another player character is fetched from the connected game device. When the two player characters cooperate at their respective game devices, the giant rock is able to be moved by the two player characters.

An extensive form interpretation of the private core

Abstract: The private core of an economy with differential information, (Yannelis (1991)), is the set of all state-wise feasible and private information measurable allocations which cannot be dominated, in terms of ex ante expected utility functions, by state-wise feasible and private information measurable net trades of any coalition It is coalitionally Bayesian incentive compatible and also takes into account the information superiority of an individual We provide a noncooperative extensive form interpretation of the private core for three person games We construct game trees which indicate the sequence of decisions and the information sets, and explain the rules for calculating ex ante expected payoffs In the spirit of the Nash programme, the private core is thus shown to be supported by the perfect Bayesian equilibrium of a noncooperative game The discussion contributes not only to the development of ideas but also to the understanding of the dynamics of how coalitionally incentive compatible contracts can be realized

Game device, game method, game program, and game system

Abstract: PROBLEM TO BE SOLVED: To provide a game device having reality. SOLUTION: The game system has a sword-shape actually operating article 51. The location in an actual space of the sword-shape actually operating article 51 is detected by a location-detecting unit 6, and converted into game space coordinates by a three-dimensional input-converting means 13. When a player moves the sword-shape actually operating article 51, the movement of a sword object in the game space is displayed in the same manner as the movement of the sword-actually operating article 51. The movement of the sword object is stored as a location in the past in the game space. Based on the stored location, whether or not the sword object hits other objects in the game space is determined. The player moves by himself rather than controlling the object in the game space. Thus, the game can be performed without feeling the sense of incongruity between the actual space and the game space. COPYRIGHT: (C)2003,JPO

Educational word game and method for employing same

Abstract: The present invention is an educational word game and method of playing same that may be provided in single or bi-lingual versions and that challenges players to form as many new words from a set of at least two base words as possible within a limited amount of time. The word game provides players greater and more varied entertainment and educational challenges over previous word games by requiring that the players define a set of rules for each game prior to play and by the random selection of round prize amounts and the letter length of the at least two base words, and thus the number and type of letters players may use to form new words. A pointer centrally attached to a game board is spun to determine the base word letter length and prize amounts for each of at least one round of play that comprise a game, by where the pointer lands on the board. Players fill in a game rules sheet by selecting from among optional rule definitions for each of a plurality of rules to define the set of rules for each game. The rules of a game include a time limit for a round of play, a type of new words to form that qualify for credit, a criterion for determining a round winner, a criterion for determining a game winner and, in bi-lingual versions of the game, a language of play. By requiring that two or more base words be used, the number, length, and sophistication of words a player may potentially make is greatly expanded over comparable games in which only one base word, or a limited number of individual letters, are provided. The entertainment, as well as educational, value of the game is also increased by requiring the players to define the set of rules for each game. The variety of combinations of rules options possible allow players to experience new levels of fun and challenge with each game they play.

Multi-functional game board with rotating mechanism

Abstract: A novel game board comprises a base board ( 100 ) with rotating tiers ( 105, 405, 410, and 415 ) which rotate on a shaft ( 430 ) and bearings ( 402, 404, and 407 ) or a lazy susan ( 115 ), a pointer 120 or a rotating pointer knob ( 425 ) which points at numbers ( 305 ) and game fields ( 310 ) on a tier ( 300 ) Progress through the game is indicated by individual players' tokens ( 135 ) Game cards and play money ( 140, 320, 325, 330, and 335 ) are also provided Multiple results can arise from the same players' moves Hidden game fields ( 700 ) under the edges of square or rectangular tiers ( 405, 410, and 415 ) provide added excitement Instructions in the game fields ( 300, 406, etc) can apply to a single player or to all players simultaneously, resulting in advantages or disadvantages for one or all No dice are used to play, only a rotating pointer knob ( 425 ) or a rotating tier 105 with a stationary pointer ( 120 ) are required to urge progress through the game The same mechanical arrangement is applicable in a variety of games, resulting in an economy of scale for manufacturers

Systems and methods to ensure that a threshold game result is possible

Abstract: Systems and methods are provided to ensure that a threshold game result is possible. According to one embodiment, a game condition associated with a game of skill is established. The game of skill may be, for example, a puzzle game (e.g., a word puzzle game or a graphical puzzle game) or an arcade-style game. It is determined that at least one set of possible player inputs during game play will produce at least a threshold game result given the established game condition. The threshold game result may be associated with, for example, prizes provided to players based on game results.

DNA Starts to Learn Poker

Abstract: DNA is used to implement a simplified version of poker. Strategies are evolved that mix bluffing with telling the truth. The essential features are (1) to wait your turn, (2) to default to the most conservative course, (3) to probabilistically override the default in some cases, and (4) to learn from payoffs. Two players each use an independent population of strategies that adapt and learn from their experiences in competition.

Progressing pattern memory game and its associated method of play

Abstract: A game and its associated method of play. The game contains a plurality of object areas in which game objects may be placed. Game objects are randomly added to, or removed from, the object areas one by one. Before the addition or removal of each new object, the player is made to visualize a neutral field of play that is either completely filled with game objects or devoid of game objects. As such, each time a player views the object areas, an additional game object has been added or removed, but the player does not know which object has just been added. Using memories of the object areas when last viewed, a player tries to identify which of the game objects present is the game object that was just added or removed. If the player selects correctly, the cycle is repeated and another game object is randomly added or removed. If the player selects the wrong game object, the game ends.

Game method for effecting aging of competing characters independent of game player participation

Abstract: Using terminal apparatuses 1A to 1E connected to a server 3 by a network 2, original characters are trained by the game players executing a character training game, and data relating to those original characters are stored in a database 31 in the server 3. When two or more game players directly contest the same game in real time via the network 2, data relating to the original characters of the game players stored in the database 31 are downloaded to the terminal apparatuses 1A to 1E and used as character data.

Estimating a Game Theoretic Model

Abstract: Applied game theory generally shows possible game situations, discussing their implications. This paper derives an estimation procedure for non-cooperative games, using cross-section data. During the transformation of the data an attempt is made to pick extreme points, to find the outer borders for the actual game. The estimation procedure is an algorithm that switches between several software packages. In an application a motivated choice can be made for the transformation functions such that the estimated game comes closest to the actual game of the empirical problem under study. To demonstrate the estimation procedure, a situation is studied in which a villager voluntarily chooses a level of participation in forest management.

Parallel controlled conspiracy number search

Abstract: Tree search algorithms play an important role in many applications in the field of artificial intelligence. When playing board games like chess etc., computers use game tree search algorithms to evaluate a position. In this paper, we present a procedure that we call Parallel Controlled Conspiracy Number Search (Parallel CCNS). Shortly, we describe the principles of the sequential CCNS algorithm, which bases its approximation-results on irregular subtrees of the entire game tree. We have parallelized CCNS and implemented it in our chess program P. ConNerS, which now is the first in the world, that could win a high-ranked Grandmaster chess-tournament. We add experiments that show a speedup of about 50 on 159 processors running on an SCI-workstation-cluster.