Search results
Results From The WOW.Com Content Network
The graphical form is an alternate compact representation of a game using the interaction among participants. Consider a game with players with strategies each. We will represent the players as nodes in a graph in which each player has a utility function that depends only on him and his neighbors. As the utility function depends on fewer other ...
The first player unable to extend the path loses. An illustration of the game (containing some cities in Michigan) is shown in the figure below. In a generalized geography (GG) game, we replace the graph of city names with an arbitrary directed graph. The following graph is an example of a generalized geography game.
The Tower of Hanoi (also called The problem of Benares Temple [1], Tower of Brahma or Lucas' Tower [2], and sometimes pluralized as Towers, or simply pyramid puzzle [3]) is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod.
The ingredients of a stochastic game are: a finite set of players ; a state space (either a finite set or a measurable space (,)); for each player , an action set (either a finite set or a measurable space (,)); a transition probability from , where = is the action profiles, to , where (,) is the probability that the next state is in given the current state and the current action profile ; and ...
The normal-form representation of a game includes all perceptible and conceivable strategies, and their corresponding payoffs, for each player. In static games of complete, perfect information, a normal-form representation of a game is a specification of players' strategy spaces and payoff functions. A strategy space for a player is the set of ...
In algorithmic game theory, a succinct game or a succinctly representable game is a game which may be represented in a size much smaller than its normal form representation. Without placing constraints on player utilities, describing a game of n {\displaystyle n} players, each facing s {\displaystyle s} strategies , requires listing n s n ...
Solving a parity game played on a finite graph means deciding, for a given starting position, which of the two players has a winning strategy. It has been shown that this problem is in NP and co-NP, more precisely UP and co-UP, [6] as well as in QP (quasipolynomial time). [7] It remains an open question whether this decision problem is solvable ...
The graph coloring game is a mathematical game related to graph theory. Coloring game problems arose as game-theoretic versions of well-known graph coloring problems. In a coloring game, two players use a given set of colors to construct a coloring of a graph, following specific rules depending on the game we consider.