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succinct versions of many graph problems, with graphs represented as Boolean circuits, [43] ordered binary decision diagrams [44] or other related representations: s-t reachability problem for succinct graphs. This is essentially the same as the simplest plan existence problem in automated planning and scheduling. planarity of succinct graphs
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 ...
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 ...
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 ...
For solving game trees with proof-number search family of algorithms, game trees are to be mapped to and–or trees. MAX-nodes (i.e. maximizing player to move) are represented as OR nodes, MIN-nodes map to AND nodes. The mapping is possible, when the search is done with only a binary goal, which usually is "player to move wins the game".
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 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 ...
Example graph with the state variables s(v) indicated A possible finite firing sequence, with the vertex to be fired in red – the game ends as each vertex has s smaller than its degree. The chip-firing game is a one-player game on a graph which was invented around 1983 and since has become an important part of the study of structural ...