Related papers: Chess Pure Strategies are Probably Chaotic
Poker is a family of card games that includes many variations. We hypothesize that most poker games can be solved as a pattern matching problem, and propose creating a strong poker playing system based on a unified poker representation. Our…
Recent theories from complexity science argue that complex dynamics are ubiquitous in social and economic systems. These claims emerge from the analysis of individually simple agents whose collective behavior is surprisingly complicated.…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
We consider a card guessing game with complete feedback. An ordered deck of $n$ cards labeled $1$ up to $n$ is shelf-shuffled exactly one time. One after the other a single card is drawn from the shuffled deck. The guesser makes has guess…
With the growing adoption of self-adaptive systems in various domains, there is an increasing need for strategies to assess their correct behavior. In particular self-healing systems, which aim to provide resilience and fault-tolerance,…
We introduce the game of infinite Hex, extending the familiar finite game to natural play on the infinite hexagonal lattice. Whereas the finite game is a win for the first player, we prove in contrast that infinite Hex is a draw -- both…
In competitive games, it is common to assign each player a real number rating signifying their skill level. A rating system is a procedure by which player ratings are adjusted upwards each time they win, or downwards each time they lose.…
We propose a general framework for strategic voting when a voter may lack knowledge about other votes or about other voters' knowledge about her own vote. In this setting we define notions of manipulation and equilibrium. We also model…
We consider deterministic totally-ordered-time games. We present three axioms for strategies. We show that for any tuple of strategies that satisfy the axioms, there exists a unique complete history that is consistent with the strategy…
It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We…
MANIAC Challenge raises a problem of game theory, different players strategies intertwine and the success of any player is dependent on the actions of all players in the system. A truly fair scenario is when all the strategies are…
Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g. uninsurable labor…
We develop a new method for stochastic optimization using the Bayesian statistics approach. More precisely, we optimize parameters of chess engines as those data are available to us, but the method should apply to all situations where we…
We consider the computational complexity of the question whether a certain strategy can be removed from a game by means of iterated elimination of dominated strategies. In particular, we study the influence of different definitions of…
Probabilistic concurrent/distributed strategies have so far not been investigated thoroughly in the context of imperfect information, where the Player has only partial knowledge of the moves made by the Opponent. In a situation where the…
This note provides a general construction, and gives a concrete example of, forced ordinary differential equation systems that have these two properties: (a) for each constant input u, all solutions converge to a steady state but (b) for…
We study the voting game where agents' preferences are endogenously decided by the information they receive, and they can collaborate in a group. We show that strategic voting behaviors have a positive impact on leading to the ``correct''…
This paper demonstrates the use of genetic algorithms for evolving a grandmaster-level evaluation function for a chess program. This is achieved by combining supervised and unsupervised learning. In the supervised learning phase the…
In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation…
Two chaotic systems which interact by mutually exchanging a signal built from their delayed internal variables, can synchronize. A third unit may be able to record and to manipulate the exchanged signal. Can the third unit synchronize to…