Related papers: Chess Pure Strategies are Probably Chaotic

The long-term behaviour of dynamic systems can be classified in two different regimes, regular or chaotic, depending on the values of the control parameters, which are kept constant during the time evolution. Starting from slightly…

We consider solutions of normal form games that are invariant under strategic equivalence. We consider additional properties that can be expected (or be desired) from a solution of a game, and we observe the following: - Even the weakest…

Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning…

Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many…

In a generalized tournament, players may have an arbitrary number of matches against each other and the outcome of the games is measured on a cardinal scale with a lower and upper bound. An axiomatic approach is applied to the problem of…

Several notions of game enjoy a Nash-like notion of equilibrium without guarantee of existence. There are different ways of weakening a definition of Nash-like equilibrium in order to guarantee the existence of a weakened equilibrium.…

Moves in chess games are usually analyzed on a case-by-case basis by professional players, but thanks to the availability of large game databases, we can envision another approach of the game. Here, we indeed adopt a very different point of…

Repetition-based draw rules in deterministic games like chess ensure termination but introduce strategic artifacts, allowing players to enforce draws independent of positional value. We propose an asymmetric modification: threefold…

Zero Determinant (ZD) strategies are a new class of probabilistic and conditional strategies that are able to unilaterally set the expected payoff of an opponent in iterated plays of the Prisoner's Dilemma irrespective of the opponent's…

Game balancing is an important part of the (computer) game design process, in which designers adapt a game prototype so that the resulting gameplay is as entertaining as possible. In industry, the evaluation of a game is often based on…

Bayesian rationality in strategic games presumes that it is possible to translate strategic uncertainty into imperfect information. Correlated equilibrium is guided by the idea that players are Bayes rational, have a common prior, and…

Much of the theoretical work on strategic voting makes strong assumptions about what voters know about the voting situation. A strategizing voter is typically assumed to know how other voters will vote and to know the rules of the voting…

In this paper we present results from recent experiments that suggest that chess players associate emotions to game situations and reactively use these associations to guide search for planning and problem solving. We describe the design of…

Poker is ideal for testing automated reasoning under uncertainty. It introduces uncertainty both by physical randomization and by incomplete information about opponents hands.Another source OF uncertainty IS the limited information…

We study adaptive learning in a typical p-player game. The payoffs of the games are randomly generated and then held fixed. The strategies of the players evolve through time as the players learn. The trajectories in the strategy space…

The strength of chess engines together with the availability of numerous chess games have attracted the attention of chess players, data scientists, and researchers during the last decades. State-of-the-art engines now provide an…

For time inconsistent optimal control problems, a quite popular approach is the equilibrium approach, taken by the sophisticated agents. In this short note we construct a deterministic continuous time example where the unique equilibrium is…

Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish,…

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…

Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system…