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Infinite chess is chess played on an infinite edgeless chessboard. The familiar chess pieces move about according to their usual chess rules, and each player strives to place the opposing king into checkmate. The mate-in-n problem of…
In two-player zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have…
Quantum phenomena have remained largely inaccessible to the general public. This can be attributed to the fact that we do not experience quantum mechanics on a tangible level in our daily lives. Games can provide an environment in which…
AI has surpassed humans across a variety of tasks such as image classification, playing games (e.g., go, "Starcraft" and poker), and protein structure prediction. However, at the same time, AI is also bearing serious controversies. Many…
We study noncooperative games, in which each player's objective is composed of a sequence of ordered- and potentially conflicting-preferences. Problems of this type naturally model a wide variety of scenarios: for example, drivers at a busy…
A checkers-like model game with a simplified set of rules is studied through extensive simulations of agents with different expertise and strategies. The introduction of complementary strategies, in a quite general way, provides a tool to…
This paper investigates Nash equilibria (NEs) in multi-player turn-based games on graphs, where player preferences are modeled as $\omega$-automatic relations via deterministic parity automata. Unlike much of the existing literature, which…
In many competitive settings, from education to politics, rules do not reward effort evenly, and thresholds (e.g., grade cutoffs or electoral majorities) make some moments disproportionately important. Success thus depends on efficiently…
The study of cultural evolution benefits from detailed analysis of cultural transmission in specific human domains. Chess provides a platform for understanding the transmission of knowledge due to its active community of players, precise…
In recent years, deep reinforcement learning has been shown to be adept at solving sequential decision processes with high-dimensional state spaces such as in the Atari games. Many reinforcement learning problems, however, involve…
The game of Go is more challenging than other board games, due to the difficulty of constructing a position or move evaluation function. In this paper we investigate whether deep convolutional networks can be used to directly represent and…
Positions of chess players in intransitive (rock-paper-scissors) relations are considered. Namely, position A of White is preferable (it should be chosen if choice is possible) to position B of Black, position B of Black is preferable to…
Many real-world human behaviors can be characterized as a sequential decision making processes, such as urban travelers choices of transport modes and routes (Wu et al. 2017). Differing from choices controlled by machines, which in general…
We use the indirect evolutionary approach to study evolutionarily stable preferences against multiple mutations in single- and multi-population matching settings, respectively. Players choose strategies to maximize their subjective…
Competitor rating systems for head-to-head games are typically used to measure playing strength from game outcomes. Ratings computed from these systems are often used to select top competitors for elite events, for pairing players of…
In this paper we apply model predictive control (MPC), rollout, and reinforcement learning (RL) methodologies to computer chess. We introduce a new architecture for move selection, within which available chess engines are used as…
Experiments on the ultimatum game have revealed that humans are remarkably fond of fair play. When asked to share an amount of money, unfair offers are rare and their acceptance rate small. While empathy and spatiality may lead to the…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
Observable games are game situations that reach one of possibly many Nash equilibria. Before an instance of the game starts, an external observer does not know, a priori, what is the exact profile of actions that will occur; thus, he…
Computing an equilibrium in congestion games can be challenging when the number of players is large. Yet, it is a problem to be addressed in practice, for instance to forecast the state of the system and be able to control it. In this work,…