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The preferences of players in non-cooperative games represent their choice in the set of available options, which meet the completeness property if players are able to compare any pair of available options. In the existing literature, the…
As the complexity and scope of games increase, game testing, also called playtesting, becomes an essential activity to ensure the quality of video games. Yet, the manual, ad-hoc nature of game testing leaves space for automation. In this…
Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…
Chess has long been a testbed for AI's quest to match human intelligence, and in recent years, chess AI systems have surpassed the strongest humans at the game. However, these systems are not human-aligned; they are unable to match the…
In this study, we present models where participants strategically select their risk levels and earn corresponding rewards, mirroring real-world competition across various sectors. Our analysis starts with a normal form game involving two…
Decision making in modern large-scale and complex systems such as communication networks, smart electricity grids, and cyber-physical systems motivate novel game-theoretic approaches. This paper investigates big strategic (non-cooperative)…
Nonzero sum games typically have multiple Nash equilibriums (or no equilibrium), and unlike the zero sum case, they may have different values at different equilibriums. Instead of focusing on the existence of individual equilibriums, we…
We propose a simple yet rich model to extend the notions of Nash equilibria and correlated equilibria of strategic games to the quantum setting, in which we then study the relations between classical and quantum equilibria. Unlike the…
We consider a class of Wasserstein distributionally robust Nash equilibrium problems, where agents construct heterogeneous data-driven Wasserstein ambiguity sets using private samples and radii, in line with their individual risk-averse…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
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…
Endgame studies have long served as a tool for testing human creativity and intelligence. We find that they can serve as a tool for testing machine ability as well. Two of the leading chess engines, Stockfish and Leela Chess Zero (LCZero),…
This paper contributes a new way to evaluate AI. Much as one might evaluate a machine in terms of its performance at chess, this approach involves evaluating a machine in terms of its performance at a game called "MAD Chairs". At the time…
We study linear quadratic dynamic games where players are uncertain about each other's control policies or goals and consequently seek to be strategically robust. Building on recent work on strategically robust and risk-averse game theory,…
Blackjack or "21" is a popular card-based game of chance and skill. The objective of the game is to win by obtaining a hand total higher than the dealer's without exceeding 21. The ideal blackjack strategy will maximize financial return in…
We study a modified prisoner's dilemma game taking place on two-dimensional disordered square lattices. The players are pure strategists and can either cooperate or defect with their immediate neighbors. In the generations each player…
In this work we propose and develop modified quantum games (zero and non-zero sum) in which payoffs and strategies are entangled. For the games studied, Nash and Pareto equilibriums are always obtained indicating that there are some…
Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, finding applications in diverse fields such as economics, political science, and biology. However, the Nash…
We use logistic regression to estimate the value of the pieces in standard chess and several chess variants, namely Chess 960, Atomic chess, Antichess, and Horde chess. We perform our regressions on several years of data from Lichess, the…
There are an increasing number of domains in which artificial intelligence (AI) systems both surpass human ability and accurately model human behavior. This introduces the possibility of algorithmically-informed teaching in these domains…