Related papers: Simultaneous Go via quantum collapse
This work, based on the author's MA thesis, concentrates on simultaneous move quantum games of two players. A numerical algorithm based on the method of best response functions, designed to search for pure strategy Nash equilibrium in…
We present a quantum implementation of Parrondo's game with randomly switched strategies using 1) a quantum walk as a source of ``randomness'' and 2) a completely positive (CP) map as a randomized evolution. The game exhibits the same…
We consider a dynamical approach to sequential games. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding restriction…
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…
An evolutionarily stable strategy (ESS) was originally defined as a static concept but later given a dynamic characterization. A well known theorem in evolutionary game theory says that an ESS is an attractor of replicator dynamics but not…
This paper investigates online stochastic aggregative games subject to local set constraints and time-varying coupled inequality constraints, where each player possesses a time-varying expectation-valued cost function relying on not only…
We present a new tool for the study of multiplayer stochastic games, namely the modified game, which is a normal-form game that depends on the discount factor, the initial state, and for every player a partition of the set of states and a…
In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play…
In competitive multi-player interactions, simultaneous optimality is a key requirement for establishing strategic equilibria. This property is explicit when the game-theoretic equilibrium is the simultaneously optimal solution of coupled…
Game theory is usually considered applied mathematics, but a few game-theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e. the…
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…
Mastering the game of Go has remained a long standing challenge to the field of AI. Modern computer Go systems rely on processing millions of possible future positions to play well, but intuitively a stronger and more 'humanlike' way to…
Game theory is a well established branch of mathematics whose formalism has a vast range of applications from the social sciences, biology, to economics. Motivated by quantum information science, there has been a leap in the formulation of…
Dynamic games are powerful tools to model multi-agent decision-making, yet computing Nash (generalized Nash) equilibria remains a central challenge in such settings. Complexity arises from tightly coupled optimality conditions, nested…
Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the…
We study optimal behavior of energy producers under a CO_2 emission abatement program. We focus on a two-player discrete-time model where each producer is sequentially optimizing her emission and production schedules. The game-theoretic…
Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is…
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth transforms. The framework shows that…
Symmetric quantum games for 2-player, 2-qubit strategies are analyzed in detail by using a scheme in which all pure states in the 2-qubit Hilbert space are utilized for strategies. We consider two different types of symmetric games…
Scalable board games, including Five in a Row (or gomoku) and weiqi (or go), are generalized so that they can be played on or by quantum computers. We adopt three principles for the generalization: the first two are to ensure that the games…