Class Of Games Research Articles

Quantum game theory and the complexity of approximating quantum Nash equilibria

This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information. In particular, we prove that the computational problem of finding an approximate Nash equilibrium in a broad class of quantum games is, like the analogous problem for classical games, included in (and therefore complete for) the complexity class PPAD. Our main technical contribution, which facilitates this inclusion, is an extension of prior methods in computational game theory to strategy spaces that are characterized by semidefinite programs.

Decentralized strategies for finite population linear–quadratic–Gaussian games and teams

This paper is concerned with a new class of mean-field games which involve a finite number of agents. Necessary and sufficient conditions are obtained for the existence of the decentralized open-loop Nash equilibrium in terms of non-standard forward–backward stochastic differential equations (FBSDEs). By solving the FBSDEs, we design a set of decentralized strategies by virtue of two differential Riccati equations. Instead of the ɛ-Nash equilibrium in classical mean-field games, the set of decentralized strategies is shown to be a Nash equilibrium. For the infinite-horizon problem, a simple condition is given for the solvability of the algebraic Riccati equation arising from consensus. Furthermore, the social optimal control problem is studied. Under a mild condition, the decentralized social optimal control and the corresponding social cost are given.

Joint optimization of delay and energy in partial offloading using Dual-population replicator dynamics

Due to the growing demand for delay-sensitive applications, partial offloading is very important in fog/cloud computing. In partial offloading, different parts of each task are run in parallel on the end device, fog device, and remote cloud. Generally, a fog/cloud environment consists of independent, selfish agents who want to get more resources. Game theory is a well-known mathematical tool for modeling the interactions of these selfish agents. In traditional game-theoretical models, the mobile user is considered a player. A significant problem with such modeling is scalability. When the number of players is very large, the algorithm may require a long time to converge. The reason is that with the increase in the number of users, the search space for strategies becomes larger. The player must have complete knowledge about competitors to make the best decision. Moreover, the dynamic changes in the fog environment have been ignored in almost all previous studies. This paper presents dual-population modeling using replicator dynamics considering the interaction between the user and the fog environment. Unlike classical game theory, here, the offloading decision (strategy) is viewed as the player. The proposed method can very efficiently model the growing/shrinking behavior of two populations of CPU cycles on both the user and the network sides. It is scalable and converges to a stable equilibrium point regardless of the number of mobile users. We derive conditions under which agents can update their decisions according to the dynamics of the environment. The simulation results reveal the superiority of the proposed method over the full local execution, full offloading, evolutionary algorithms, and the Stackelberg methods. It saves 180% and 380% of the time and energy compared to the best state-of-the-art and baseline methods.

Asymmetric interaction and diverse forms in public goods production in volunteer dilemma game

Theoretical prediction of classical evolutionary games shows that public goods is contributed either by strong players in asymmetric games or by all of the involved players in symmetric games. However, it is inconsistency with experimental observations that weak players could also contribute to public goods in real cooperation systems. To reconciling these conflicts, we here study an evolutionary volunteer's dilemma game by assuming different roles can be interchangeable. In this model, not only the existence of multiple equilibria is possible but also the evolutionary result of the system depends on initial conditions, which can be interpreted as the production modes of public goods under different circumstances. Specifically, we found that the survival of strong individuals with mixed strategies is associated with two different outcomes: one is similar to Selten's model, that is, public goods are produced by strong players if the defectors are weak players and strong defectors are scarce in the initial condition; and the other is that the weak individuals with mixed strategies produce public goods if the defectors are strong individuals, where the strong cooperators are absent in the initial condition. Moreover, the weak individuals with mixed strategies produce public goods while strong individuals mainly display defection if the cooperation of strong players is absent in the initial condition. Our main results may help to explain the emergence of diverse forms of cooperation in asymmetric evolutionary games.

Games over Probability Distributions Revisited: New Equilibrium Models and Refinements

This article is an overview of recent progress on a theory of games, whose payoffs are probability distributions rather than real numbers, and which have their equilibria defined and computed over a (suitably restricted yet dense) set of distributions. While the classical method of defining game models with real-valued utility functions has proven strikingly successful in many domains, some use cases from the security area revealed shortcomings of the classical real-valued game models. These issues motivated the use of probability distributions as a more complex object to express revenues. The resulting class of games displays a variety of phenomena not encountered in classical games, such as games that have continuous payoff functions but still no equilibrium, or games that are zero-sum but for which fictitious play does not converge. We discuss suitable restrictions of how such games should be defined to allow the definition of equilibria, and show the notion of a lexicographic Nash equilibrium, as a proposed solution concept in this generalized class of games.

Behavioral Strategies between Government and Real Estate Developers on Prefabricated Buildings Based on Triangular Fuzzy Matrix Game

The subsidies provided by the local government to real estate developers are an important and common practice to promote the development of prefabricated buildings worldwide. However, there is a lack of current research on how government subsidies affect the decision-making of real estate developers with respect to adopting prefabricated construction methods. This study developed a fuzzy game model integrating classical game theory with the triangular fuzzy number approach between the local government and a real estate developer, with different behavioral strategies regarding whether or not to develop prefabricated buildings. It analyzed the Nash equilibriums under the circumstances of pure and mixed strategies and probed the influencing factors of the game equilibrium results via numerical simulation. The research conclusions are as follows: (1) the government should encourage real estate developers to actively participate in prefabricated building by using financial subsidies, fund rewards, process supervision and economic penalties comprehensively; (2) the pure strategy (no manufacturing process supervision, active development) between the government and real estate developers is feasible when the benefit of “active development” for real estate developers is larger than that of “passive development”; (3) positive incentives, such as offering financial subsidies, reducing the cost of prefabricated building development and improving the popularity of prefabricated construction in the building market, should be taken to motivate real estate developers; and (4) negative incentives, such as increasing economic punishment and enhancing manufacturing process supervision, can also facilitate real estate developers to actively participate in the development of prefabricated buildings. Incentives are more effective when the economic penalties are greater than the incremental costs of developing prefabricated buildings. Some policy implications are given to guide prefabricated building market development. Finally, the main problems that need further study in the future are highlighted.

The Costliness of US Residency Applications: Moving Toward Preference Signaling and Caps.

The Costliness of US Residency Applications: Moving Toward Preference Signaling and Caps.

Rationality Now!

Rationality Now!

Nash Equilibria of Quantum Games in the Special Two-Parameter Strategy Space

The aim of the paper is to examine pure Nash equilibria in a quantum game that extends the classical bimatrix game of dimension 2. The strategies of quantum players are specific types of two-parameter unitary operations such that the resulting quantum game is invariant under isomorphic transformations of the input classical game. We formulate general statements for the existence and form of Nash equilibria and discuss their Pareto efficiency. We prove that, depending on the payoffs of a classical game, the corresponding quantum game may or may not have Nash equilibria in the set of unitary strategies under study. Some of the equilibria cease to be equilibria if the players’ strategy set is the three-parameter special unitary group.

The Effect of Schedule Thinning on Student Behavior During the Caught Being Good Game.

The Caught Being Good Game (CBGG) is a classroom management intervention which is described as a variation of the classic Good Behavior Game (GBG). It is based on the principle of positive reinforcement, such that teams of students can earn points for following the class rules during the game. Points are awarded by the teacher at different intervals during the game and these intervals were the focus of the current study. We aimed to determine if the CBGG is effective with an initially dense schedule of reinforcement which is progressively thinned. The efficacy of the CBGG in targeting academic engagement and disruptive behavior was demonstrated for one primary school class and for two target students in that class. The game remained effective when the reinforcement schedule was thinned from 2 minutes, up to 5 minutes. This has potential implications for teacher time saving while playing the game.

Evolutionary Kuramoto dynamics

Biological systems have a variety of time-keeping mechanisms ranging from molecular clocks within cells to a complex interconnected unit across an entire organism. The suprachiasmatic nucleus, comprising interconnected oscillatory neurons, serves as a master-clock in mammals. The ubiquity of such systems indicates an evolutionary benefit that outweighs the cost of establishing and maintaining them, but little is known about the process of evolutionary development. To begin to address this shortfall, we introduce and analyse a new evolutionary game theoretic framework modelling the behaviour and evolution of systems of coupled oscillators. Each oscillator is characterized by a pair of dynamic behavioural dimensions, a phase and a communication strategy, along which evolution occurs. We measure success of mutations by comparing the benefit of synchronization balanced against the cost of connections between the oscillators. Despite the simple set-up, this model exhibits non-trivial behaviours mimicking several different classical games-the Prisoner's Dilemma, snowdrift games, coordination games-as the landscape of the oscillators changes over time. Across many situations, we find a surprisingly simple characterization of synchronization through connectivity and communication: if the benefit of synchronization is greater than twice the cost, the system will evolve towards complete communication and phase synchronization.

Polynomial Life: the Structure of Adaptive Systems

We extend our earlier work on the compositional structure of cybernetic systems in order to account for the embodiment of such systems. All their interactions proceed through their bodies' boundaries: sensations impinge on their surfaces, and actions correspond to changes in their configurations. We formalize this morphological perspective using polynomial functors. The 'internal universes' of systems are shown to constitute an indexed category of statistical games over polynomials; their dynamics form an indexed category of behaviours. We characterize 'active inference doctrines' as indexed functors between such categories, resolving a number of open problems in our earlier work, and pointing to a formalization of the 'free energy principle' as adjoint to such doctrines. We illustrate our framework through fundamental examples from biology, including homeostasis, morphogenesis, and autopoiesis, and suggest a formal connection between spatial navigation and the process of proof.

Characterizing Agent Behavior in Revision Games with Uncertain Deadline

Revision game is a very recent advance in dynamic game theory and it can be used to analyze the trading in the pre-opening stock market. In such games, players prepare actions that will be implemented at a given deadline, before which they may have opportunities to revise actions. For the first time, we study the role of the deadline in revision games, which is the core component that distinguishes revision games from classic games. We introduce the deadline distribution into revision game model and characterize the sufficient and necessary condition for players’ strategies to constitute an equilibrium. The equilibrium strategy with respect to the deadline uncertainty is given by a simple differential equation set. Governed by this differential equation set, players initially fully cooperate, and the cooperation level decreases as time progresses. The uncertainty has a great impact on players’ behavior. As the uncertainty increases, players become more risk averse, in the sense that they prefer lower mutual cooperation rate rather than higher payoff with higher uncertainty. Specifically, they will not stay in full cooperation for a long time, while after they deviate from the full cooperation, they adjust their plans more slowly and cautiously. The deadline uncertainty can improve the competition and avoid collusion in games, which could be utilized for auction design and pre-opening stock market regulations.

Does Video Game Play Elevate Suicide Risk? A Cross‐sectional Study of Japanese Young Adults1,2

AbstractThe present study explored the relationship between video/online game playing and suicide risk among Japanese young adults using the interpersonal–psychological theory of suicide. A sample of 310 players aged 20–39 years was recruited through an Internet research company. Each participant completed a questionnaire containing items that measured time spent on games, game addiction (GA), game categories, suicidal ideation (SI), suicide attempt (SA), perceived burdensomeness, thwarted belongingness, acquired capability for suicide (ACS), depression, and demographic variables (including age and sex). Multiple regression analyses revealed that depression and the GA × depression interaction significantly explained SI. However, the effect was limited. Additionally, the results revealed that SI was a strong predictor of SA, but the SI × ACS interaction and the SI × ACS × time spent on games interaction were also significant. It should be noted that the time spent on games explained the SA only when SI was low and ACS was high. These results may indicate the necessity of examining suicide risk in GA interventions for young adults; however, more research is needed.

The quantum-to-classical graph homomorphism game

Motivated by non-local games and quantum coloring problems, we introduce a graph homomorphism game between quantum graphs and classical graphs. This game is naturally cast as a “quantum–classical game,” that is, a non-local game of two players involving quantum questions and classical answers. This game generalizes the graph homomorphism game between classical graphs. We show that winning strategies in the various quantum models for the game is an analog of the notion of non-commutative graph homomorphisms due to Stahlke [IEEE Trans. Inf. Theory 62(1), 554–577 (2016)]. Moreover, we present a game algebra in this context that generalizes the game algebra for graph homomorphisms given by Helton et al. [New York J. Math. 25, 328–361 (2019)]. We also demonstrate explicit quantum colorings of all quantum complete graphs, yielding the surprising fact that the algebra of the four coloring game for a quantum graph is always non-trivial, extending a result of Helton et al. [New York J. Math. 25, 328–361 (2019)].

Cooperation in regular lattices

In the context of Evolutionary Game Theory, one of the most noteworthy mechanisms to support cooperation is spatial reciprocity, usually accomplished by distributing players in a spatial structure allowing cooperators to cluster together and avoid exploitation. This raises an important question: how is the survival of cooperation affected by different topologies? Here, to address this question, we explore the Focal Public Goods (FPGG) and classic Public Goods Games (PGG), and the Prisoner’s Dilemma (PD) on several regular lattices: honeycomb, square (with von Neumann and Moore neighborhoods), kagome, triangular, cubic, and 4D hypercubic lattices using both analytical methods and agent-based Monte Carlo simulations. We found that for both Public Goods Games, a consistent trend appears on all two-dimensional lattices: as the number of first neighbors increases, cooperation is enhanced. Besides this, clustered topologies, i.e., those that allow two connected players to share neighbors, are the most beneficial to cooperation for the FPGG. The same is not always true for the classic PGG, where having shared neighbors between connected players may or may not benefit cooperation. We also provide a reinterpretation of the classic PGG as a focal game by representing the lattice structure of this category of games as a single interaction game with longer-ranged, weighted neighborhoods, an approach valid for any regular lattice topology. Finally, we show that depending on the payoff parametrization of the PD, there can be an equivalency between the PD and the FPGG; when the mapping between the two games is imperfect, the definition of an effective synergy parameter can still be useful to show their similarities.

Psychological Nash equilibria under ambiguity

Psychological games aim to represent situations in which players may have belief-dependent motivations. In this setting, utility functions are directly dependent on the entire hierarchy of beliefs of each player. On the other hand, the literature on strategic ambiguity in classical games highlights that players may have ambiguous (or imprecise) beliefs about opponents’ strategy choices. In this paper, we look at the issue of ambiguity in the framework of simultaneous psychological games by taking into account ambiguous hierarchies of beliefs and study a natural generalization of the psychological Nash equilibrium concept to this framework. We give an existence result for this new concept of equilibrium and provide examples that show that even an infinitesimal amount of ambiguity may alter significantly the equilibria of the game or can work as an equilibrium selection device. Finally, we look at the problem of stability of psychological equilibria with respect to ambiguous trembles on the entire hierarchy of correct beliefs and we provide a limit result that gives conditions so that sequences of psychological equilibria under ambiguous perturbation converge to psychological equilibria of the unperturbed game.

The Dudeney–Stockmeyer Conjecture

Consider a variant of the famous Tower of Hanoi problem where moves of the discs are allowed along the edges of a connected simple graph D whose vertices represent the vertical pegs of the puzzle. The task is to transfer a tower of n ∈ N discs from one peg to another according to the well-known rules of the classical game corresponding to D ≅ K 3 . Apart from its recreational appeal, the problem brings about fascinating integer sequences engendered by the respective minimum number of moves, i.e. the distance in the canonical metric of the state graph H D n . We construct an algorithm which solves the task for all cases but the exceptional instance of the Linear Tower of Hanoi (i.e. where D is a path graph) in which the transfer is between the two end vertices of D . Optimality of this algorithm is claimed in our central conjecture which is supported by large-scale computational explorations.

Application of Cublak-Cublak Suweng Traditional Game in Thematic Learning of Early Childhood Education

Along with the increasing sophistication of learning systems and learning facilities today, where learning can be done anytime and anywhere. This has a positive value for the presence of technology in the world of education. But besides that, there is a negative impact in that many children are not familiar with traditional games, which can be a means of learning for them and can even have a good effect on social-emotional and cognitive development. However, today's children will find it difficult to find models of traditional games independently if they are not started by the teacher or other people familiar with these classic games. This study uses a qualitative research method with an analytical descriptive approach. As for how to apply the cublak-cublak suweng game, teams or groups are played between 4-5 children. In the division of tasks, one child becomes a game table by bending over, and four become game actors. Children use small stones as tools circled between players by singing cublak-cublak suweng songs. In this game, there is a system of losing and winning. Those who fail are assigned to the game table, while those who win continue the game. The educational value of this game is that each child tries to coordinate with the other, understand and obey the game's rules, and think carefully in guessing questions. There is togetherness between the group or team. This game is straightforward and doesn't take long.

A Q-Learning-Based Approximate Solving Algorithm for Vehicular Route Game

Route game is recognized as an effective method to alleviate Braess’ paradox, which generates a new traffic congestion since numerous vehicles obey the same guidance from the selfish route guidance (such as Google Maps). The conventional route games have symmetry since vehicles’ payoffs depend only on the selected route distribution but not who chose, which leads to the precise Nash equilibrium being able to be solved by constructing a special potential function. However, with the arrival of smart cities, the real-time of route schemes is more of a concerned of engineers than the absolute optimality in real traffic. It is not an easy task to re-construct the new potential functions of the route games due to the dynamic traffic conditions. In this paper, compared with the hard-solvable potential function-based precise method, a matched Q-learning algorithm is designed to generate the approximate Nash equilibrium of the classic route game for real-time traffic. An experimental study shows that the Nash equilibrium coefficients generated by the Q-learning-based approximate solving algorithm all converge to 1.00, and still have the required convergence in the different traffic parameters.