Linear Games Research Articles

Research on Fuzzy Logic Approach to Cost-Benefit Analysis of Multimodal Transportation for China-Europe Liner Game

Abstract The implementation of the “Belt and Road” initiative provides unprecedented development opportunities for China-Europe liner multimodal transportation. In this paper, we constrain the cost-effectiveness of multimodal transportation between China and Europe using linear games from three perspectives: transportation cost, transportation time, and cargo time value. We also establish a cost-effective decision-making model. At the same time, a simulated annealing algorithm is introduced on the basis of a genetic algorithm, an adaptive genetic algorithm based on simulated annealing is designed to solve the model, and the optimal cost-benefit path assessment of China-Europe liner multimodal transportation is carried out based on the fuzzy logic method. Example analysis is carried out with three demands, and the advantages and disadvantages of the set of transportation route schemes are obtained. The optimal cost-effective scheme is selected as Scheme III, which has the highest scheme sticker schedule of 0.841, which verifies the feasibility of the model. The sensitivity analysis of transportation costs and transportation time shows that different transportation costs and times have certain influences on the transportation route selection of other goods. The cost-benefit analysis method for China-European liner multimodal transportation constructed in this paper provides scientific and reasonable guidance for multimodal transportation operators on path selection, which is of certain practical significance.

Fibonacci Level Adjustment for Optimizing Player’s Performance and Engagement

Players’ engagement intensity in computer games is influenced by the level of difficulty the game offers. Traditional game-level plots adopt linear increases that sometimes do not match the users’ skill growth, causing boredom and hampering the users’ further skill growth. In this study, a nonlinear level adjustment scenario was proposed based on the Fibonacci sequence that provides gradual increases in the early stages of the games but more drastic changes in later phases. Here, the game’s difficulty level was automatically decided by a machine learning method. To test the proposed method, comparisons between four level adjustments in computer games: traditional plots, self-selected plots, linear adaptive plots, and the proposed nonlinear adaptive plots were run. The experiment was carried out with 40 testers. The experiment results show that the best player’s peak level in the proposed nonlinear adjustment was twice as high as that of linear adjustment. Also, the number of stages required to reach the peak under the proposed scenario was half that of linear games. This high playing performance goes hand in hand with deep playing engagement. The results demonstrate the efficiency of the proposed level adjustment algorithm.

Near-Vector Spaces Constructed over Z<sub><i>p</i></sub>, for <i>p</i> a Prime

The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Zp for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.

Evolutionary Game Dynamics in a Finite Continental Island Population Model and Emergence of Cooperation

We consider the continental island model for a finite haploid population with a total number of \({\textit{n}}\) demes consisting of one continent and \(n-1\) islands. We assume viability differences in the population captured by a linear game within each deme as a result of pairwise interactions. Assuming weak selection, conservative migration and the limit case of the structured coalescent assumptions, we derive the first-order approximation for the fixation probability of a single mutant, initially introduced in the continent, with respect to the intensity of selection. This result is applied to the case of the iterated Prisoner’s Dilemma, when the resident strategy is always defect and the mutant cooperative strategy is tit-for-tat. In this context, we investigate the condition under which selection favors the emergence of cooperation and we derive an extension of the “one-third law” of evolution. When the continent and the islands are of the same size, we compare the continental island model to its Wright’s island model counterpart. When the islands have the same size, but this size differs from the size of the continent, we investigate how the asymmetry in the deme sizes can better promote the evolution of tit-for-tat compared to its equal deme sizes model counterpart.

Finite-time fuzzy game-based attitude control for on-orbit cooperative transporting

Substructure transporting is an important phase for on-orbit assembly. This paper investigates a problem of designing a control approach for multiple transporting agents attached to one substructure, so as to complete the task of attitude tracking and stabilization of the substructure in the transportation process. A finite-time fuzzy game control method is developed to solve this problem. Using the framework of differential game, a finite-time nonlinear game is formulated based on the individual performance index functions of agents and attitude dynamics of the combination consisting of transporting agents and the substructure, which can reflect the cooperation and coordination between agents. In order to realize finite-time convergence which is more suitable for engineering requirement, a speed function is introduced to transfer finite-time game into infinite-time game. Considering the limited computational ability of agents, Takagi-Sugeno (T-S) fuzzy is incorporated to divide the nonlinear game problem into weighted average of multiple linear games which are easy to get the Nash equilibrium. Numerical simulations validate the efficiency of the proposed method for attitude control and the advantage in less calculation and better performance in dynamics and steady state than the existing methods.

At Play in the Cosmos

At Play in the Cosmos is a game for University-level Astronomy courses. Designed as a collaboration between the Games + Learning + Society Center, an academic center at the University of Wisconsin-Madison, and Norton & Company, Cosmos is intended to support a “game-first” model of curriculum in which students play the game before engaging in other activities. Cosmos includes about 4 hours of game play and spans the entirety of course. It includes over 25 embedded simulations that are also used for homework, lectures, and demonstrations. The design process and resulting artifact was colored by institutional constraints, specifically a lengthy pre-production that demanded extensive documentation. The subsequent development process followed a relatively linear, waterfall process and resulted in linear game. Designers attempted to mediate this linearity through a crafting system that enabled players to explore the Universe and mine celestial bodies for resources. As a game intended to compete in the market, Cosmos included a relatively high production quality led by a team experienced in AAA development processes, and the chapter focuses on the development of art styles, interfaces, and fitting voice overs in on a constrained budget and timeline.

The effect of variability in payoffs on average abundance in two-player linear games under symmetric mutation

Classical studies in evolutionary game theory assume constant payoffs. Randomly fluctuating environments in real populations make this assumption idealistic. In this paper, we study randomized two-player linear games in a finite population in a succession of birth-death events according to a Moran process and in the presence of symmetric mutation. Introducing identity measures under neutrality that depend on the mutation rate and calculating these in the limit of a large population size by using the coalescent process, we study the first-order effect of the means, variances and covariances of the payoffs on average abundance in the stationary state under mutation and selection. This shows how the average abundance of a strategy is driven not only by its mean payoffs but also by the variances and covariances of its payoffs. In Prisoner’s Dilemmas with additive cost and benefit for cooperation, where constant payoffs always favor the abundance of defection, stochastic fluctuations in the payoffs can change the strategy that is more abundant on average in the stationary state. The average abundance of cooperation is increased if the variance of any payoff to cooperation against cooperation or defection, or their covariance, is decreased, or if the variance of any payoff to defection against cooperation or defection, or their covariance, is increased. This is also the case for a Prisoner’s Dilemma with independent payoffs that is repeated a random number of times. As for the mutation rate, it comes into play in the coefficients of the variances and covariances that determine average abundance. Increasing the mutation rate can enhance or lessen the condition for a strategy to be more abundant on average than another.

Pretending volunteers

I introduce the ability to pretend in generalized public goods games. Pretending contributes nothing, but it costs less than helping and confers honor if believed and shame otherwise. The ability to pretend weakly decreases provision. High values of honor increase provision, especially when coupled with high shame. In the long run, pretenders dilute honor and discourage real helpers; authenticated help at a premium can remedy this. Heterogeneity in looking versus feeling good explains why helpers, bystanders, and pretenders often coexist. High thresholds increase helpers and also pretenders, who come mostly from would-be helpers. Linear games have three possible equilibria.

A game-theoretic approach for stochastic estimation of equilibrium in land use data: stochastic estimation of equilibrium in land use data

This work is focused on the use of linear games in the normal form for evaluation of Nash equilibria probability distribution in spatial data eg land use. Spatial data with varied content represent the observed state and, as a rule, do not automatically offer information about what that state is the result of. However, individual cases can be defined in such data, representing, for example, different sizes or degrees of representation of selected characteristics. The essence of the proposed approach is that such data pertaining to individual cases are regarded as payoff values of multiple interacting entities and can form a matrix of a symmetric linear game in the normal form. For this game, an NE representing a particular distribution of strategies of interacting entities can then be determined. This distribution assigns to each case the share of NE depending on the respective location in the symmetric game matrix. However, spatial data does not provide any information for the specific design of this deployment. The proposed solution is therefore stochastic: all effective permutations of the game matrix or a multidimensional symmetric game configuration leading to a different result for the NE distribution are evaluated. The result are values of the occurrence of NE probability for individual evaluated cases. The properties of the method are tested on the example of a practical application. The results show that the method is applicable for evaluating the spatial distribution of the land use stability.

Backward induction in games without perfect recall

The equilibrium concepts that we now think of as various forms of backwards induction, namely, subgame perfect equilibrium (Selten, 1965), perfect equilibrium (Selten, 1975), sequential equilibrium (Kreps and Wilson, 1982), and quasi-perfect equilibrium (van Damme, 1984), while formally well defined in a wider class of games, are explicitly restricted to games with perfect recall.We argue that in games without perfect recall the original definitions are inappropriate. Our reading of the original papers is that the authors were aware that their definitions did not formally require the assumption of perfect recall but they were also aware that without the assumption of perfect recall the definitions they gave were not the “correct” ones. We give definitions of these concepts that identify the same outcomes in games with perfect recall and behave well in linear games without perfect recall.

Using Number Games to Support Mathematical Learning in Preschool and Home Environments

ABSTRACT Research Findings: This study evaluated the effects of an early mathematics intervention designed to engage preschool children, their teachers, and their families in an interactive mathematics game. Previous research shows that playing this specific type of linear board game results in increased numerical skills and understanding in young children under controlled conditions. The current study explores the game’s effectiveness under more natural conditions – a classroom-based intervention with teachers and a related family engagement component. A pilot study informed a larger-scale experiment, comparing outcomes in multiple skill domains (verbal counting, counting on, number line estimation, numeral magnitude, and numeral recognition) with those of control group children who played memory matching games. The analysis sample included 256 children in classrooms that were randomly selected from volunteer teachers and randomly assigned within 10 centers to either the treatment group (mathematics games, 23 teachers) or the comparison condition (matching games, 22 teachers). The intervention resulted in positive impacts for numeral identification, but not the other domains. The number of math games played was positively associated with verbal counting. No impact of family game play was found; however, implementation challenges could have influenced this finding. Practice or Policy: Including simple, research-informed mathematics board games in the preschool classroom can support mathematical learning. Future work must include families and educators in the design of these supports.

English

In this paper, we define bi-linear games as a generalization of the bimatrix games. In particular, we generalize concepts like the value and equilibrium of a bimatrix game to the general linear transformations defined on a finite dimensional space. For a special type of Z-transformation we observe relationship between the values of the linear and bi-linear games. Using this relationship, we prove some known classical results in the theory of linear complementarity problems for this type of Z-transformations.

The Pursuit Problem for Linear Games with Integral Constraints on Players’ Controls

The Pursuit Problem for Linear Games with Integral Constraints on Players’ Controls

Задача преследования для линейных игр с интегральными ограничениями на управления игроков

Задача преследования для линейных игр с интегральными ограничениями на управления игроков

A Linear Game Framework for Defending Power Systems Against Intelligent Physical Attacks

Game theory has recently been applied for analyzing the security of power systems under intelligent attack threats. This letter presents a linear game framework for optimal allocation of a defense budget to confront intelligent attacks on power systems. The presented framework offers the advantage that it can be applied in large power systems with a large number of components under attack threat without too much complexity. The presented linear framework is successfully applied on test systems.

Fuzzy Harsanyi solution for a kind of fuzzy coalition games

The fuzzy linear game in Ref. [32] is a class of fuzzy cooperative games with fuzzy coalition (fuzzy coalition game for short), which admits the difference of interactions for different fuzzy coalitions. The fuzzy Shapley value for fuzzy linear game has been studied. As Shapley value is just one point in the Harsanyi solution, it is interesting to study the explicit form of Harsanyi solution in the fuzzy coalition game. This paper defines the fuzzy Harsanyi solution which distributes the Harsanyi dividends such that the dividend shares of players in each fuzzy coalition are proportional to the corresponding players' participation index. When the fuzzy coalition payoff is average distributed between players in the fuzzy coalition, the fuzzy Harsanyi solution also coincides with the fuzzy Shapley value just as their relationship in a crisp cooperative game. We provide two axiomatic characterizations for the fuzzy Harsanyi solution: one uses axioms, and the other uses distribution matrices. The fuzzy Harsanyi solution is a unique value on the fuzzy linear game that satisfies fuzzy efficiency, fuzzy null player and fuzzy additivity property. Meanwhile, based on probability distribution, fuzzy Harsanyi solution is seen as an expected marginal contribution of each player in the fuzzy coalition, which provides more choices for players in the fuzzy coalition.

Device-independent quantum secret sharing in arbitrary even dimensions

We present a device independent quantum secret sharing scheme in arbitrary even dimension. We propose a $d$-dimensional $N$-partite linear game, utilizing a generic multipartite higher dimensional Bell inequality, a generalization of Mermin's inequality in the higher dimension. Probability to win this linear game defines the device independence test of the proposed scheme. The security is proved under causal independence of measurement devices and it is based on the polygamy property of entanglement. By defining $\epsilon_{cor}$-correctness and $\epsilon^c$-completeness for a quantum secret sharing scheme, we have also shown that the proposed scheme is $\epsilon_{cor}$-correct and $\epsilon^c$-complete.

Do Young People Adapt Their Prosocial Behaviour to That of Their Peers? An Experimental Exploration

Moral decisions – that is, decisions that consider the consequences for the welfare of others – can be highly inconsistent across contexts. Here, we explore whether the altruism of young people is related to their willingness to cooperate with others, even in groups comprising non-reciprocating peers. Using the distinction between normative and cognitive expectations, we address this topic conducting several lab-in-the-field experiments with high-school students who played the dictator and linear public good games. We found that the altruism of young people in the dictator game and cooperation in the public good game were related, but only in the first rounds of the public good game. This indicates that young people orient their prosocial behaviour based on cognitive expectations, that is, they consider the information they receive regarding the free riding behaviour of peers and adapt their own. Nonetheless, young people who demonstrated high altruism tended to cooperate unconditionally, regardless of whether they belonged to a cooperative or uncooperative group, and despite disappointments. Finally, self-regarding young people were less likely to defect among cooperative peers. Therefore, group characteristics provide the boundary conditions for the consistency of the prosocial behaviour of young people. Some conceptual and policy implications are discussed.

Formation of Bidding Zones Based on Linear Bottleneck Games

Predefined bidding zone formation is an essential requirement in some of the congestion management schemes. In a meshed network, forming bidding zones commensurate with the transmission bottlenecks is a challenge. A rare or no occurrence of congestion within zonal periphery is usually the basis for its formation. In this paper, the concept of linear bottleneck games is proposed for the formation of congestion-free bidding zones that include nodes with similar contribution to the congestion. This is achieved in two primary steps: first is to split the network into multiple zones on the basis of locational marginal prices using diakoptics; second is to identify the optimal zonal combination and crucial nodes by solving a primal-dual linear programming model. Its efficacy is explained on a six-bus system with additional results on the IEEE 39-bus system and the 193-bus Western regional grid of India.

Research on the Optimization of Capital for the Governance of Bulk Coal in Beijing-Tianjin-Hebei Region

Beijing, Tianjin and Hebei each contributed to the comprehensive governance of bulk coal to treat bulk coal pollution in a mutually beneficial way in 2017. The cooperative game theory is used in this paper to study the environmental benefits and cost effectiveness brought about by this comprehensive governance strategy, primarily focusing on the issue of how to maximize the environmental benefits by choosing an appropriate strategy since the benefits to Beijing, Tianjin and Hebei are closely related. Therefore, the linear optimization, game theory and Shapley value method in the cooperative game model are used to find the ways to minimize the total governance cost of bulk coal in the three areas. In addition, the issues of how to carry out rational distribution and transfer of governance capital among the three places are explored according to the actual amounts of consumption of bulk coal, the influence of the coal burning on the PM2.5 and the actual cost of coal governance in Beijing, Tianjin and Hebei in 2017. The results show that the governance task in Hebei Province is the most onerous, and requires more investment than the other two cities. Thus, it requires the support from other two cities, with the amount of increased capital required of about 600 million Yuan. At the same time, the cost saved after optimization in Tianjin is calculated to be the largest, which thus can be adjusted appropriately and allocated to Hebei for the governance of bulk coal. The model constructed in this paper can not only be used to solve the issues related to bulk coal consumption in Beijing, Tianjin and Hebei, but also to carry out the effective distribution of capital, by which a win-win scenario among the three places can be achieved.