Pure-strategy Game Research Articles

Using Game Theory to Analyze the Interaction between Teachers and Students in the Teaching of Civics in College Courses

Abstract In this paper, firstly, on the basis of Marx’s theory of intersubjectivity, we use the concept of teachers and students as the main body of each other to construct the interactive teaching mode and mechanism of teachers and students in Civics courses and actively explore the path and prospect of interactive teaching of Civics in courses in the new era. Then we use the pure strategy game in game theory to determine the performance production function, and then we use Nash equilibrium to obtain the teacher utility function and student utility function on the basis of the performance production function so as to further construct the game model of teacher-student behavior in the teaching process of Civics courses, and analyze the teacher-student interaction in the Civics of higher education courses by using the game model. The results show that in the pure strategy game analysis of teacher-student behavior, 0.3872 teachers will choose to reduce teaching inputs, while the other 0.6128 teachers will choose to reduce teaching inputs to “almost no” or “very little”, i.e., the optimal choice strategy is “no” or “very little”, i.e., the optimal choice strategy is “no” or “very little”. The optimal choice strategy is “no reduction in instructional inputs”. In the Nash equilibrium analysis of teacher-student behavior, the equilibrium value of the teacher-student behavior game is (42.22% and 64.59%), and teachers and students need to continuously improve their behavioral strategy choices in order to achieve the maximum utility value of each other. This study improves the quality of teaching and ultimately achieves the objective of Civic Education.

Attacker-Centric View of a Detection Game against Advanced Persistent Threats

Advanced persistent threats (APTs) are a major threat to cyber-security, causing significant financial and privacy losses each year. In this paper, cumulative prospect theory (CPT) is applied to study the interactions between a cyber system and an APT attacker when each of them makes subjective decisions to choose their scan interval and attack interval, respectively. Both the probability distortion effect and the framing effect are applied to model the deviation of subjective decisions of end-users from the objective decisions governed by expected utility theory, under uncertain attack durations in a pure-strategy game and scan interval in a mixed-strategy game. The CPT-based APT detection game incorporates both the probability weighting distortion and the framing effect of the subjective attacker and security agent of the cyber system, rather than discrete decision weights, as in earlier prospect theoretic study of APT detection. The Nash equilibria of the APT detection game are derived, showing that a subjective attacker becomes risk-seeking if the frame of reference for evaluating the utility is large, and becomes risk-averse if the frame of reference for evaluating the utility is small. A policy hill-climbing (PHC) based detection scheme is proposed to increase the policy uncertainty to fool the attacker in the dynamic game, and a “hotbooting” technique that exploits experiences in similar scenarios to initialize the quality values is developed to accelerate the learning speed of PHC-based detection. A practical example of a mobile network is presented to evaluate the performance of the proposed detection strategy. Simulation results show that the proposed strategy can improve detection performance with a higher data protection level and utilities of the cloud in the presence of an attacker compared with a standard Q-learning strategy.

Development and application of coupled system dynamics and game theory: A dynamic water conflict resolution method.

Conflicts over water resources can be highly dynamic and complex due to the various factors which can affect such systems, including economic, engineering, social, hydrologic, environmental and even political, as well as the inherent uncertainty involved in many of these factors. Furthermore, the conflicting behavior, preferences and goals of stakeholders can often make such conflicts even more challenging. While many game models, both cooperative and non-cooperative, have been suggested to deal with problems over utilizing and sharing water resources, most of these are based on a static viewpoint of demand points during optimization procedures. Moreover, such models are usually developed for a single reservoir system, and so are not really suitable for application to an integrated decision support system involving more than one reservoir. This paper outlines a coupled simulation-optimization modeling method based on a combination of system dynamics (SD) and game theory (GT). The method harnesses SD to capture the dynamic behavior of the water system, utilizing feedback loops between the system components in the course of the simulation. In addition, it uses GT concepts, including pure-strategy and mixed-strategy games as well as the Nash Bargaining Solution (NBS) method, to find the optimum allocation decisions over available water in the system. To test the capability of the proposed method to resolve multi-reservoir and multi-objective conflicts, two different deterministic simulation-optimization models with increasing levels of complexity were developed for the Langat River basin in Malaysia. The later is a strategic water catchment that has a range of different stakeholders and managerial bodies, which are however willing to cooperate in order to avoid unmet demand. In our first model, all water users play a dynamic pure-strategy game. The second model then adds in dynamic behaviors to reservoirs to factor in inflow uncertainty and adjust the strategies for the reservoirs using the mixed-strategy game and Markov chain methods. The two models were then evaluated against three performance indices: Reliability, Resilience and Vulnerability (R-R-V). The results showed that, while both models were well capable of dealing with conflict resolution over water resources in the Langat River basin, the second model achieved a substantially improved performance through its ability to deal with dynamicity, complexity and uncertainty in the river system.

Coordinated multi-aircraft 4D trajectories planning considering buffer safety distance and fuel consumption optimization via pure-strategy game

In this paper, we consider a coordinated multi-aircraft 4D (3D space plus time) trajectories planning problem which is illustrated by planning 4D trajectories for aircraft traversing an Air Traffic Control (ATC) sector. The planned 4D trajectories need to specify each aircraft’s position at any time, ensuring conflict-free and reducing fuel and delay costs, with possible aircraft maneuvers such as speed adjustment and flight level change. Different from most existing literature, the impact of buffer safety distance is also under consideration, and conflict-free is guaranteed at any given time (not only at discrete time instances). The problem is formulated as a pure-strategy game with aircraft as players and all possible 4D trajectories as strategies. An efficient maximum improvement distributed algorithm is developed to find equilibrium at which every aircraft cannot unilaterally improve further, without enumerating all possible 4D trajectories in advance. Proof of existence of the equilibrium and convergence of the algorithm are given. A case study based on real air traffic data shows that the algorithm is able to solve 4D trajectories for online application with estimated 16.7% reduction in monetary costs, and allocate abundant buffer safety distance at minimum separation point. Scalability of the algorithm is verified by computational experiments.

On the IENBR-solvability of two-person finite games

We show that a two-person finite game is solved by the iterated elimination of never best responses (IENBR) if and only if it is best response acyclic and strongly solvable in the sense of Nash (1951). Thus the rationalizable strategies (Bernheim, 1984; Pearce, 1984) are equivalent to the Nash equilibrium strategies in two-person finite games if and only if the two conditions are met. We prove this for both mixed strategy games and pure strategy games.

Evolutionary stability of mixed strategies on graphs

Up to the present time, the study of evolutionary dynamics mostly focused on pure strategy games in finite discrete strategy space, either in well-mixed or structured populations. In this paper, we study mixed strategy games in continuous strategy space on graphs of degree k. Each player is arranged on a vertex of the graph. The edges denote the interaction between two individuals. In the limit of weak selection, we first derive the payoff functions of two mixed strategies under three different updating rules, named birth–death, death–birth and imitation. Then we obtain the conditions for a strategy being a continuously stable strategy (CSS), and we also confirm that the equilibrium distribution corresponding to the CSS is neighborhood attracting and strongly uninvadable. Finally, we apply our theory to the prisoner’s dilemma and the snowdrift game to obtain possible CSS. Simulations are performed for the two special games and the results are well consistent with the conclusions we made.

UTILIZAÇÃO DA ESTRATÉGIA PURA DA TEORIA DOS JOGOS PARA DETERMINAÇÃO DO PREÇO DE VENDA

<p>O estudo teve por objetivo verificar o preço de venda ideal de acordo com a estratégia pura da Teoria dos Jogos em uma empresa hoteleira. A metodologia utilizada foi descritiva, quantitativa e trata-se de um estudo de caso. O estudo de caso foi realizado em uma empresa de prestação de serviços no ramo hoteleiro localizada no norte do estado do Rio Grande do Sul, a qual oferece três tipos de diárias, <em>standard</em>, <em>standard</em> superior e suíte. Foram gerados oito preços de venda para cada serviço ofertado por quatro sistemas de custeio e duas métricas de rateio dos gastos indiretos, com a finalidade de encontrar o preço concorrente com as demais empresas. Constatou-se que os preços de venda gerados pelo sistema de custeio direto ou variável foi o retratado pelos três tipos de serviços, o que representa a melhor opção diante dos preços da concorrência.</p>

Demand-Aware Network Function Placement

Network function virtualization is an emerging network resource utilization approach which decouples network functions from proprietary hardware and enables adaptive services to end-user requests. To accommodate the network function requests, network function instances are created and deployed at runtime. In this paper, we study a network virtualization scheme to orchestrate and manage networking and network function services. We propose an integrated design for network function instance allocation and end-to-end demand realization sharing the same physical substrate network and demonstrate that the corresponding network design problem is NP complete. A mixed-integer programming formulation is proposed first to find its optimal solution, followed by a two-player pure-strategy game model which captures the competition on physical resources between network function instance allocation and routing. We then design an algorithm based on iterative weakly dominated elimination in Game Theory. Computational results demonstrate the value of the integrated approach and its ability to allocate network function instances supporting end-to-end requests with limited physical resources in optical networks.

A Game Theoretic Bus Selection Method for Loads in Multibus DC Power Systems

DC power systems with multiple buses for redundancy are more reliable and provide reconfiguration options. A game-theoretic-based modeling approach for bus selection is proposed in this paper, which is based on local information of the player and does not require a centralized controller. The initial section provides the modeling and optimization of a single-input player. This modeling mainly follows on the players' local objectives and discrete choices of bus connections. Therefore, in this case, the controller obtains Nash equilibrium (NE) for the pure strategy game. Then, the approach is extended for the integration of global objectives with minimal communication. In addition, different objective priorities are integrated into the optimization routine. Next, the analysis is extended to multi-input player situations which are related to the class of mixed and continuous strategy games. This modeling is important, since the payoff matrix approach does not find an NE in all cases. Finally, the bus selection modeling is carried out by taking the system dynamics into account. This is important for the cases where the system has sudden load or source fluctuations. Experimental results are obtained, which validate the theory.

Repeated Goofspiel: A Game of Pure Strategy

In this paper, we examine a pure strategy game known as Goofspiel and report on the results of round-robin competitions between 14 programs designed to play this game. Goofspiel is a two-person card game that is easy to play. However, playing this game successfully has proven to be a difficult task. There is no known “good” strategy for Goofspiel. This is the first time that playing Goofspiel has been examined in a context of a round-robin competition between programs. None of the participating programs won consistently against its rivals. Thus, no clear dominating strategy of play has emerged. In this respect, Goofspiel is similar to the Prisoner's Dilemma where Tit-for-Tat has proven to be a good strategy against many but not against all. This paper introduces Repeated Goofspiel and presents preliminary experimental results. We hope it will motivate further research into this fascinating game.

Coalition-Proofness in Aggregative Games with Strategic Substitutes and Externalities

We examine the welfare properties, coalition-proofness and order-theoretical structure of the set of Nash equilibria in pure strategy games with a-aggregative simple strategic substitutes and monotone a-aggregative externalities. For these games, we prove the equivalence among the set of Nash equilibria, the set of coalition-proof Nash equilibria under strong Pareto dominance and the set of Nash equilibria that are strongly Pareto undominated by other Nash equilibria; besides, we prove that the fixed points of some extremal selections from the joint best reply correspondence are both coalition-proof Nash equilibria under weak Pareto dominance and weakly Pareto undominated by other Nash equilibria. We also point out some errors in the relevant literature. Finally, we show various applications of our results to classes of games of economic interest.

Modelling social evolution: the relative merits and limitations of a Hamilton's rule-based approach

Lehmann & Keller (2006) convincingly argue that cooperation or altruism can evolve only when at least one of the following conditions are met: (i) cooperation has direct personal benefits, (ii) individuals are genetically related, (iii) individuals have information on the likely behaviour of others or (iv) individuals recognize other cooperators through a phenotypic label (green beard recognition). The first condition is quite obvious. The three others are also intuitive, given that they provide various conditions under which interacting individuals are positively related, meaning more likely than chance to interact with fellow cooperators (Frank, 1998; Pepper & Smuts, 2002; Foster & Wenseleers, 2006; Foster et al., 2006). By focusing on costs and benefits and relatedness, Lehmann and Keller (2006) are adopting an inclusive fitness or Hamilton’s rule-based approach to classify social evolution models (Hamilton, 1964). Personally, I believe a Hamiltonian perspective is indeed a very intuitive one, and should be adopted more widely. This is true particularly in the area of game theory, where currently little effort is made to interpret results this way, and models are frequently simulation-based, making general, intuitive interpretation of results difficult. In fact, in my own work, Hamilton’s rule has always taken a central place in the derivation and interpretation of model results (e.g. Wenseleers et al., 2003, 2004a, b; Ratnieks et al., 2006). At the same time, however, one may also wonder whether it is possible to translate every single social evolution model into the form of Hamilton’s rule. Here, I am skeptical, the reason being that Hamilton’s rule has well-known limitations. In particular, Hamilton’s rule only works correctly under weak selection and additive gene action (Cavalli-Sforza & Feldman, 1978; Michod, 1982; Grafen, 1985; Bulmer, 1994; Hamilton, 1964, 1995; Frank, 1997; Roze & Rousset, 2003; Rousset, 2004). In addition, evolution is normally assumed to be close to equilibrium, with most of the population fixed for a single type (Frank, 1998). Finally, with Hamilton’s rule being a deterministic equation, it entirely neglects stochasticity, and thus ignores the possibility for deleterious altruistic genotypes to go to fixation as a result of drift (Frank, 1997), which models have shown to be quite possible in small populations (Eshel, 1972; Rousset, 2004). In the section below I will give two worked-out examples where some of these limitations come into play and where, due to violations of assumptions, Hamilton’s rule does not correctly predict evolutionary change. The implication is that partitioning selection into direct and indirect fitness components is not always as straightforward as Lehmann and Keller make out. In many cases, the conditions under which a cooperative genotype would spread relative to a noncooperative one simply cannot be written in the form of Hamilton’s rule. In such situations, the inclusive fitness framework of Lehmann and Keller cannot be used to accurately classify models.

An Econometric Analysis of Brand‐Level Strategic Pricing Between Coca‐Cola Company and PepsiCo.

We investigate market structure and strategic pricing for leading brands sold by Coca‐Cola Company and PepsiCo. in the context of a flexible demand specification (i.e., nonlinear AIDS) and structural price equations. Our flexible and generalized approach does not rely upon the often used ad hoc linear approximations to demand and profit‐maximizing first‐order conditions, and the assumption of Nash‐Bertrand competition. We estimate a conjectural variation model and test for different brand‐level pure strategy games. This approach of modeling market competition using the nonlinear Full Information Maximum Likelihood (FIML) estimation method provides insights into the nature of imperfect competition and the extent of market power. We find no support for a Nash‐Bertrand or Stackelberg Leadership equilibrium in the brand‐level pricing game. Results also provide insights into the unique positioning of PepsiCo.'s Mountain Dew brand.