Pure Strategy Research Articles

Stationary Markov Equilibrium Strategies in Asynchronous Stochastic Games: Existence and Computation

We study Asynchronous Dynamic games and show that in games with a finite state space and finite action sets, one can obtain the pure strategy Markov perfect equilibrium by using a simple backward induction method when the time period for the game is finite. The equilibrium strategies for games with an infinite horizon are then obtained as the point-wise limit of the equilibrium strategies of a sequence of finite horizon games, where the finite horizon games are truncated versions of the original game with successively longer time periods. We also show that if the game has a fixed K-period cycle, then there is a stationary Markov equilibrium. Using these results, we derive an algorithm to compute the equilibrium strategies. We test the algorithm in three experiments. The first is a two-player asynchronous game with three states and three actions. In the second experiment, we compute the equilibrium of a cybersecurity game in which there are two players, an attacker and a defender. In the third experiment, we compute the stationary equilibrium of a duopoly game with two firms that choose an output in alternate periods.

Penerapan Teori Permainan dalam Menentukan Strategi Pemasaran Optimum pada Produk Mi Instan (Mie Sedaap, Gaga, dan Supermi) di Lingkungan Mahasiswa Matematika Universitas Sumatera Utara

Instant noodle consumption in Indonesia has continued to increase in the last few years, which indicates that there are more business opportunities for instant noodle products in Indonesia. Proved by the number of instant noodle brands scattered on the market. This has led to increased competition among companies in order to be the best in the eyes of consumers. Marketing strategies are needed to win competition as well as increase sales, ranging from taste innovations, prices, product quality, promotions, and so on. In this study, game theory is used to investigate the competition between Mie Sedaap, Gaga, and Supermi. Using pure strategy is obtained game value that shows that the optimal strategy for Mie Sedaap is ease of purchase, the optimum strategy for Gaga is packaging strategy, and the optimum strategy for Supermi is price strategy.

Enhancing Production in Robot-Enabled Manufacturing Systems: A Dynamic Model and Moving Horizon Control Strategy for Mobile Robot Assignment

Abstract This paper presents a dynamic mathematical model for a robot-enabled manufacturing system, where mobile robots independently manage workstation tasks. Each robot possesses one or multiple skills, enabling collaborative work at workstations. A real-time robot assignment problem is formulated to maximize production of the system, and a novel control strategy is developed to address this problem. Leveraging system properties derived from the model and moving window downtime prediction, the problem of maximizing system production is transformed into a more tractable control problem focused on identifying and achieving a defined ideal clean configurations. The proposed solution significantly outperforms various benchmarks, including a pure reinforcement learning-based strategy, underscoring the importance of system understanding and its crucial role in enhancing flexibility and productivity in manufacturing systems.

Insider trading in discrete time Kyle games

AbstractWe present a new discrete time version of Kyle’s (Econometrica 53(6):1315–1335, 1985) classic model of insider trading, formulated as a generalised extensive form game. The model has three kinds of traders: an insider, random noise traders, and a market maker. The insider aims to exploit her informational advantage and maximise expected profits while the market maker observes the total order flow and sets prices accordingly. First, we show how the multi-period model with finitely many pure strategies can be reduced to a (static) social system in the sense of Debreu (Proc Natl Acad Sci 38(10):886–893, 1952) and prove the existence of a sequential Kyle equilibrium, following Kreps and Wilson (Econometrica 50(4):863–894, 1982). This works for any probability distribution with finite support of the noise trader’s demand and the true value, and for any finite information flow of the insider. In contrast to Kyle (1985) with normal distributions, equilibria exist in general only in mixed strategies and not in pure strategies. In the single-period model we establish bounds for the insider’s strategy in equilibrium. Finally, we prove the existence of an equilibrium for the game with a continuum of actions, by considering an approximating sequence of games with finitely many actions. Because of the lack of compactness of the set of measurable price functions, standard infinite-dimensional fixed point theorems are not applicable.

Taxation Can Significantly Enhance The Effectiveness of Reward and Punishment Mechanisms in The N-Person Snowdrift Game

We extend the reward and punishment mechanisms in the N-person evolutionary snowdrift game (NSG) model by constructing a tax-based pure punishment NSG model and a tax-based pure reward NSG model. Using replicator dynamics, we established two sets of dynamic equations that describe the evolution of the frequencies of the three strategies. Over longer time scales, both systems exhibit stable states involving two strategies, with the exclusion of the third. Introducing tax factors into the reward and punishment mechanisms significantly increases the proportion of cooperators in the steady state and eliminates defectors, with the time to reach the steady state depending on the tax rate. Moreover, we found that tax-based pure reward strategies are more conducive to fostering cooperative behavior within the system compared to tax-based pure punishment strategies. We employed numerical algorithms to simulate the replicator dynamics, and the results of the dynamic equations were in perfect agreement with the numerical simulations.

Multi-iteration active learning for the composition design of potassium–sodium niobate ceramics with enhanced piezoelectric coefficient

The piezoelectricity of piezoceramics considerably depends on the doped compositions. However, the conventional trial-and-error approach to composition design is time-consuming and inefficient when searching for high-performance piezoceramics with various dopants. In this study, we introduce a data-driven framework to accelerate the design and discovery of lead-free (K,Na)NbO3 (KNN) materials with enhanced piezoelectric performance. The proposed framework integrates machine learning with feature engineering, surrogate-based optimisation, and experimentation in an active learning loop. Using feature engineering techniques, we demonstrated that the piezoelectric coefficient d33 of KNN materials can be predicted based on a set of elemental and atomic properties. We evaluated six machine learning models and found that support vector regression with a radial basis function kernel achieved high accuracy in predicting the d33 values of KNN ceramics. After three iterations of experimentation and optimisation, we identified an optimal composition with a relatively high d33 of ∼353 pC/N from thousands of possible compositions using a pure exploitation strategy. This study demonstrates an efficient and systematic approach to the composition design of KNN-based piezoceramics, which can be applied to investigate the diverse functional properties of other materials.

OPTIMIZING PROCESSOR WORKLOADS AND SYSTEM EFFICIENCY THROUGH GAME-THEORETIC MODELS IN DISTRIBUTED SYSTEMS

The primary goal of this research is to examine how different strategic behaviors adopted by processors affect the workload management and overall efficiency of the system. Specifically, the study focuses on the attainment of a pure strategy Nash Equilibrium and explores its implications on system performance. In this context, Nash Equilibrium is considered as a state where no player has anything to gain by changing only their own strategy unilaterally, suggesting a stable, yet not necessarily optimal, configuration under strategic interactions. The paper rigorously develops a formal mathematical model and employs extensive simulations to validate the theoretical findings, thus ensuring the reliability of the proposed model. Additionally, adaptive algorithms for dynamic task allocation are proposed, aimed at enhancing system flexibility and efficiency in real-time processing environments. Key results from this study highlight that while Nash Equilibrium fosters stability within the system, the adoption of optimal cooperative strategies significantly improves operational efficiency and minimizes transaction costs. These findings are illustrated through detailed 3D plots and tabulated results, which provide a detailed examination of how strategic decisions influence system performance under varying conditions, such as fluctuating system loads and migration costs. The analysis also examines the balance between individual processor job satisfaction and overall system performance, highlighting the effect of rigid task reallocation frameworks. Through this study, the paper not only improves our understanding of strategic interactions within computational systems but also provides key ideas that could guide the development of more efficient computational frameworks for various applications.

The evolution of fear-acquisition strategies under predation

Fear is a taxonomically widespread behavioral response that functions to keep individuals out of danger. Empirical research has demonstrated that a diverse set of strategies are used in order to acquire a fear response across animals. Animals often use a mixed strategy: fear is acquired both innately and through learning. Despite the ubiquity of the fear response, and its established importance for shaping predator–prey interactions, little is known about why different fear acquisition strategies evolve or why mixed strategies appear common. Here, we model the evolution of fear acquisition (learning versus innate) under predation. We assume a tradeoff where individuals that learn fear are at higher risk from predators initially, but eventually obtain a lower risk as they survive predation attempts. We find that frequent predator encounters, predators that are not very dangerous, and effective learning favor the evolution of learned fear. Only pure strategies of fear acquisition evolve unless individuals suffer from either a cost to fear or, especially, a cost to learning, either of which can lead to the evolution of mixed strategies. Our results thus shed light onto the evolution of mixed fear acquisition strategies and open the door to further research on the evolution of fear acquisition.

Tullock contest with reference‐dependent preferences

AbstractWe study the Tullock contest model with loss aversion and endogenously formed reference points. In a contest with n possibly heterogeneous players and convex effort costs, we establish sufficient conditions for a unique Nash equilibrium in pure strategies. Subsequently, we analyze the impact of loss aversion on players' spending behavior, probability of winning, and rent dissipation.

The Minimax Property in Infinite Two-Person Win-Lose Games

We explore a version of the minimax theorem for two-person win-lose games with infinitely many pure strategies. In the countable case, we give a combinatorial condition on the game which implies the minimax property. In the general case, we prove that a game satisfies the minimax property along with all its subgames if and only if none of its subgames is isomorphic to the “larger number game.” This generalizes a recent theorem of Hanneke, Livni, and Moran. We also propose several applications of our results outside of game theory.

2D Janus carrier-enabled trojan horse: Gallium delivery for the sequential therapy of biofilm associated infection

Biofilm-associated infections (BAIs) continue to pose a major challenge in the medical field. Nanomedicine, in particular, promises significant advances in combating BAIs through the introduction of a variety of nanomaterials and nano-antimicrobial strategies. However, studies to date have primarily focused on the removal of the bacterial biofilm and neglect the subsequent post-biofilm therapeutic measures for BAIs, rendering pure anti-biofilm strategies insufficient for the holistic recovery of affected patients. Herein, we construct an emerging dual-functional composite nanosheet (SiHx@Ga) that responds to pHs fluctuation in the biofilm microenvironment to enable a sequential therapy of BAIs. In the acidic environment of biofilm, SiHx@Ga employs the self-sensitized photothermal Trojan horse strategy to effectively impair the reactive oxygen species (ROS) defense system while triggering oxidative stress and lipid peroxidation of bacteria, engendering potent antibacterial and anti-biofilm effects. Surprisingly, in the post-treatment phase, SiHx@Ga adsorbs free pathogenic nucleic acids released after biofilm destruction, generates hydrogen with ROS-scavenging and promotes macrophage polarization to the M2 type, effectively mitigating damaging inflammatory burst and promoting tissue healing. This well-orchestrated strategy provides a sequential therapy of BAIs by utilizing microenvironmental variations, offering a conceptual paradigm shift in the field of nanomedicine anti-infectives.

Strict liability versus negligence in the case of data breach

This study compares the efficiency of the strict liability and negligence rules in the case of a data breach. Contrary to standard results, we demonstrate that the strict liability rule cannot induce the efficient activity and care levels of a data controller. This is mainly due to possible positive externalities from data breaches, unlike in usual tort cases. We show that the negligence rule is more efficient than the strict liability rule if the positive externality is sufficiently large. The main insight is carried over to the case where a data controller uses a data processor to process personal information before selling it in the market. If hackers are explicitly introduced into the model, the care level of the data controller increases with the hacking activity, whereas the latter level decreases with the former. In this model, if the hacker’s gain is sufficiently small, the negligence rule can be made more efficient by adjusting due care to a harsher level than the equilibrium care level under strict liability to reduce hacking activity, although a pure strategy equilibrium may not exist for some due care levels.

Hybrid strategy and its effect on the market performance of family-business SMEs: the mediating role of innovation

Purpose For this paper, the authors focus on Porter’s competitive advantage. Hybrid strategy refers to how a firm creates value vis-à-vis competitors by simultaneously relying on lower costs and greater differentiation to achieve a competitive advantage. This strategy emphasises both and aims to provide much more monetary value to customers through the combination of reduced cost and a higher rate of differentiation. In addition, this research focuses on family small and medium-sized enterprises (SMEs), because they have particularities arising from the incorporation of family members both as owners of the SME and in managerial positions. The porpose of this study is to analyse whether the existing differences produced by the role of the family in strategic decision-making and the concentration of family power have a higher impact on performance and innovation than non-family SMEs. Design/methodology/approach Structural equation modelling was used to analyse Spanish firms with fewer than 250 employees. This study randomly selected SMEs operating in Spain from the Spanish Central Business Directory (2021) database. The overall sample design was based on stratified sampling. Findings SMEs are facing new challenges, and this has led to the emergence of new competitive strategies. Companies have started to combine differentiation strategies with cost strategies to achieve superior performance and better adapt to these changes. This study confirms a positive relationship between the adoption of hybrid strategies and market performance in SMEs. In addition, hybrid strategy reinforces innovation, which has a mediating role between hybrid strategy and market performance. Finally, the findings indicate that family SMEs achieve a greater impact of hybrid strategy on innovation than non-family SMEs. Moreover, innovation plays a mediating role only in the case of family firms, which enhances the relationship between hybrid strategy and market performance. Originality/value For SMEs to survive in turbulent environments, this study proposes the adoption of hybrid strategies instead of pure strategies. The novel model links hybrid strategy (as opposed to “stuck in the middle”), innovation and market performance. The research is valuable for owners and managers of family SMEs because this study finds differences in the relationships studied compared to non-family SMEs.

Bertrand‐Edgeworth game under oligopoly. General results and comparisons with duopoly

AbstractThis paper studies price competition among a given number of capacity‐constrained producers of a homogeneous commodity under the efficient rationing rule and constant (and identical) marginal cost until full capacity, when demand is a continuous, non‐increasing, and non‐negative function defined on the set of non‐negative prices and is positive, strictly decreasing, twice differentiable and (weakly) concave when positive. The focus is on general properties of equilibria in the region of the capacity space in which no pure strategy equilibria exist. We study how the properties that are known to hold for the duopoly are generalized to the oligopoly and we highlight the new properties that can arise in asymmetric oligopoly, which include the existence of an atom in the support of the equilibrium strategy of a firm smaller than the largest one, the properties that such an atom entails, the existence of gaps in the supports, and asymmetries in the equilibrium distributions of equally‐sized firms smaller than the largest one. Further, we provide results about the boundaries of the supports. Although the characterization of equilibria is far from being complete, this paper provides substantial elements in this direction.

An analysis of the equilibrium strategies for route-choosing customers in a two-station queueing system

We investigate a two-station queueing system where strategic customers must be sequentially serviced at both stations. We prove that an established property — that the distribution of the total time spent in a two-station system is independent of the chosen route when services times are exponentially distributed — is not a general one by providing a counterexample with deterministic service times. In doing so, we also prove a concomitant property — that any routing strategy is an equilibrium — is peculiar to a system with a particular assumption of an exponential service time distribution. Using simulations, we show that — depending on the distribution of service times — there can be (1) cases with three equilibria, (2) cases with one pure strategy equilibrium, and (3) cases with one mixed strategy equilibrium.

A Nash equilibrium against gun control

This work constructs a non-cooperative, static game of gun control between the citizen and a pacifistic society characterised by law enforcement imperfection, by which the retention of firearms and the certitude of punishment against all crimes emerge both as a strict Nash equilibrium, in pure strategies, and as a strict dominant strategy equilibrium. The reason is that ratified by the Second Amendment to the American Constitution, discerning the necessity of a militia to the individual and societal security of a free state, by which the right of the people to keep and bear arms cannot be infringed.

Pure Strategy Saddle Points in the Generalized Progressive Discrete Silent Duel with Identical Linear Accuracy Functions

Pure Strategy Saddle Points in the Generalized Progressive Discrete Silent Duel with Identical Linear Accuracy Functions

CREATIVE AND PURE IMITATION UNDER ENVIRONMENTAL TURBULENCE: EVIDENCE FROM AN EMERGING ECONOMY

Due to the significance of imitation in business success and economic growth, there is an increasing interest of scholars in exploring different dimensions of imitation, illuminating the ‘black box’ of imitation. Given the increasingly turbulent nature of business environments, this study aims to investigate creative and pure imitation-based competitive strategies and their performance under different levels of environmental turbulence. A theoretical framework was tested using a sample of manufacturing firms in Vietnam. The results revealed that creative imitation is positively associated with sustained competitive advantage, while the impact of pure imitation on sustained competitive advantage is negligible. Furthermore, environmental turbulence affects both creative and pure imitation, with only creative imitation mediating the effects of environmental turbulence on sustained competitive advantage. Lastly, environmental turbulence amplifies the effect of pure imitation on sustained competitive advantage, while it has minimal moderating effects on the relationship between creative imitation and sustained competitive advantage. This study contributes to the literature by being the first to examine the effect of environmental turbulence on the performance of both creative and pure imitation strategies.

Photonic implementation of the quantum Morra game

The Morra game, an age-old noncooperative game, traditionally played on one's hand, has proved to be a rich setting to study game-theoretic strategies, both classically and within the quantum realm. In this paper, we study a faithful translation of a two-player quantum Morra game, which builds on previous study by including the classical game as a special case. We propose a natural deformation of the game in the quantum regime in which Alice has a winning advantage, breaking the balance of the classical game. A Nash equilibrium can be found in some cases by employing a pure strategy, which is impossible in the classical game where a mixed strategy is always required. We prepared our states using photonic qubits on a linear optics setup, with an average deviation ≤2% with respect to the measured outcome probabilities. Finally, we discuss potential applications of the quantum Morra game to the study of quantum information and communication. Published by the American Physical Society 2024

The Pure and Hybrid Corporate Strategies Performance during the Crisis Periods for Sustainable Performance

This research investigates pure and hybrid corporate strategic responses to crises for sustainable corporate financial performance (CFP). The study used a panel data technique for 374 non-financial firms on the Pakistan Stock Exchange from 2006-2021. The generalised least squares regression was used to control heteroscedasticity and autocorrelation. The results proved that corporate business strategy (CBS): prospector, analyser, and defender strategies positively affect CFP, and reactor strategy reported a negative association with CFP during the crisis period. The study results reveal that the pure strategies, defender and prospector, outperformed the hybrid strategy during the crisis. The reactor strategy somewhere shows positive performance in the crisis period for a few industries. The study's findings support contingency theory and offer theoretical contributions and policy implications for executives and practitioners seeking sustainable performance during crises. It guides practitioners to concentrate on CBS typology and internal and external environments to achieve higher competitive performance.