Static Game Research Articles

ESTIMATION OF (STATIC OR DYNAMIC) GAMES UNDER EQUILIBRIUM MULTIPLICITY

AbstractWe propose a multiplicity‐robust estimation method for static or dynamic games. The method allows for distinct behaviors and strategies across markets by treating market‐specific behaviors as correlated latent variables, with their conditional probability measure treated as an infinite‐dimensional nuisance parameter. Instead of solving the intermediate infinite‐dimensional optimization problem, we consider the equivalent finite‐dimensional dual problem. This property allows for a practically feasible characterization of the identified region for the structural parameters. We apply the estimation method to newspaper market previously studied in Gentzkow et al. (American Economic Review 104 (2014), 3073–114) to characterize the identified region of marginal costs.

RENT-SEEKING DECISIONS OF THE MAIN PARTICIPANTS IN CONSTRUCTION PROJECTS BASED ON EVOLUTIONARY-GAME AND SYSTEM DYNAMICS

The performance of a construction project can be severely harmed by its participants’ rent-seeking. In order to prevent such attempt, this research integrates the evolutionary game theory with system dynamics method to simulate the impact of the change of some factors that may cause/reduce rent-seeking. Based on the analysis of the behavioral characteristics and interactive relationships of the main participants (the owner, supervisor, and contractor), an evolutionary game model is constructed and simulated with the method of system dynamics based on the replication dynamic equation of the mixed strategy solution of the three-party static game model. By assigning the parameters of project scale, supervision likelihood, supervision success rate, supervision cost, and penalty intensity, the interaction mechanism of the participants on each factor is revealed through a case-based simulation. The results show that the impacts of these factors on participants’ rent-seeking decisions are significantly different. Furthermore, some management suggestions are provided to prevent rent-seeking for project owner according to the research conclusions. This research can help the project owners take proper measures to prevent rent-seeking of the supervisors and the contractors to improve the performances of the projects.

A Survey of Opponent Modeling in Adversarial Domains

Opponent modeling is the ability to use prior knowledge and observations in order to predict the behavior of an opponent. This survey presents a comprehensive overview of existing opponent modeling techniques for adversarial domains, many of which must address stochastic, continuous, or concurrent actions, and sparse, partially observable payoff structures. We discuss all the components of opponent modeling systems, including feature extraction, learning algorithms, and strategy abstractions. These discussions lead us to propose a new form of analysis for describing and predicting the evolution of game states over time. We then introduce a new framework that facilitates method comparison, analyze a representative selection of techniques using the proposed framework, and highlight common trends among recently proposed methods. Finally, we list several open problems and discuss future research directions inspired by AI research on opponent modeling and related research in other disciplines.

Supply Chain Governance of Agricultural Products under Big Data Platform Based on Blockchain Technology

The present work serves to improve the stable cooperation relationship among subjects of supply chain such as enterprises, farmers, intermediary organizations, and retailers and enhance the governance and optimization of agricultural product supply chain, thus strengthening the competitiveness of China’s agricultural industry. The supply chain governance of agricultural products is taken as the research object. Initially, the stabilities of two supply chain organization modes, “company and farmer” and “company, intermediary organization and farmer,” are analyzed by static game analysis. Then, based on the above analysis and the characteristics of blockchain institutional technology, a detailed analyzation is made on the mechanism of supply chain of agricultural products governance based on blockchain technology. Finally, the functional framework of agricultural supply chain governance is designed based on the basic framework of blockchain technology, and analyzation is made on the trust mechanism and contract mechanism of agricultural supply chain governance based on blockchain technology. The research results show that problems such as information and cognitive constraints in agricultural supply chain governance cannot be completely solved only through the evolution of blockchain organizational structure and the supply of governance mechanism, and speculative behavior will still appear. Optimizing the governance of supply chain of agricultural products based on blockchain technology can realize the transformation of its governance scenario. Meanwhile, the blockchain technologies such as deintermediation, demistrust, and intelligent contract play an important role in the process of agricultural supply chain governance, which can make it change in many aspects such as organization mode, application operation, and governance mechanism. The rapid development of new generation information technologies such as blockchain, the Internet of Things, and computer technology makes it possible to comprehensively digitize economic activities such as production and transaction in the supply chain of agricultural products. The present work combines the technical logic of blockchain digital governance with the institutional logic of agricultural product supply chain governance and tries to solve the instability problems caused by imperfect organization, lack of trust, and incomplete contract in agricultural product supply chain governance with the characteristics of blockchain such as deintermediation, demistrust, and intelligent contract.

Dynamic Games with Incomplete Knowledge in Metric Spaces

We describe a model of a discrete time dynamic system with active elements (players) and states in a metric space. Each state is associated with the common utility value and player shares. Coalitions of players can change the system state, but each move requires their expenses. The players may have only restricted and local knowledge about the system. We define the concept of an equilibrium state in this dynamic game and present iterative algorithms that create feasible trajectories tending to equilibrium states under rather general conditions.

When Virtual Network Operator Meets E-Commerce Platform: Advertising via Data Reward

In China, some e-commerce platform (EP) companies such as Alibaba and JD are now allowed to partner with network operators (NOs) to act as virtual network operators (VNOs) to provide mobile data services for mobile users (MUs). However, it is a question worth researching on how to generate more profits for all network players, with EP companies being VNOs, through appropriate integration of the VNO business and the companies' own e-commerce business. To address this issue, in this work we propose a novel incentive mechanism for advertising via mobile data reward, and model it as a three-stage static Stackelberg game. We obtain the closed-form optimal solution of the Nash equilibrium by backward induction. Besides, for the scenario lack of knowledge on the interaction between the NO and VNO in a dynamic game, we propose a deep Q-network (DQN) based algorithm to derive the optimal strategies of the NO and VNO. Simulation results show impact of system parameters on the utilities of game players and social welfare. We also study the impact of system parameters on different algorithms and discover that the proposed DQN-based algorithm can learn a good strategy as compared with the Stackelberg equilibrium solution.

Research on Cobot Action Decision-Making Method Based on Intuitionistic Fuzzy Set and Game Theory

The bounded rational properties of humans in human-robot collaboration (HRC) is a fundamental reason for collisions in proximity HRC. As HRC scenarios in manufacturing become increasingly popular, robot action decision-making needs to consider such properties of humans. In previous studies, humans are usually considered as rational agents whose behaviors are predictable and planned, but humans are susceptible to distractions caused by external disturbances, and different cognitive processes of the task can produce unpredictable behaviors. To better simulate human bounded rational behavior, based on an intuitionistic fuzzy (IF) multi-attribute decision algorithm, we propose a cobot action decision-making method that integrates human intention, safety, and efficiency, to produce a human-like decision. The proposed decision-making method integrates the bounded rational behavior of humans and establishes the IF set of human action intention for efficiency and comfort using cumulative prospect theory(CPT) and IF set. The proposed method lights on the human decision-making mechanism for proximity HRC actions. We use IF set to calculate the score and accuracy values of two Nash equilibria of a static chicken game, which can predict human action intentions with collision risk and provide optimal action decisions for the robot simultaneously. We generated 10,000 sets of data using the Monte Carlo method and validated the effectiveness of our proposed method by comparing it with MDP and POMDP methods. The results showed that the decision-making method could effectively perform the task of making action decisions for the robot. Simulation experiments and Turing test results show that our proposed method can predict a human’s subjective action decision intention in a situation with potential collision risk with 87.53% accuracy. At the same time, the experimental participants believe that the robot can get 4.83 out of 5 satisfaction points for an action decision.

Analysis of Dynamic game with government subsidy in the telecommunication industry

With the development of the telecommunication industry, 5G service has become the core focus point in every country. This paper establishes a three-oligarchs game model in the Chinese communication service industry to study the oligarch game of communication service based on the 5G service and the influence of relevant government policies. Combined with the game theory and complex system theory, this paper analyzes the three oligarchs in the Chinese telecommunication industry from static and dynamic games perspectives. Firstly, the government's incentives and subsidies are conducive to enhancing the 5G service level in telecommunication oligarchs. Secondly, the cost subsidy and lump-sum incentive will have different impacts on the stability of the dynamic system; Thirdly, the government's incentive and subsidy are not conducive to the enthusiasm of enterprises' desire to get profit. Therefore, the government should not over encourage and subsidize mature enterprises when making relevant decisions and could fully consider the proportions of different incentives and subsidies when making decisions, combined with the actual demand situation to achieve the best effect.

The optimal quantity decision and complex analysis of duopoly game under low-carbon transformation

This paper explored the equilibrium relationship between technology investment and profit return when the duopoly green transformation. The investment in low-carbon technology can increase profits and provide low-carbon products for society. However, the low-carbon level of products may be reduced simultaneously when both companies undergo a low-carbon transformation. Counterintuitive, by analyzing the feasible region of parameters, it can be found that joint decision-making is not necessarily the best choice. Moreover, we expand the static single-period game to the multi-period game and discuss the complex dynamic behaviors and characteristics.

Exploring the strategy of direct power purchase transac- tions in the power market based on game theory

In the mode of direct power purchase transactions for large customers, improv- ing the efficiency of transactions is a prominent issue. The transaction volume and unit price in the electricity market belong to public information, which is the basis for negotiating the price between large users and power generators, and the final transaction price is lower than the market transaction price, which becomes the motivation for large users to choose to con- tinue the transaction. In the game on the transaction volume and transaction price, the expec- tations of both parties on the transaction price and the type of both parties belong to private information. In this paper, based on the knowledge of the static game with incomplete infor- mation, the conditions for transaction realization are constrained, the payment matrix is ex- pressed based on the consideration factors, the Bayesian Nash equilibrium model is established to design the offer strategy, and the expression of the optimal response strategy is finally given.

Optimisation of group batch scheduling in flexible flow shop based on multi-player cooperative game

In a flexible flow shop, if there are group batch processes, the processing task needs to form multiple batches for production in the batch operation. In order to make up batch processing, there will be job-waiting time thereby extending the total working hours of the production process, and the conflict between various production indexes is further intensified. Therefore, this paper first establishes the group batch scheduling of flexible flow shop (GBSFFS) mathematical model, and proposes a local scheduling method based on multi-player cooperation and complete information static game, establishes a method of game elements such as game information, game player, game strategy, game payoff for group batch processing, and uses the method for behaviour prediction of various game players, that is, the valuation indexes, which reduce the evaluation indexes conflict in the GBSFFS problem. On the premise of reducing the waiting time, other evaluation indexes have been increased.

Games of social distancing during an epidemic: Local vs statistical information

The choices of a population to apply social distancing are modeled as a Nash game, where the agents determine their social interactions. The interconnections among the agents are modeled by a network. The main contribution of this work is the study of an agent-based epidemic model coupled with a social distancing game, which are both determined by the networked structure of human interconnections. The information available to the agents plays a crucial role. We examine the case that the agents know exactly the health states of their neighbors and the case they have only statistical information for the global prevalence of the epidemic. The agents are considered to be myopic, and thus, the Nash equilibria of static games for each day are studied. Through theoretical analysis, we characterize these Nash equilibria and we propose algorithms to compute them. Interestingly, in the case of statistical information the equilibrium strategies for an agent, at each day, are either full isolation or no social distancing at all. Through experimental studies, we observe that in the case of local information, the agents can significantly affect the prevalence of the epidemic with low social distancing, while in the other case, they can also affect the prevalence of the epidemic, but they have to pay the burden of not being well informed by applying strict social distancing. Moreover, the effects of the network structure, the virus transmissibility, the number of vulnerable agents, the health care system capacity and the information quality (fake news) are discussed and relevant simulations are provided.

In-game win probability models for Canadian football

ABSTRACT This article presents in-game win probability models for Canadian football. Play-by-play and wagering data for games from the Canadian Football League for the 2015 to 2019 seasons is used to create logistic regression and gradient boosting models. Models with and without the effect of pregame spread and total (over/under) data are presented and discussed. The resulting win probability models are well-calibrated and can be used to support in-game decision-making, review coaching decisions, estimate the magnitude of team “comebacks”, and potentially identify in-game wagering opportunities. An R Shiny application is provided to allow for estimation of in-game win probability for user-provided game state inputs. Opportunities for future work are identified and described.

A sequential Stackelberg game for dynamic inspection problems

We introduce an inspection game where one inspector has the role of monitoring a group of inspectees. The inspector has the resources to visit only a few of them. Visits are performed sequentially with no repetitions. The inspectees report and share the sequence of inspections as they occur, but otherwise, they do not cooperate. We formulate two Stackelberg models, a static game where the inspector commits to play a sequence of visits announced at the start of the game, and a dynamic game where visits will depend on who was visited previously. In the static game, we characterize the (randomized) inspection paths in an equilibrium using linear programs. In the dynamic game, we determine the inspection paths in an equilibrium using backward induction.Our paper focuses on the mathematical structure of the equilibria of this sequential inspection game, where the inspector can perform exactly two visits. In the static game, the inspection paths are solutions to a transportation problem. We use this equivalence to determine an explicit solution to the game and to show that set of inspection path probabilities in an equilibrium, projected onto its first and second visit marginals, is convex. We discuss how the static and dynamic games relate to each other and how to use these models in practical settings.

Operational decisions and game analysis in the agricultural supply chain: invest or not?

PurposeWith the rapid growth of the economy, people have increasingly higher living standards, and although people simply pursued material wealth in the past, they now pay more attention to material quality and safety and environmental protection. This paper discusses the lack of motivation for investing in fresh-keeping technology for agricultural products by individual members of an agricultural supply chain composed of a supplier and a retailer by means of mathematical models and data simulations and discuss the optimal price-invest strategies under different sales models.Design/methodology/approachFirst, based on the model of no investment by both sides (NN), this paper considers three models: supplier only (MN), retailer only (NR) and cooperative investment (MR). Then, the authors analyze the influence of consumer price sensitivity and freshness sensitivity on the investment motivation of agricultural products under four models. Subsequently, the paper makes a sensitivity analysis of the optimal strategies under several models, and makes a game analysis of the suppliers and retailers of agricultural products. Finally, we conduct an empirical analysis through specific values.FindingsThe results show that (a) when the two sides cooperate, the amount of investment is largest, the freshness of the agricultural products is highest, and the sales volume is greatest; however, when both sides do not invest, the freshness of agricultural products and sales volume are lowest. (b) The price and freshness sensitivity of the consumer have an impact on investment decisions. Greater freshness sensitivity corresponds to a higher investment, higher agricultural product price, greater sales volume, and greater supply chain member income and overall income; however, greater price sensitivity corresponds to a lower investment, lower agricultural product price, lower sales volume, fewer supply chain members and lower overall income. (c) The investment game between the supplier and retailer is not only related to the sensitivity to price and freshness but also to the coordination coefficients of interest. At the same time, the market position of agricultural products should be considered when making decisions. The market share of agricultural products will affect the final game equilibrium and then affect the final benefit of the supply chain and individual members.Practical implicationsThese results provide managerial insights for enterprises preparing to invest in agricultural products preservation technology.Originality/valueAt present, the main problem is that member enterprises of agricultural supply chains operate based on their own benefits and are resistant to investing alone to improve the freshness of agricultural products. Instead, they would prefer that other members invest so that they may reap the benefits at no cost. Therefore, the enterprises in each node of the agricultural product supply chain are not motivated enough to invest, and competition and game states are observed among them, and such behavior is definitely not conducive to improving the freshness of agricultural products. However, the current research on agricultural products is more about price, quality and greenness, etc., and there are few studies on agricultural investment. Through the establishment of the model, this paper is expected to provide theoretical suggestions for the supply chain enterprises that plan to invest in agricultural products preservation technology.

Role-Playing Game as Learning Media To Support Online Learning

Lack of learning media will affect the learning process in the classroom. Various learning media can motivate students in online learning activities. It causes learning media to be essential in the learning process. In the current era of online learning, students are prone to boredom and stress. Therefore this study aims to develop learning media with RPG (Role Playing Games). This research is exploratory because the field of play is vast, with validation using an E-GameFlow survey to assess the level of comfort of players when gaining knowledge. The research will be conducted on 15 junior high school students by distributing online questionnaires. The methods used to collect data are observation and questionnaires. The instrument used to collect data is a questionnaire. The technique used to analyze the data is descriptive qualitative and quantitative analysis. The results of each question on each aspect of E-GameFlow will be analyzed to find conclusions about the games that have been made. The results of the data obtained show that the lowest value is 5.49 in the challenge aspect, which is caused by a static game map and lack of guidance regarding the game. The overall results of E-GameFlow show that the game can provide comfort to players while providing learning materials. This is evident from no aspect with a score below the average.

Large deviations principle for discrete-time mean-field games

In this paper, we establish a large deviations principle (LDP) for interacting particle systems that arise from state and action dynamics of discrete-time mean-field games under the equilibrium policy of the infinite-population limit. The LDP is proved under weak Feller continuity of state and action dynamics. The proof is based on transferring LDP for empirical measures of initial states and noise variables under setwise topology to the original game model via contraction principle, which was first suggested by Delarue, Lacker, and Ramanan to establish LDP for continuous-time mean-field games under common noise. We also compare our work with LDP results established in prior literature for interacting particle systems, which are in a sense uncontrolled versions of mean-field games.

Simulation Research on the Complexity of Life Game

The relationship between complexity and various factors is explored through the simulation of the three neighbor ways of the game of life. It mainly discusses the state evolution process of cell populations under various evolutionary laws, various environmental scales and various initial states. Based on the discovery of a novel, long-lived and simple cell with an initial state, the periodic and stable cell morphology in Game of Life is introduced, thus reflecting the related complexity factors and changes. By simulating various environmental boundaries and comparing the steady-state graphs, it is concluded that a closed system will cause certain limitations in the final outcome. The limited environment will prevent the cell from expanding outward, but it can also create more periodic patterns. A limited environment is simultaneously an important factor in simplifying the system. In addition to the environment, the edge of chaos is also an important factor in the complexity of the system. An appropriate evolution rule can help the entire system find a balance in the chaos and present stable and interesting patterns. In addition, the correct neighbor method has a positive effect on the change of the cell. Finally, an infinite loop mode is set up to illustrate once again the wonder and complexity of Game of Life.

Uniendo los estudios de caso con la teoría de juegos

This essay shows that case studies can become explanatory through analytical narratives, in particular by applying static game theory analysis. This methodological conjunction is enhanced through process tracing, the mechanism approach and the interpretation of motives. Interpretation, a type of intentional explanation, is essential not only for the construction of analytical narratives, but also for bringing game theory closer to the expanded perspective of rationality. The article also offers some theoretical rudiments for the construction of an analytical narrative, useful for studying cases of collective action.

Rationalizability, Observability, and Common Knowledge

Abstract We study the strategic impact of players’ higher-order uncertainty over the observability of actions in general two-player games. More specifically, we consider the space of all belief hierarchies generated by the uncertainty over whether the game will be played as a static game or with perfect information. Over this space, we characterize the correspondence of a solution concept which captures the behavioural implications of Rationality and Common Belief in Rationality (RCBR), where “rationality” is understood as sequential whenever the game is dynamic. We show that such a correspondence is generically single-valued, and that its structure supports a robust refinement of rationalizability, which often has very sharp implications. For instance, (1) in a class of games which includes both zero-sum games with a pure equilibrium and coordination games with a unique efficient equilibrium, RCBR generically ensures efficient equilibrium outcomes (eductive coordination); (2) in a class of games which also includes other well-known families of coordination games, RCBR generically selects components of the Stackelberg profiles (Stackelberg selection); (3) if it is commonly known that player $2$’s action is not observable (e.g. because $1$ is commonly known to move earlier, etc.), in a class of games which includes all of the above RCBR generically selects the equilibrium of the static game most favourable to player $1$ (pervasiveness of first-mover advantage).