Game-theoretic Context Research Articles

GANs and synthetic financial data: calculating VaR*

ABSTRACT Generative Adversarial Neural nets (GANs) are a new branch of machine learning techniques. A GAN learns to generate new data from the training data set. We examine the characteristics of the fake financial data using GANs trained on samples of daily S&P 500 and FTSE 100 index values. GANs feature two competing neural networks in a game theoretic context. The Generator net generates pseudo data that is presented to the discriminator net which then attempts to distinguish between the real and the fake data. This facilitates unsupervised learning on the dataset. The generative network generates data sets, while the discriminative network evaluates them. Equilibrium is reached when the generator can fool the discriminator half the time. Potential convergence difficulties led to the development of Wasserstein GANs, which we use in the analysis. We examine the characteristics of the generated fake S&P500 and FTSE 100 data sets. A key issue is how closely does the fake series mimic the real series? We explore this using a variety of metrics including regression analysis, applications of moments and characteristic functions, plus Random Forest analysis. We provide a practical application using the fake data to calculate Value at Risk (VaR).

Game-theoretic modeling in regulating greenhouse gas emissions

This research introduces an innovative framework for addressing the escalating issue of greenhouse gas emissions through the integration of game theory with differential equations, proposing a novel model to simulate the regulatory dynamics between emission sources and legislative actions. By blending advanced mathematical modeling with environmental science, this paper underscores the critical necessity for pioneering, proactive strategies in environmental management and policy formulation. Central to our approach is the simulation of interactions within a game-theoretic context, aiming to delineate optimal strategies for emission sources and regulatory bodies, factoring in legislative constraints and environmental ramifications. The methodology employs a system of ordinary differential equations, capturing the dynamic, non-stationary nature of atmospheric processes and offering a realistic portrayal of the challenges in mitigating greenhouse gas emissions. Furthermore, the study introduces a fee-based regulatory mechanism designed to encourage emission reductions, highlighting the economic implications of such strategies. Significantly contributing to environmental management, this research presents a detailed model capable of predicting the trajectory of greenhouse gas emissions over a decade, considering the potential impact of technological innovations in emission control. The conclusion emphasizes the promising role of artificial intelligence in refining environmental governance, acknowledging the complexities and limitations inherent in predictive modeling. Aimed at policymakers and environmental scientists, this paper serves as a strategic tool for informed decision-making, advocating for a multidisciplinary approach to develop sustainable, effective solutions to combat one of the most critical environmental challenges facing the globe today.

Computational Transcendence: Responsibility and agency.

Emergence of responsible behavior is explored in non-cooperative games involving autonomous agents. Rather than imposing constraints or external reinforcements, agents are endowed with an elastic “sense of self” or an elastic identity that they curate based on rational considerations. This approach is called “computational transcendence (CT).” We show that agents using this model make choices for collective welfare instead of individual benefit. First, relevance of this model in game theoretic contexts like Prisoners’ dilemma and collusion is presented. Next, a generic multi-agent framework for simulating dilemmas around responsible agency is also proposed. CT implemented on this framework, is shown to be versatile in acting responsibly to different kinds of circumstances–including modifying their strategy based on their interaction with other agents in the system as well as interacting with adversaries that are rational maximizers, and who have a rationale to exploit responsible behavior from other agents. CT is also shown to outperform reciprocity as a strategy for responsible autonomy. Thus, we present CT as a framework for building autonomous agents which can intrinsically act responsibly in multi-agent systems. The core model for computational ethics presented in this paper can potentially be adapted to the needs of applications in areas like supply chains, traffic management, and autonomous vehicles. This paper hopes to motivate further research on responsible AI, by exploring computational modeling of this elusive concept called the “sense of self” that is a central element of existential inquiry in humans.

Compositional Analysis of Interconnected Systems Using Delta Dissipativity

This letter extends the notion of delta dissipativity, originally introduced in a game theoretic context, to general interconnections of dynamical systems. The main contribution of this letter is a compositionality result that presents conditions under which a large-scale interconnection of delta dissipative systems is delta dissipative. We adapt this result to also analyze stability and asymptotic stability of equilibrium points for the interconnection. Additionally, we formulate a sum-of-squares program for verifying delta dissipativity of a (polynomial) system. The results are illustrated with examples.

A game theoretic perspective on the management of shared North Sea fishery resources: Pre and post Brexit

Since the introduction of the 200 nautical mile Exclusive Economic Zone (EEZ) regime, North Sea coastal states have cooperated in the management of shared stocks. Norway and the EU have jointly managed six shared stocks through the 1980 Agreement which includes the annual setting of total allowable catch quotas (TACs), quota shares and access agreements. This article first attempts to explain in a game theoretic context why cooperative management of shared North Sea fish stocks has been stable for more than 40 years. Brexit represented a shock to the cooperative agreement, and there are now three parties to the negotiations. The UK EEZ is important not only for British fishermen, but also for Norway and the EU27. The UK and the EU have agreed on a Trade and Cooperation Agreement which includes fisheries, but Norway and the UK have not yet reached a fisheries agreement. In the second part of the article we analyse the UK-EU fisheries agreement, the continuation of the 1980 Agreement, and the future fisheries relationship between the UK and Norway.

Chaotic dynamics in the presence of medical malpractice litigation: A topological proof via linked twist maps for two evolutionary game theoretic contexts

In the present work we reconsider the evolutionary game theoretic models by Antoci et al. (2016, 2018) describing the dynamic outcomes arising from the interactions between patients and physicians, whose behavior is subject to clinical and legal risks. In particular, Antoci et al. (2016) analyzed the case of positive defensive medicine, while Antoci et al. (2018) dealt with the case of negative defensive medicine. We show that, when the models admit a nonisochronous center, it is possible to prove the existence of chaotic dynamics for the Poincaré map associated with those systems via the method of Linked Twist Maps (LTMs). To such aim we exploit in both frameworks, using a similar rationale, the periodic dependence on time of a model parameter influencing the position of the center and describing some risk associated with certain medical interventions, whose seasonal variation is empirically grounded. We also recall the ecological interpretation of the same model proposed by Harvie et al. (2007) and connected with intraspecific competition and environmental carrying capacity in predator-prey settings. In this case, it is sensible to assume a seasonal variation both for the carrying capacities and for the intrinsic growth rates of the two populations. Although such parameters influence the shape of the orbits, but do not affect the center position, we show that it is still possible to prove the existence of chaotic dynamics for the associated Poincaré map via the LTMs technique dealing with a different geometrical configuration for orbits in the phase plane.

Student evaluation of teaching, social influence dynamics, and teachers\u2019 choices: An evolutionary model

The issue of Student Evaluation of Teaching has been explored by a large literature across many decades. However, the role of social influence factors in determining teachers’ responses to a given incentive and evaluation framework has been left basically unexplored. This paper makes a first attempt in this vein by considering an evolutionary game-theoretic context where teachers face a two-stage process in which their rating depends on both students’ evaluation of their course and on retrospective students’ evaluation of their teaching output in view of students’ performance in a related follow-up course. We find that both high effort (difficult course offered) and low effort (easy course offered) outcomes may emerge, leading either to a socially optimal outcome for teachers or not, according to cases. Moreover, there may be a potential conflict between the optimal outcome for students and for teachers. We also consider possible ways to generalize our model in future research.

Beyond convexity-Contraction and global convergence of gradient descent.

This paper considers the analysis of continuous time gradient-based optimization algorithms through the lens of nonlinear contraction theory. It demonstrates that in the case of a time-invariant objective, most elementary results on gradient descent based on convexity can be replaced by much more general results based on contraction. In particular, gradient descent converges to a unique equilibrium if its dynamics are contracting in any metric, with convexity of the cost corresponding to the special case of contraction in the identity metric. More broadly, contraction analysis provides new insights for the case of geodesically-convex optimization, wherein non-convex problems in Euclidean space can be transformed to convex ones posed over a Riemannian manifold. In this case, natural gradient descent converges to a unique equilibrium if it is contracting in any metric, with geodesic convexity of the cost corresponding to contraction in the natural metric. New results using semi-contraction provide additional insights into the topology of the set of optimizers in the case when multiple optima exist. Furthermore, they show how semi-contraction may be combined with specific additional information to reach broad conclusions about a dynamical system. The contraction perspective also easily extends to time-varying optimization settings and allows one to recursively build large optimization structures out of simpler elements. Extensions to natural primal-dual optimization and game-theoretic contexts further illustrate the potential reach of these new perspectives.

Learning Through Fictitious Play in a Game-Theoretic Model of Natural Resource Consumption

Understanding the emergence of sustainable behavior in dynamic models of resource consumption is essential for control of coupled human and natural systems. In this letter, we analyze a mathematical model of resource exploitation recently reported by the authors. The model incorporates the cognitive decision-making process of consumers and has previously been studied in a game-theoretic context as a static two-player game. In this letter, we extend the analysis by allowing the agents to adapt their psychological characteristics according to simple best-response learning dynamics. We show that, under the selected learning scheme, the Nash Equilibrium is reachable provided certain conditions on the psychological attributes of the consumers are fulfilled. Moreover, the equilibrium solution obtained is found to be sustainable in the sense that no players exhibit free-riding behavior, a phenomenon which occurs in the original open-loop system. In the process, via a Lyapunov-function based approach, we also provide a proof for the asymptotic global stability of the original system which was previously known to be only locally stable.

Corporate social responsibility in a game-theoretic context

Using a simple Cournot duopoly model with differentiated products, this work studies the firms’ strategic choice of whether to adopt Corporate Social Responsibility (CSR) rules. The proposed game-theoretic approach shows that, depending on the degree of product differentiation and firms’ social concern, different equilibria arise: (1) all firms in the industry follow CSR rules, (2) all firms are profit-maximising (PM), (3) asymmetric equilibria are present (one CSR firm, one PM firm), and (4) multiple symmetric equilibria are present. Under Bertrand competition, universal PM is the unique equilibrium in which the social welfare is the least desirable: this implies that, in contrast to the conventional wisdom, Bertrand may appear as welfare dominated by Cournot. This work can help to explain the widely observed phenomenon, in the real world, of different industries in which firms’ CSR behaviours are more or less commonly widespread.

Routing Games With Progressive Filling

Max-min fairness (MMF) is a widely known approach to a fair allocation of bandwidth to each of the users in a network. This allocation can be computed by uniformly raising the bandwidths of all users without violating capacity constraints. We consider an extension of these allocations by raising the bandwidth with arbitrary and not necessarily uniform time-depending velocities (allocation rates). These allocations are used in a game-theoretic context for routing choices, which we formalize in progressive filling games (PFGs). We present a variety of results for equilibria in PFGs. We show that these games possess pure Nash and strong equilibria. While computation in general is NP-hard, there are polynomial-time algorithms for prominent classes of Max-Min-Fair Games (MMFG), including the case when all users have the same source-destination pair. We characterize prices of anarchy and stability for pure Nash and strong equilibria in PFGs and MMFGs when players have different or the same source-destination pairs. In addition, we show that when a designer can adjust allocation rates, it is possible to design games with optimal strong equilibria. Some initial results on polynomial-time algorithms in this direction are also derived.

Demand with Consumption Externalities

Consider an economic model whose equilibrium can be represented as the …xed point of a system of dierentiable equations. Using the theory of B matrices, I show that comparative statics are well-behaved if the interactions between the equations are not too large, and the negative interactions are not too varied. When there are only positive interactions, for example when strategic comple- ments prevail in a strategic setting, I prove a version of Samuleson's (1947) Correspondence Principle in that equilibrium is nondecreasing for any positive parameter shock if and only if equilibrium is exponentially stable under dis- crete time best reply dynamics. If there are only negative interactions, like when strategic substitutes prevail in a game theoretic context, I use the theory of inverse M matrices to signi…cantly relax Dixit's (1986) conditions under which comparative statics are well-behaved. For every comparative statics result I show that if the conditions apply globally then equilibrium is unique. Applications are provided to dierentiated products Cournot oligopoly, market demand with interdependent preferences, and games on …xed networks.

Fitness maximization by dispersal: evidence from an invasion experiment

Dispersal is essential for population persistence in transient environments. While costs of dispersal are ubiquitous, individual advantages of dispersal remain poorly understood. Not all individuals from a population disperse, and individual heterogeneity in costs and benefits of dispersal underlie phenotype‐dependent dispersal strategies. Dispersing phenotypes are always expected to maximize their fitness by adaptive decision making relative to the alternative strategy of remaining philopatric. While this first principle is well acknowledged in theoretical ecology, empirical verification is extremely difficult, due to a plethora of experimental constraints. We studied fitness prospects of dispersal in a game theoretical context using the two‐spotted spider mite Tetranychus urticae as a model species. We demonstrate that dispersing phenotypes represent those individuals able to maximize their fitness in a novel, less populated environment reached after dispersal. In contrast to philopatric phenotypes, successful dispersers performed better in a low density post‐dispersal context, but worse in a high density philopatric context. They increased fitness about 450% relative to the strategy of remaining philopatric. The optimization of phenotype‐dependent dispersal, thus, maximizes fitness.

Dissonance Minimization as a Microfoundation of Social Influence in Models of Opinion Formation

Models of opinion formation are used to investigate many collective phenomena. While social influence often constitutes a basic mechanism, its implementation differs between the models. In this article, we provide a general framework of social influence based on dissonance minimization. We only premise that individuals strive to minimize dissonance resulting from different opinions compared to individuals in a given social network. Within a game theoretic context, we show that our concept of dissonance minimization resembles a coordination process when interactions are homogeneous. We further show that different models of opinion formation can be represented as best response dynamics within our framework. Thus, we offer a unifying perspective on these heterogeneous models and link them to rational choice theory.

Boundedly rational versus optimization-based models of strategic thinking and learning in games

The paper is a comment on the article by R. Harstad and R. Selten and considers the tradeoff between bounded rationality and optimization models in the game-theoretic context. The author shows that in most of the models elements of opimization are still retained and that it is thus more productive to further improve the optimization-based modeling rather than to abandon them altogether in favour of bounded rationality.

A Game-Theoretical Propensity Score Analysis of Multimarket Contingencies

After two decades of multimarket competition studies in strategic management, this area has developed into two distinct streams: namely, multimarket collusion and competitive dynamics. While the former topic more generally hypothesized mutually forbearing results of firm competitions, the latter rather stressed the patterns of competitions in an intricate competing context. Nonconforming results of both areas have been resulted in treating both areas as separate topics. By means of propensity score matching (PSM) method in a game theoretical context, this study tries to show that both strategies sequentially can be linked. Using accounting-based financial data of major soft drink manufacturers in the U.S. market, I show that both market competition forms most likely result in two separating equilibria, while still providing a potential for disequilibrating opportunities.

Maximizing the minimum load: The cost of selfishness

We consider a scheduling problem on m machines, where each job is controlled by a selfish agent. Each agent is only interested in minimizing its own cost, defined as the total load of the machine that its job is assigned to. We consider the objective of maximizing the minimum load (the value of the cover) over the machines. Unlike the regular makespan minimization problem, which was extensively studied in a game-theoretic context, this problem has not been considered in this setting before.We study the price of anarchy (poa) and the price of stability (pos). These measures are unbounded already for two uniformly related machines [11], and therefore we focus on identical machines. We show that the pos is 1, and derive tight bounds on the pure poa for m≤7 and on the overall pure poa, showing that its value is exactly 1.7. To achieve the upper bound of 1.7, we make an unusual use of weighting functions. Finally, we show that the mixed poa grows exponentially with m for this problem.In addition, we consider a similar setting of selfish jobs with a different objective of minimizing the maximum ratio between the loads of any pair of machines in the schedule. We show that under this objective the pos is 1 and the pure poa is 2, for any m≥2.

The cost of selfishness for maximizing the minimum load on uniformly related machines

Consider the following scheduling game. A set of jobs, each controlled by a selfish agent, are to be assigned to m uniformly related machines. The cost of a job is defined as the total load of the machine that its job is assigned to. A job is interested in minimizing its cost, while the social objective is maximizing the minimum load (the value of the cover) over the machines. This goal is different from the regular makespan minimization goal, which was extensively studied in a game theoretic context. We study the price of anarchy (poa) and the price of stability (pos) for uniformly related machines. The results are expressed in terms of s, which is the maximum speed ratio between any two machines. For uniformly related machines, we prove that the pos is unbounded for s>2, and the poa is unbounded for s?2. For the remaining cases we show that while the poa grows to infinity as s tends to 2, the pos is at most 2 for any s≤2.

Telecom service provider portal: Revenue sharing and outsourcing

Early mobile phones only provided voice transmission, for a fee. They have now evolved into voice and online data portals for providing additional services through 3rd party vendors. These service providers (vendors) are given access to a customer base “owned” by the mobile phone companies, for a fee. Typically customers make two payments: to the mobile phone company for phone services and to the 3rd party vendors for specific services bought from them. Variations to the above business model may involve outsourcing the online portal and/or acquiring customers from other independent portals. For these scenarios, we study how the fees for phone service and customer access are established and how they may relate to the prices of vendor services, and which services should be located on the portal – all in a game-theoretic context. Our results prove that it is possible to reorganize revenue flows through an invoicing process that may benefit the mobile network operator more than the other parties. In addition, we establish optimality in terms of the number of vendors on the portal, and determine a rank-ordering of vendors for their inclusion into the portal.

Cooperative and non-cooperative management of the Northeast Atlantic cod fishery

The fishery for Northeast Atlantic cod (Gadus morhua) in the Barents Sea is one of the most valuable fisheries in the North Atlantic. After the introduction of Extended Fisheries Jurisdiction, cod is a shared stock between Norway and Russia. Overfishing of quotas has been a concern for a number of years. The purpose of this article is to analyse cooperative and non-cooperative management of the Northeast Atlantic cod fishery. This will be done in a game theoretic context, based on different assumptions regarding important variables such as cost of effort and initial stock size. The game theoretic analysis will be based on an empirical bioeconomic model developed and estimated by Hannesson (Mar Policy 31:698–705, 2007; J Bioecon forthcoming). The case of cooperative management is analysed for different cost parameters and starting values of the stock. An interesting result is that the optimal policy gives rise to pulse fishing. As this involves effort (and harvests) varying from year to year, potentially imposing substantial social costs on the industry in years when the fishery is closed, a policy of constant effort is also considered. Finally, non-cooperative management is analysed.