Uncertain Payoffs Research Articles

Protecting Infrastructure Networks: Solving the Stackelberg Game with Interval-Valued Intuitionistic Fuzzy Number Payoffs

Critical infrastructure is essential for the stability and development of modern society, and a combination of complex network theory and game theory has become a new research direction in the field of infrastructure protection. However, existing studies do not consider the fuzziness and subjective factors of human judgment, leading to challenges when analyzing strategic interactions between decision makers. This paper employs interval-valued intuitionistic fuzzy numbers (IVIFN) to depict the uncertain payoffs in a Stackelberg game of infrastructure networks and then proposes an algorithm to solve it. First, we construct IVIFN payoffs by considering the different complex network metrics and subjective preferences of decision makers. Next, we propose a lexicographic algorithm to solve this game based on the concept of a strong Stackelberg equilibrium (SSE). Finally, we conduct experiments on target scale-free networks. Our results illustrate that in an SSE, for the defender in a weak position, it is better to defend nodes with high degrees. The experiments also indicate that taking fuzziness into account leads to higher SSE payoffs for the defender. Our work aims to solve a Stackelberg game with IVIFN payoffs and apply it to enhance the protection of infrastructure networks, thereby improving their overall security.

Ising models to study effects of risk aversion in socially interacting individuals

Ising models have been applied not only to describe physical systems but also systems of interacting animals and humans. In contrast to physical entities, animal and humans exhibit more complex behaviour such as risk aversion, so that certain payoffs are, for given expected payoff, preferred to uncertain payoffs. Here I extend the classical Ising model to consider risk aversion, and show that this affects the model’s stability domains: if individuals are risk averse and their choices differ by the associated risk levels, then higher coupling constants are required to sustain system states in which the riskier choice is abundant; otherwise the risky choice is accompanied (bistability) or even replaced in the system by the less risky choice. The model and results are applied to an economic incentive scheme for the conservation of biodiversity, the agglomeration bonus, that induces not only conservation measures but rewards their spatial agglomeration. Here conservation is the risky choice whose abundance in the land-use system is shown to decline if the landowners are risk-averse.

Identity, Information, and Situations

Abstract This paper introduces a model of individual behavior based on identity, a person’s sense of self. The individual evaluates situations, that is, sets of available actions given a belief about the actions’ uncertain payoffs. In some situations, a psychological cost arises because the individual’s identity prescribes an action that differs from the one maximizing material benefits. The model shows that a common process of weighing psychological costs and material benefits drives the choice of both information and future opportunities. As a result, information avoidance is akin to preferring fewer opportunities, such as crossing the street to avoid a fundraiser. The model provides a coherent rationalization for diverse behaviors, including willful ignorance, opting out of social dilemmas, and excess entry into competitive environments. The psychological cost varies non-monotonically with the quality of information or with having more opportunities. Non-monotonicity complicates the identification of prescriptions from behavior, a difficulty that is partially resolvable by observing specific choices.

Capitalism and Distributive Justice: Musings of a Mormon Economist

Capitalism and Distributive Justice: Musings of a Mormon Economist

Data Offloading in UAV-Assisted Multi-Access Edge Computing Systems Under Resource Uncertainty

In this paper, a novel data offloading decision-making framework is proposed, where users have the option to partially offload their data to a complex Multi-access Edge Computing (MEC) environment, consisting of both ground and UAV-mounted MEC servers. The problem is treated under the perspective of risk-aware user behavior as captured via prospect-theoretic utility functions, while accounting for the inherent computing environment uncertainties. The UAV-mounted MEC servers act as a common pool of resources with potentially superior but uncertain payoff for the users, while the local computation and ground server alternatives constitute safe and guaranteed options, respectively. The optimal user task offloading to the available computing choices is formulated as a maximization problem of each user’s satisfaction, and confronted as a non-cooperative game. The existence and uniqueness of a Pure Nash Equilibrium (PNE) are proven, and convergence to the PNE is shown. Detailed numerical results highlight the convergence of the system to the PNE in few only iterations, while the impact of user behavior heterogeneity is evaluated. The introduced framework’s consideration of the user risk-aware characteristics and computing uncertainties, results to a sophisticated exploitation of the system resources, which in turn leads to superior users’ experienced performance compared to alternative approaches.

Probabilistic linguistic evolutionary game with risk perception in applications to carbon emission reduction decision making

Carbon emission reduction, an effective way to facilitate carbon neutrality, has gained increasing attention in government policy and scientific research. However, the establishment of a sustainable carbon emission reduction market is a complex game between governments and enterprises. In addition, it is difficult to obtain precise evaluations of the political and environmental factors in most cases. Irrational enterprises with a profit-seeking nature bring challenges to the strategy selection. To bridge this gap, we propose a probabilistic linguistic evolutionary game to model strategic behavior in carbon emission reduction assistant decision making. First, we introduce a probabilistic linguistic payoff matrix to describe the uncertain payoffs of players. A new distance measure for the probabilistic variables is also proposed to construct the prospect payoff matrix in the prospect theory framework. Then, the evolutionary dynamics and the probabilistic linguistic evolutionary stability of the proposed methods are analyzed. A comprehensive case study for carbon emission reduction with comparisons is presented for validation.

Human-computer gaming decision-making method in air combat under an incomplete strategy set

In thereal air combat environment, uncertainty is widespread. This paper considers the air combat decision-making problem in the human-computer gaming scenario, and a game decision-making method is proposed under anincomplete strategy set.First, the dynamic game process of unmanned and manned air vehicle swarms is decomposed into different decision-making stages, and the current decision-making stage is modeled as a zero-sum game model.In the established model, the situation where the strategy of the manned air vehicle swarm is not completely known is considered, and an uncertain payoff matrix is used to describe the incomplete strategies. Then, a solutionmethod of the established game under anincomplete strategy setis proposed based on the concept of the maximum-minimum strategy in matrix games. Thus, the decision sequence of unmanned air vehicle swarms is given. Finally, the effectiveness of the proposed method is verified through simulation experiments.

On the strategic learning of signal associations

AbstractSignal detection theory (SDT) has been widely used to identify the optimal response of a receiver to a stimulus when it could be generated by more than one signaler type. While SDT assumes that the receiver adopts the optimal response at the outset, in reality, receivers often have to learn how to respond. We, therefore, recast a simple signal detection problem as a multi-armed bandit (MAB) in which inexperienced receivers chose between accepting a signaler (gaining information and an uncertain payoff) and rejecting it (gaining no information but a certain payoff). An exact solution to this exploration–exploitation dilemma can be identified by solving the relevant dynamic programming equation (DPE). However, to evaluate how the problem is solved in practice, we conducted an experiment. Here humans (n = 135) were repeatedly presented with a four readily discriminable signaler types, some of which were on average profitable, and others unprofitable to accept in the long term. We then compared the performance of SDT, DPE, and three candidate exploration–exploitation models (Softmax, Thompson, and Greedy) in explaining the observed sequences of acceptance and rejection. All of the models predicted volunteer behavior well when signalers were clearly profitable or clearly unprofitable to accept. Overall however, the Softmax and Thompson sampling models, which predict the optimal (SDT) response towards signalers with borderline profitability only after extensive learning, explained the responses of volunteers significantly better. By highlighting the relationship between the MAB and SDT models, we encourage others to evaluate how receivers strategically learn about their environments.

Rather doomed than uncertain: risk attitudes and transmissive behavior under asymptomatic infection

We analyze the relation between individuals’ risk aversion and their willingness to expose themselves to infection when faced with an asymptomatic infectious disease. We show that in a high prevalence environment, increasing individuals’ risk aversion increases their propensity to engage in transmissive behavior. The reason for this result is that as risk aversion increases, exposure which leads to infection with certainty becomes relatively more attractive than the uncertain payoffs from protected behavior. We provide evidence from a laboratory experiment which is consistent with our theoretical findings.

Regulation with Experimentation: Ex Ante Approval, Ex Post Withdrawal, and Liability

We analyze the optimal mix of ex ante experimentation and ex post learning for the dynamic adoption of activities with uncertain payoffs in a two-phase model of information diffusion. In a first preintroduction phase, costly experimentation is undertaken to decide whether to adopt an activity or abandon experimentation. In a second stage following adoption, learning can continue possibly at a different pace while the activity remains in place; the withdrawal option is exercised following the accumulation of sufficiently bad news. We compare from a law and economics perspective the performance of three regulatory frameworks commonly adopted to govern private experimentation and adoption incentives: liability, withdrawal, and authorization regulation. Liability should be preempted to avoid chilling of activities that generate large positive externalities consistent with the preemption doctrine. Liability should be used to discourage excessive experimentation for activities that generate small positive externalities. Authorization regulation should be lenient whenever it is used consistent with the organization of regulation in a number of areas, ranging from product safety to antitrust. This paper was accepted by Joshua Gans, business strategy.

Should I Play or Should I Go? Individuals’ Characteristics and Preference for Uncertainty

This paper presents an incentivized experiment analyzing the role of demographic characteristics in individual decision-making under uncertainty. Reactions to a natural source of uncertainty, payoffs in a TV game show, were measured using Fuzzy-set Qualitative Comparative Analysis (fsQCA), allowing us to identify multiple configurations of causal conditions that are sufficient for individuals to prefer an uncertain payoff to a sure gain, and, thus, lower risk aversion. This paper found evidence of preference for uncertainty, measured as willingness to play for an uncertain payoff, in individuals with characteristics most commonly present in the literature: being male; young; childless; with studies in finance or similar areas. This paper also shows that conditions that would not justify the preference for uncertainty according to the literature (an older individual or having children), when combined with other conditions, change contestants’ behavior regarding preference for uncertainty. Individuals that are both older and single, and individuals that have children combined with education in finance, show an inverse effect on preference for uncertainty.

Designing a public-private co-investment mechanism to foster venture capital

In this paper we develop a co-investment mechanism for promoting early investment in Start-up Firms. Focusing on the (uncertain) payoffs earned by a Public Venture Capitalist (PVC) and an Independent Venture Capitalist (IVC), we model each of the alternative mechanisms as an investment timing real option and illustrate that co-investing might be the most effective mechanism to foster investment in Entrepreneurial Firms. Grounded on this theoretical framework, we list a set of both public policy and managerial implications.

Energy-Aware Collaborative Service Caching in a 5G-Enabled MEC With Uncertain Payoffs

Mobile edge computing (MEC) is an enabling technology for low-latency AI applications, by caching AI services originally deployed in remote data centers to 5G base stations in network edge. Due to limited computing resource of 5G base stations, not all services can be cached in base stations to meet the resource demands of user requests. Also, if the workload of a 5G base station reaches to its resource capacity, the energy consumption of the base station will be pushed up exponentially. To reduce the energy consumption and overcome resource limitations on base stations, an alternative is to allow the base stations to collaborate with each other to admit user requests. In this paper, we investigate the problem of collaborative service caching and request offloading between a 5G-enabled MEC and remote data centers, while meeting the quality of service (QoS) requirements of users, and resource capacities on base stations that are operated by multiple selfish network service providers. We aim to maximize the total payoff of all base stations. To this end, we first propose a two-stage optimization framework: In the first stage, we develop a mechanism that adopts a best-reply rule for dynamically distributed coalition formation. In the second stage, we propose a near-optimal payoff allocation method by devising a randomized algorithm with a provable approximation ratio. We then evaluate the performance of the proposed optimization framework by extensive experimental simulations. Simulation results show that the proposed framework outperforms its counterparts by achieving at least 30% higher payoff and 20% lower energy consumption of base stations.

IT Governance mechanism and IT-enabled dynamic capabilities drives firm performance: An empirical study in Sri Lanka

Despite the growing amount of IT investment, IT governance decisions have ever more become complicated due to vague cost relationships, uncertain payoffs, rapid technological changes, and uncertain business environments. This study examines how IT governance mechanism and IT-enabled dynamic capabilities (ITDC) impact on firm performance in the turbulent environment. Drawing on the resource-based theory and dynamic capability theory this study conceptualizes that IT governance mechanism positively effect ITDC, that in turn positively impact on business process agility and firm innovative capability to achieve firm performance. Further, the moderating effect of turbulent environment is hypothesized between ITDC - business process agility and ITDC - firm innovative capability relationship. The finding from 188 senior IT and business manager's responses from Sri Lanka reveals the strong and positive relationship in the hypothesized relationship. In contrary to the expectation, the turbulent environment's both hypotheses (H6a and H6b) failed to show a significant moderating effect. This study proposes the theoretical and practical implications by empirically testing the proposed model in the Sri Lankan context. This study adds to the existing literature and extends the managerial practice by focusing on the key constructs such as IT governance mechanism, ITDC, Turbulent environment, and firm performance

Integrated Online Learning and Adaptive Control in Queueing Systems with Uncertain Payoffs

Many online service platforms have dedicated algorithms to match their available resources to incoming clients to maximize client satisfaction. One of the key challenges is to balance the generation of higher payoffs from existing clients and exploration of new clients’ unknown characteristics while at the same time satisfy the resource capacity constraints. In “Integrated Online Learning and Adaptive Control in Queueing Systems with Uncertain Payoffs,” Hsu, Xu, Lin, and Bell show that traditional approaches such as maximizing instantaneous payoffs with current knowledge or using queue-length based controls guided by “shadow prices,” would lead to suboptimal long-term payoffs. Instead, they propose a novel utility-guided assignment algorithm that seamlessly integrates online learning and adaptive control to provide high system payoffs with performance guarantees. The theoretical performance bound also lends system design insights into the impact of uncertain client dynamics, payoff learning, and backlogged clients. They further develop a decentralized version of the algorithm, which is applicable to large systems and performs well even when the service rates are random.

Simple noncooperative games with intuitionistic fuzzy information and application in ecological management

The matrix game and bi-matrix game are typical non-cooperative games. Nowadays, interactive game decisions on social management are mainly concerned, especially when players are faced with uncertain payoffs. The aim of this paper is to develop simple and effective parameterized linear programming methods for solving two types of matrix games with payoffs expressed by intuitionistic fuzzy (IF) information. In these methods, the expected values of players are regarded as monotonic functions with their risk preferences. Hereby we construct two models of auxiliary bilinear programming, and the corresponding optimal strategies can be easily obtained by explicit computation. The models and methods proposed in this paper are applied in two ecological management problems, and the validity and applicability are verified.

Corporate diversification and innovation: Managerial myopia or inefficient internal capital markets?

Which is more innovative: the decentralized, diversified firm, or the centralized, more narrowly focused firm? The economics and finance literatures argue that diversified firms have innovation advantages as their operating units have access to an internal capital market. In contrast, the strategy and entrepreneurship literatures argue that managers of these firms suffer from “managerial myopia,” discouraging them from investing in projects with long‐term, uncertain payoffs. We take a fresh look at the relationship between innovation and diversification using a comprehensive sample of diversified and nondiversified firms and a novel approach that teases out the mechanisms influencing the relationship between diversification and innovation. Consistent with conceptual and empirical work in strategy, we find a robust negative correlation between diversification and R&D intensity, suggesting that diversification reduces innovation by discouraging investment. However, our analysis suggests that internal capital market inefficiencies, rather than managerial myopia, is responsible for this observed negative relationship.

Corporate governance and firms’ acquisition behavior: The role of antitakeover provisions

Mergers and acquisitions (M&As) are strategically important investments that can drive corporate growth and development. However, they offer uncertain payoffs over the long term and could cost top executives their jobs when results are disappointing. As a result, risk-averse top executives can be reluctant to strategically decide to support even promising M&As. We integrate insights from upper echelon and managerial risk-aversion perspectives to determine whether and when antitakeover provisions can foster firms’ acquisition frequency. Drawing on a sample of 8438 M&As by 1301 public companies in the United States, we report evidence that these provisions positively affect firms’ acquisition frequency. We also find that the positive impact of these provisions on firms’ acquisition frequency is weaker when chief executive officers own a larger proportion of their firms’ equity and when firms operate in industries with higher competition. We discuss the theoretical and practical significance of our findings.

The Valuator’s Curse: Decision Analysis of Overvaluation and Disappointment in Acquisition

Initial valuations of entrepreneurial ventures offering uncertain payoffs can often be overvalued by investors; namely, the expected payoff postacquisition is smaller than the expected payoff prior to acquisition when the investor harbors uncertainties about various components of the business. Common explanations involve irrationality such as psychological preference for potential over realized payoffs. We provide a different, rational explanation, which we term the valuator’s curse. It is similar in nature to the winner’s curse in auctions and the optimizer’s curse in decision analysis, but the source of the curse is neither from the competitive effects of an auction-type mechanism nor from the optimization effects in a choice among alternatives. Rather the effect is generated from the nonlinear evaluation of the payoffs, even though the inputs to the evaluation are unbiased. We formalize the valuator’s curse and discuss its implications to entrepreneur’s learning. The valuator’s curse proves a boon to the entrepreneur as it leads to larger capitalizations.

Green Technology Development and Adoption: Competition, Regulation, and Uncertainty—A Global Game Approach

When a government agency considers tightening a standard on a pollutant, the agency often takes into account the proportion of firms that are able to meet the new standard (what we refer to as the industry’s “voluntary adoption level”) because a higher proportion indicates a more feasible standard. We develop a novel model of regulation in which the probability of a stricter standard being enacted increases with an industry’s voluntary adoption level. In addition, in our model, the benefit of a new green technology is both uncertain and correlated across firms, and firms’ decisions exhibit both strategic substitutability (because the marketing benefit of a new green technology decreases as more firms adopt it) and complementarity (because the stricter standard is more likely to be enforced as more firms adopt it). To analyze such strategic interaction among firms’ decisions under correlated and uncertain payoffs, we use the global game framework recently developed in economics. Our analysis shows that regulation that considers an industry’s voluntary adoption level, compared with regulation that ignores it, can more effectively motivate development of a new green technology. Interestingly, uncertainty in the payoff can, in some situations, help promote development of a new green technology. Finally, we find that more aggressive regulation (a higher probability of enforcing a stricter standard for a given voluntary adoption level) encourages more firms to adopt a green technology once the technology becomes available but may discourage a firm from developing it in the first place when facing intense competition. Therefore, for an industry with intense competition, a government agency should exercise caution about being too aggressive with regulation, which could potentially stifle innovation.This paper was accepted by Vishal Gaur, operations management.