Rare-disease treatment financing is challenging because high-cost therapies, clinical need, and budget constraints create interdependent decisions among manufacturers, public payers, and healthcare providers. This article combines patient-level time-driven activity-based costing (TDABC) with a sequential reimbursement benchmark and a fixed-budget coverage analysis for severe haemophilia A. Using institutional pathway data and a representative clinical profile, the study estimates an annual treatment cost of EUR 105,429.14 for the representative patient, of which EUR 98,514.04, or 93.4%, corresponds to pharmaceutical expenditure. TDABC is used to identify the clinical and operational resources consumed throughout the treatment pathway and the practical capacity allocated to its delivery. The analytical model then translates the resulting cost structure into reimbursement, provider-adoption, and population-coverage conditions. The results show that treatment feasibility and budget-constrained coverage are driven primarily by drug price, body weight, dose intensity, and administration frequency, while non-drug operational costs have a comparatively limited effect. The article contributes by connecting institution-specific patient-level costing with the interdependent implications of treatment cost for manufacturers, payers, providers, and patient access. The framework provides a transparent reimbursement benchmark rather than a complete bargaining model and supports affordability, budget-impact, and treatment-capacity assessments in rare diseases.
Multi-agent interaction in linear–quadratic (LQ) differential games gives rise to open-loop Nash equilibria that rarely admit closed-form expressions, motivating the development of reliable numerical solvers. Classical approaches such as shooting and spectral collocation are sensitive to the initial guess on the unknown boundary values and accumulate discretisation error over long horizons, while deep-learning alternatives require iterative gradient-based training with architecture- and convergence-specific overhead. To overcome these limitations, we recast the LQ nonzero-sum game as a linear two-point boundary value problem (TPBVP) via the Pontryagin maximum principle (PMP) and solve it with a single-layer feedforward neural network (SLFN) in which hidden-layer parameters are sampled once and fixed. The state and all player-specific costates are parameterised by random hidden features on a uniform time grid, the boundary conditions are appended as dedicated rows of the linear collocation system, and the output weights follow from a single Moore–Penrose pseudoinverse, entirely bypassing gradient-based iteration. For the scalar LQ optimal-control TPBVP, a residual-to-solution stability theorem converts the continuous equation and boundary residuals into uniform state, costate, control, and cost error bounds. Validation across two-player low- and high-dimensional benchmarks, a heterogeneous three-player game, and paired seed sweeps confirms high accuracy against analytical and matrix-exponential references, while revealing that no single activation function dominates across all problem types: tanh is most accurate in one-dimensional settings, and Gaussian RBF leads in multidimensional cases.
This paper studies the interaction between status incentives and organizational design in a two-agent moral hazard framework with limited liability. A risk-neutral principal chooses between two regimes: favouritism, under which one agent receives exclusive decision rights and status recognition for successful project implementation, and fairness, under which both agents share equal decision rights and status is distributed across agents. We show that status incentives can make ex-post favouritism optimal even when the principal does not exhibit any ex-ante preferential bias toward any particular agent. Introduction of status incentives shrink the parameter region supporting interior inefficient favouritism, and eliminate it entirely whenever project returns are large enough to sustain interior contracts for both agents. We also show that, for a non-empty set of primitive parameter values, the principal’s optimal regime can be non-monotonic in status: favouritism is optimal when status valuation is sufficiently low or sufficiently high, while fairness may dominate for intermediate values. The results shed light on why selective, hierarchical recognition systems coexist with flat team-credit structures across organizations.
This paper investigates two marketing strategies a reward-based crowdfunding platform employs to align its preferences with an entrepreneur’s choice of pledge and target levels. These are (a) how to promote campaigns to potential backers, and (b) how to share campaign revenues with the entrepreneur. Kickstarter, for instance, promotes a set of campaigns by compiling a list of “recommended” projects. This research shows that the platform’s choice of the promotion rule may expose entrepreneurs to the risk of not generating sufficient funds to start production, which can damage their and the platform’s reputation. When the platform’s reputational risk is not very high, it reduces the risk of non-delivery by increasing the revenue share of the entrepreneur. The platform’s strategies are likely to ensure production when backers derive warm glow from pledging, when the entrepreneur’s development cost is low, or when the entrepreneur has minimal reputational cost if production fails. However, low reputational costs motivate the entrepreneur to lower the target, thus increasing the likelihood of insufficient funds to start production. We propose strategies the platform can use, including customizing the revenue share based on the campaign characteristics, to rectify such misalignments.
In this work we consider an evolutionary game in which a small population repeatedly plays the Iterated Prisoner’s Dilemma (IPD) game using the pairwise proportional imitation (PPI) revision protocol. Since we are dealing with a small population, we can explicitly formulate a Markov chain (MC) model of the evolutionary game and study its properties. In particular, we identify the absorbing states and their basins of attraction. In addition, we briefly study the replicator dynamics of the same game for the case of a large population. We find that, as the size of the population increases, the Markovian dynamics approximate the replicator dynamics.
Many engineering problems must account for the non-cooperative decisions and actions of multiple players. These problems can be modeled within a game-theoretic framework. The approach herein is to model such problems as mathematical games, convert them to semi-infinite programs, and utilize a semi-infinite program solver whose output is provably an ϵ-optimal Nash equilibrium. The approach is successfully benchmarked on two low-dimensional problems. Two types of higher-dimensional linear quadratic dynamic games are then investigated: ones where each player’s problem is convex and ones where at least one player’s problem is nonconvex. Within each type, variations based on information structure, control constraints, number of players, and semi-infinite objective are considered. The algorithm is tested with different internal solvers, and it successfully solves all test problems using MATLAB’s fmincon. The numerical solutions approximate analytical solutions (when they are known) within approximately one percent. For a three-player game with input saturation constraints, hundreds of variables, and no analytical solution, the computational time is approximately five minutes.
This paper develops a dynamic game-theoretic model to evaluate market competitiveness in industries characterized by price competition and adjustment stickiness. We extend the dynamic oligopoly framework for estimating market competitiveness in the literature from a quantity-setting to a price-setting context with differentiated goods. By deriving the subgame perfect equilibrium in a linear-quadratic structure, we utilize an index analogous to the price conjectural variation to measure market competitiveness with differentiated goods. The model is applied to the Chinese retail oil market, and we find that the Chinese retail oil market, particularly dominated by two state firms, exhibits characteristics close to a collusive benchmark within the maintained model. The dynamic game model provides a tractable analytical tool for antitrust authorities to monitor strategic coordination in dynamic environments where price transparency or regulation may facilitate tacit coordination of pricing behavior to a high degree.
Background: Standard consumer theory treats preferences as fixed primitives and demand as the solution to an individual optimisation problem; we instead model consumption styles as heritable strategies whose prevalence is shaped by selection and experimentation, and ask when status competition produces an over-consumption trap. Methods: We embed a reference-dependent payoff—private utility concave in own consumption, a positional benefit proportional to consumption relative to the social mean, a financial-fragility cost, and a loss-averse relative-deprivation term—into replicator–mutator dynamics over three strategies (frugal, balanced, conspicuous). Results: Status concern induces strategic complementarity, so that a rising consumption norm penalises moderate consumers and makes imitation self-reinforcing. For intermediate status weight, the system is bistable: an efficient balanced equilibrium and a Pareto-inferior conspicuous trap are separated by a tipping threshold, and the width of the bistable window equals the deprivation weight, producing hysteresis in the consumption norm. The trap persists even though the positional benefit nets to zero in any monomorphic state. Mutation—behavioural experimentation—shrinks the bistable window and can dissolve the lock-in. Conclusions: Reference-dependent demand is better captured by evolutionary dynamics than by static equilibrium, and positional externalities can lock a population into self-defeating over-consumption that interventions on the deprivation or fragility channel may unlock.
This paper examines downstream firms’ incentives to accept equity participation by an upstream supplier in a vertically related market. We develop a multi-stage model in which the upstream firm offers an equity stake and sets input prices under price discrimination, while downstream firms subsequently compete à la Cournot. We show that upstream equity ownership induces the upstream firm to lower input prices by partially internalizing downstream profits. This mechanism generates a positive market-expansion effect for downstream firms through lower input costs, while equity ownership simultaneously creates a negative equity-dilution effect by reducing the share of profits retained by downstream firms. When products are homogeneous, the equity-dilution effect dominates the market-expansion effect, leading downstream firms into a Prisoner’s Dilemma. In contrast, under product differentiation, when the ownership share is sufficiently small, the market-expansion effect dominates the equity-dilution effect, resulting in higher downstream profits. In this case, accepting equity participation can be individually optimal for downstream firms, even though mutual acceptance may reduce their retained profits.
This article offers a formal analysis of the paradoxes, dilemmas and strategic interactions explored in Liu Cixin’s trilogy The Three-Body Problem. Several games, such as the survival game, the deterrence game, the first contact game, and the big bang game, provide the foundations of cosmic sociology.
Scientific theories survive on institutional fitness, not empirical merit alone. Under Soviet Stalinism, Vygotsky and Luria’s cultural-historical psychology was suppressed while Leontiev’s Activity Theory flourished because it aligned with Marxist-Pavlovian materialism. A game-theoretic framework formalizes this dynamic through three coupled mechanisms: a researcher utility function (Ur = αT + βR − γC), a state utility function (Us(e) = δI(e) − εD(e) − κ(e)), and a replicator dynamic for institutional selection. Under sufficiently high punishment coefficients, the unique Nash equilibrium is aligned with the ideologically safe theory regardless of empirical truth, and the replicator dynamics drive empirically stronger theories to extinction in the institutional population. Classical findings on conformity and obedience from Sherif, Asch, Festinger, Schachter, and Milgram supply the foundations for the model’s parameters. This pattern—termed here as epistemological selection pressure—explains the Vygotsky case. Because the model assumes severe punishment, active enforcement, complete information, and a binary choice, it applies most directly to authoritarian science; contemporary liberal institutions correspond to the low-punishment regime in which the same model predicts that empirical merit can prevail, so the mechanism is expected to recur only in attenuated form within specific high-pressure domains where scientific truth and institutional power remain entangled.
This paper considers a multi-period two-sided asymmetric information model with infinitely long-lived sellers and short-lived buyers. I assume that two exogenously given qualities are offered in the market. Each period, a consumer, who is uncertain about the quality of the offered product, observes her pairwise matched seller’s price and a noisy signal of quality that cannot be manipulated by the seller. Prices are fixed and it is common knowledge that consumers are not willing to pay a high price for the low-quality product. A matched seller with a low-quality good can choose to be either honest (by charging the lower market price) or dishonest (by charging the higher price). Sellers’ incentives to misrepresent quality depend on how current trade outcomes affect future access to consumer traffic. I show that the strength of the informational role of prices is non-decreasing in the intensity of competition for future consumer traffic in equilibrium and that consumers do not benefit from more intense competition.
We study a continuous-time cooperative differential game of pollution control in which the pollution stock accumulates emissions and affects long-run welfare. The key feature is a one-time random increase in the public damage weight, interpreted as a regime shift in environmental policy, social damage assessment, or regulatory pressure. Using dynamic programming, we characterize the grand-coalition feedback solution from the Hamilton–Jacobi–Bellman equations and derive closed-form expressions for cooperative emissions, pollution dynamics, regime-specific steady states, and transition paths. Under emission caps, we construct the coalition characteristic function using a conservative worst-case benchmark for outsider behavior rather than an unlimited-pollution assumption. For payoff allocation, we derive a dynamic payment schedule that implements the Shapley allocation along the stochastic pollution path and keeps the remaining payoff consistent with the corresponding continuation game. Finally, we extend the framework to a threshold-triggered shifted-exponential switching mechanism. This extension gives a computable objective for the optimal threshold-hitting time and clarifies how the pollution threshold and switching hazard can be interpreted as policy-relevant indicators of regulatory or ecological regime change.
This paper examines drip pricing related to compulsory charges—a situation where firms intentionally make it costly for consumers to discover mandatory fees or surcharges that “drip” into the full (total) price, which is only revealed after incurring the hassle cost of completing a purchase. We show that drip pricing can arise as an equilibrium phenomenon with fully rational consumers and profit-maximizing firms. We also show that when consumers and firms are rational (a) situations where drip pricing raises prices and harms consumers are unlikely to arise from unilateral business decisions and (b) the most likely avenue by which drip pricing harms consumers is through the coordinated adoption of drip pricing.
Public goods provision is vulnerable to free riding, making sustained cooperation a central challenge in economics. Fehr and Schmidt’s inequity-aversion model explains how fairness concerns can support cooperation, but it treats preferences as fixed. Motivated by Kimbrough and Vostroknutov’s norm-sensitivity framework, this paper develops a reduced-form dynamic framework in which observed norm violations erode normative commitment over time. As normative commitment declines, the model maps this change into Fehr–Schmidt-style fairness parameters: guilt weakens and envy rises. These parameters provide an interpretive representation of norm erosion, while behavior is generated through a tractable contribution-scaling rule. The framework is calibrated illustratively to the public goods experiment of Fischbacher and Gächter. The calibration is not causal evidence of preference change and does not directly identify inequity-aversion parameters. It shows that a context-dependent preference channel can reproduce the observed aggregate decline in cooperation and generate testable implications. When no free-rider exposure is present, cooperation does not decline within the model. The model also predicts a nonlinear relationship between population-level free-rider prevalence and cooperation. Finally, because the model imposes a lower bound on normative commitment, this institutional floor determines long-run cooperation. The findings should be interpreted as model-based hypotheses for future experimental and field research.
Frequent occurrences of inter-regional emergencies constitute critical impediments to global security and sustainable development, necessitating enhanced intergovernmental emergency collaboration. This study employs a network evolutionary game model (NEGM) to examine how vertical interventions shape diffusion mechanisms of cooperative strategies among local governments. The results show that (1) solely intensifying penalties or rewards yields diminishing marginal returns in incentivizing local governments to adopt a proactive cooperative strategy; (2) elevating the cost-sharing index significantly accelerates the diffusion rate of cooperative strategies, effectively mobilizing broader subnational engagement in public health emergency response; and (3) the tripartite integration of penalty-based enforcement, reward incentives, and cost-sharing mechanisms demonstrates synergistic superiority over alternative policy instruments—whether implemented individually or in pairwise combinations.
This paper investigates the evolution of public cooperation within a four-strategy public goods game that incorporates both consistently and inconsistently moralistic exclusion mechanisms. Using replicator dynamics in an infinite well-mixed population, we demonstrate that the presence of Inconsistent Moralists (IMs), i.e., non-contributors who hypocritically exclude other defectors, fundamentally reshapes the dynamical structure of the multi-player social dilemma game. While the system admits no interior fixed point and the IM strategy itself is evolutionarily unstable, IM acts as a critical catalyst by destabilizing pure defection and redirecting evolutionary trajectories toward exclusion-based cooperation. Ultimately, these findings reveal that diverse enforcement strategies can qualitatively alter evolutionary outcomes by providing a previously overlooked indirect pathway for cooperation to emerge and persist in social dilemmas.
This paper investigates the interplay between oil, critical minerals, and military expenditure in the U.S. and China. The research goal is to evaluate how sensitive the military expenditure of these countries is to shocks in energy markets. It develops a stylized dynamic model of the arms race and conflict, with a particular focus on U.S.–China tensions surrounding access to these vital resources. Empirical analysis using VAR estimations reveals that: (1) shocks to China’s military spending prompt increases in U.S. military expenditure, whereas the reverse effect is not observed; (2) critical mineral production significantly influences China’s military spending; and (3) U.S. military expenditure is affected by both Chinese military spending and fluctuations in oil prices.
The digital divide between large enterprises and SMEs (Small and Medium-sized Enterprises) within industrial clusters poses a significant challenge to achieving collective digital transformation, exacerbated by the quasi-public goods, attributes of digital inclusion ecosystems, and the prevalence of free-riding behavior. This paper investigates whether platform enterprises, as core actors occupying structural holes in cluster networks, can foster the co-construction of a digitally inclusive ecosystem. We developed a complex network public goods game model, incorporating performance feedback into a modified Fermi learning to capture firms’ adaptive decision-making based on historical and social aspirations. The model simulates strategic interactions on both small-world and scale-free networks, characteristic of industrial clusters. Numerical simulations reveal that: (1) The core driver of co-construction is the investment return coefficient; (2) Performance feedback amplifies individual rationality, accelerating the formation or collapse of cooperation depending on the investment return coefficient; (3) Platform empowerment—specifically, selectively connecting and incentivizing cooperative firms—effectively promotes ecosystem co-construction, with this strategy proving most impactful when investment returns are moderate. Furthermore, while this selective empowerment strategy benefits the cluster overall, its effect on the platform’s own revenue is network-dependent, showing a more pronounced decline in small-world structures. This study provides a novel analytical framework for understanding strategic interactions in digital inclusion and offers practical insights for policymakers and platform leaders in orchestrating collaborative digital transformation.
The rapid rise of live-streaming e-commerce has fostered a new "content clipping" model, in which secondary creators edit and republish anchors' live-streaming content to promote product sales. While this model can expand market reach and enhance revenue, it also introduces copyright disputes, regulatory challenges, and profit-sharing conflicts among platforms, anchors, and secondary creators. This study develops a three-party evolutionary game model to examine strategic choices regarding platform regulation, anchor authorization, and secondary content creation. Results reveal that excessive regulation may undermine equilibrium and profitability, while appropriate authorization can balance risk and reward. Secondary creators' participation is sensitive to commission rates and cost-benefit trade-offs. This research contributes to the literature by integrating copyright governance into live-streaming e-commerce game theory and offers actionable insights for designing regulatory mechanisms, optimizing authorization policies, and fostering sustainable multi-party collaboration.
