In a cooperative game on simplicial complexes with filtration (SF), players can join the grand coalition simultaneously according to a given sequence, but the simplicial value of a cooperative game on SF (SF game) does not consider player's bargaining power in the formation of SF. Considering the influence of player's joining order in the formation of SF, we introduce a relative marginal contribution (RMC) value in this restricted coalition and the generalized simplicial value (the GS value) is proposed as an extension of the simplicial value. Furthermore, because player's joining order is deterministic in SF, which is different from a crisp cooperative game, we examine the effect of players' order on their RMCs and the MCD value is characterized. The MCD value may motivate players to contribute to SF. As extensions of the simplicial value, both the GS value and the MCD value are based on RMC, while the MCD value is friendly to the players who join the cooperation early on.
This paper studies an attack–defense game with incomplete information. The game involves two players: the defender and the attacker. The defender locks objects. The attacker then tests the objects and obtains information with random errors. When attacking an unlocked object, the attacker wins the game. Sonin’s complex “fill-and-switch” strategy is reduced to a simple threshold rule: the attacker targets nodes with a negative signal when the sum of sensitivity and specificity is greater than 1, nodes with a positive signal when the sum is less than 1, and randomizes when the sum is 1. The defender allocates locks uniformly at random. Exact expressions for the attacker’s equilibrium strategy are obtained, as well as analytical expressions for the game value. The game value satisfies duality, reaches its minimum when the sum of sensitivity and specificity is 1, and converges to the node value at rate [Formula: see text]. This makes the LBT model a practical tool for security applications.
In this paper, we characterize the coalition worth function in a generalized TU coalitional game to explain the formation, size, and composition of two particular classes of sub-coalitions, defined as the maximal proper subcoalition (MPS) and stable proper sub-coalition (SPS). In the case of MPS, the coalition worth function provides sufficient incentive to each of some (but not all) players to form the coalition, not to integrate with player(s) outside the coalition, and prevents disintegration into a smaller coalition. We label this as the definition of MPS from a micro-perspective. On the other hand, SPS is defined based on the distribution of coalition worth among the members. We also define an MPS from the macro perspective, which is based on the sub-coalition (group) worth function. We show that in order to be an MPS, the coalition worth function has to be cohesive over the set of players forming the coalition and sub-additive over the set of players outside the coalition. However, this is only necessary but not sufficient for forming an MPS. Interestingly, we find that there can be TU coalitional games where there are MPS, but there is no maximal proper sub-coalition structure (MPSS). Next, we show that an MPS is always an SPS, but the converse is not true. Thus, the results of MPS automatically extend to SPS. Finally, we show that an MPSS and/or stable proper sub-coalition structure (SPSS) has higher welfare than the grand coalition.
In this paper, we develop a continuous-time equilibrium model of futures markets in which heterogeneous hedgers and speculators trade under explicit margin constraints. Agents maximize exponential utility and take prices as given, while the equilibrium futures drift is determined endogenously through market clearing. Margin frictions interact with risk-sharing motives to generate a nonlinear fixed-point problem linking individual optimality to aggregate consistency. The equilibrium is characterized by a coupled Hamilton–Jacobi–Bellman (HJB) and backward stochastic differential equation (BSDE) system, and we establish existence and uniqueness of the equilibrium drift under mild regularity conditions. A central contribution of the framework is a new geometric characterization of margin effects: margin constraints create no-trade regions in drift space, producing a frictional wedge that forces the equilibrium drift to be the projection of the frictionless Keynes–Hicks drift onto a margin-dependent interval. This yields a kinked and convex mapping from margin tightness to liquidity premia, with one-for-one amplification when the frictionless drift lies outside the wedge and flat sensitivity once it lies inside. Unlike Brunnermeier–Pedersen [[2009] Market liquidity and funding liquidity, Rev. Financ. Stud. 22(6), 2201–2238] and Gârleanu–Pedersen [[2011] Margin-based asset pricing and deviations from the law of one price, Rev. Financ. Stud. 24(6), 1980–2028], whose margin effects are linear and exogenous, our model delivers a fully dynamic, state-dependent amplification mechanism arising endogenously from equilibrium price formation. The structure provides a tractable foundation for empirical implementation using disaggregated trader positions. By using CFTC gold-futures data and CME volatility measures, we find strong empirical support for the model’s nonlinear amplification mechanism: hedging pressure alone has no predictive power; margin tightness exerts a negative baseline effect; the interaction between hedging pressure and margin tightness generates a statistically significant kink; and volatility sharply magnifies the impact of margin tightness, producing the largest and most significant effect in the data. These findings confirm the model’s core prediction that margin constraints generate nonlinear, state-dependent, and volatility-amplified liquidity premia, providing the first structural empirical evidence for a kinked margin-pressure mechanism derived from a full HJB–BSDE equilibrium.
In this paper, we introduce and investigate a Hotelling duopoly model where the price of undifferentiated products is fixed and transportation cost is viewed as an inverse predictor of sales volume. In this model, vendors can increase sales by establishing equilibrium locations away from the center of the street. Assuming linear costs, an equilibrium occurs at locations 1/3 and 2/3, providing each vendor with an additional 44% in sales. For a street 50% longer than Main Street, where initial demand equals zero near the ends, the equilibrium locations are 0.28 and 0.72 for an 86% increase in sales. For a street half the length of Main Street, where demand never falls to zero, an equilibrium occurs at locations 0.31 and 0.69 for a 16% increase in sales. Assuming sub-linear transportation costs, vendors can increase Main Street sales by 36%, and with super-linear costs, they can achieve an increase of 73%. In general, the greater the penalty for distance from a vendor, the more vendors have to gain by spreading out. We close by presenting equilibria for three and also for four Main Street vendors.
Controlling nonpoint-source pollution is inherently challenging due to its diffuse nature and limited observability. This study develops a Cournot duopoly model in which production generates nonpoint-source pollution and firms producing differentiated goods jointly determine output and abatement technology under an ambient charge. Unlike point-source pollution, nonpoint-source pollution cannot be directly monitored; the regulator observes only ambient pollution concentrations. By explicitly incorporating this informational constraint, the model provides a tractable analytical framework for examining strategic interactions between firms and the regulator. The analysis proceeds in two stages. In the second stage, closed-form expressions for equilibrium output and abatement are derived as functions of the ambient charge, and feasibility conditions are established. It is shown that total emissions decrease monotonically with the charge rate, regardless of whether firms are homogeneous or heterogeneous, ensuring policy effectiveness even when individual firms exhibit perverse responses. In the first stage, random fluctuations in ambient pollution are introduced to characterize the optimal charge rate that maximizes expected social welfare under uncertainty. Overall, the results confirm that ambient-based regulatory instruments constitute a robust and analytically transparent approach to controlling nonpoint-source pollution, even in the presence of firm heterogeneity and uncertainty.
In this paper, we introduce multi-dimensional rules with multiple approval levels in the input, which generalize both the multi-dimensional rules introduced by Courtin, S. and Laruelle, A. [2020] Multi-dimensional rules, Math. Soc. Sci. 103, 1–7 and the games with multiple approval levels in the input studied by Freixas, J. and Zwicker, W. S [2003] Weighted voting, abstention, and multiple levels of approval, Soc. Choice Welfare 21, 399–431. The decision process of such a rule is modeled as follows: (i) there are several individuals; (ii) there are several dimensions; (iii) each individual expresses a level of approval on each dimension; (iv) a decision process maps each input profile to a final decision (“accept” or “reject”).
This note considers two existing cooperative solutions that reflect the contributions of the players — the Shapley value and the fair gain-sharing value. Given the asymmetry of the players, a crucial requirement for an acceptable cooperation solution is that it has to reflect the contributions of the players. Five aspects of these two solutions are analyzed. They are: the overage of types of games, the computation time, the avoidance of arbitrary equal sharing, the contributions measured, and the underlying optimization process.
This paper revisits Theorem 3.2 of Crettez et al. ([2025] Nash equilibrium in discontinuous games: A weakening of Reny's robust better-reply correspondence property, Int. Game Theory Rev. 27(3), 1-39), which establishes the existence of a pure-strategy Nash equilibrium in convex and compact games with possibly discontinuous payoffs under an F-pi-Pi weak robust better-reply correspondence property. Instead of the original fixed-point construction, the proof here proceeds via a single Caristi-Khamsi fixed point theorem for set-valued maps, under a mild additional lower semicontinuity assumption on the associated deviation-profit potential. The key step is to associate with each strategy profile a deviation-profit potential that measures the maximal unilateral gain from weakly robust deviations and to show that this potential decreases along the F-pi-Pi weak robust better-reply correspondence. The resulting Caristi inequality yields a fixed point of the induced better-reply map, which is a Nash equilibrium. The argument provides a structural reinterpretation of the result of Crettez et al. ([2025] Nash equilibrium in discontinuous games: A weakening of Reny's robust better-reply correspondence property, Int. Game Theory Rev. 27(3), 1-39), highlighting the potential-theoretic nature of the robustness condition and separating the economic structure of profitable deviations from the topological fixed-point machinery.
Battery-swapping (BS) offers a rapid refueling solution for electric vehicles (EVs) but faces prohibitive infrastructure costs, creating a strategic dilemma between proprietary monopoly and alliance formation. We develop a game-theoretic model to examine the optimal infrastructure deployment and cooperation incentives for a BS innovator (battery-swapping vehicle manufacturer [BVM]) and a charging-based rival (charging vehicle manufacturer [CVM]). Our base model reveals that cooperation primarily drives infrastructure consolidation, resulting in fewer stations than the competition due to the elimination of redundant investments. However, we find that incorporating station congestion triggers a strategic reversal: specifically, in large-scale markets with moderate consumer preference, the negative externality of queuing compels the alliance to expand capacity beyond competitive levels to maintain service quality. Surprisingly, cooperation is not universally optimal: the CVM is deterred by retrofit barriers in nascent markets, while the BVM guards its monopoly rents in mature markets. Consequently, a "Win-Win" equilibrium is conditional; it is achievable only under a moderate market scale and consumer preferences. Furthermore, we demonstrate that the credible threat of the rival's independent entry acts as a strategic catalyst, forcing the incumbent to embrace cooperation to preempt a destructive infrastructure arms race. These findings provide a strategic roadmap for balancing efficiency and service quality in the EV ecosystem.
In this paper, we derive optimal strategies for the discrete poker model of von Neumann and Morgenstern for deck sizes S = 2 through S = 5 for all values of p > 1, where p is the ratio of the high and low bids available to the players. Primary results are (1) for S = 2, there are two optimal pure strategies that apply to different values of p; (2) for S = 3, there are two optimal pure strategies for 1 < p <= 2, a family of optimal mixed strategies for 2 < p < 4, discontinuous at the endpoints, and an optimal pure strategy for 4 <= p; and (3) for S = 4 and S = 5, there are multiple optimal pure strategies for low and high values of p, as well as three or six optimal mixed strategies, respectively, for intermediate values of p, which exhibit multiple discontinuities. In contrast to the previous authors' results for the continuous case (where each player is "dealt" a real number between 0 and 1), for small values of p, players should always bid high, and for sufficiently large values of p, players should bid high only when dealt the maximum value S. In between, the optimal mixed strategies are numerous and behave precariously. We combine empirical results with formal analysis to explain the observed behavior and to indicate what to expect for larger values of S.
We study strategic delegation in a Cournot duopoly with linear demand and asymmetric constant marginal costs where each firm offers its manager incentive contracts that are based on either the firm's profit or its revenue. Taking the equilibrium outcomes of the Cournot stage into consideration, the reduced form delegation game is a 2 & times; 2 anti-coordination game. Using the results of Calv & oacute;-Armengol [[2003] The set of correlated equilibria of 2 & times; 2 games, Barcelona Economics Working Paper Series No. 79], we characterize the set of all correlated equilibria of this game. We show that for certain parametric configurations of the model (involving the demand intercept and cost differences), there is a continuum of correlated equilibrium outcomes under which the high-cost firm obtains a higher profit than the low-cost firm.
This paper investigates stability conditions for weighted monoplex (single-layer) networks obtained by transformation of multiplex networks. We develop two comprehensive frameworks for such a transformation that take into account information including the length of the shortest path and the number of direct links between players in different layers to analyze network stability through utility functions depending on benefits and costs. Three different cost functions are investigated. The study establishes stability conditions for key network structures, including monoplex networks obtained by transforming all-layer complete, all-layer star (with identical or different centers), and unique-over-layers network configurations. Through comparative analysis, we examine when stability properties are preserved or altered when transforming multiplex networks into weighted monoplex networks.
This paper revisits Heinrich F. von Stackelberg's original description of leader-follower games under incomplete information, exploring how learning dynamics shape strategic interaction. The leader iteratively updates its conjecture about the follower's reaction function before choosing an activity level that maximizes its payoff. The follower, in turn, responds optimally to each activity level, revealing information that the leader uses to refine its conjecture. Assuming linear conjectures, a smooth updating process & agrave; la [Jean-Marie, A. and Tidball, M. [2006] Adapting behaviors through a learning process, J. Econ. Behav. Organ. 60, 399-422, doi:10.1016/j.jebo.2004.02.007], and quadratic payoff functions, we establish conditions under which the learning process converges asymptotically to a self-confirming steady-state. We characterize the resulting activity levels and payoffs in two canonical environments: a sequential partnership game and a sequential duopoly game with quantity competition. We then compare the learning outcomes to both the (complete information) Stackelberg and the cartel solution. In the process, we find conditions under which the lack of information and the resulting strategic ambiguity lead to higher joint payoffs, and under which usual intuitions about the first-mover advantage need qualifications.
In this paper, we develop a dynamic signaling model to examine how audit fee structures shape accountants' effort choices and reveal their intrinsic integrity. A firm hires an accountant whose type - rigorous or fraudulent - is private information and offers a contract combining fixed salary and performance-based pay. Each accountant selects an observable effort level that serves as a type signal. We derive the perfect Bayesian equilibria and identify conditions under which rigorous types distinguish themselves by exerting higher effort and when imitation occurs. When performance-based pay sufficiently differentiates between types, fraudulent types are deterred from mimicry, preserving audit integrity. Conversely, when base salary differences fall within critical bounds, pooling equilibria emerge - either fraudulent types mimic rigorous effort or rigorous types reduce effort to match fraudulent behavior. These results demonstrate that high audit fees alone do not ensure quality and that poorly calibrated incentives may encourage collusion. By highlighting the dual function of audit fees as both incentives and signals, this study advances contract theory under asymmetric information and offers practical guidance for designing remuneration schemes that foster audit quality and integrity.
In an era of rapid technological change and complex industrial organization, strategic decision-making in service-oriented manufacturing (SOM) is increasingly critical. This study addresses the challenge of optimizing capacity sharing networks - where unpredictable collaborations and multi-dimensional uncertainties impede efficiency. The study develops a novel bi-layer network model grounded in graph game theory and hesitant fuzzy sets. This framework formulates capacity sharing as a dynamic game featuring strategic attachment mechanisms, where hesitant fuzzy operators adeptly capture the vagueness in partnership evaluations. A case study based on Haier's industrial practice demonstrates that the model fosters a self-organizing core-periphery network structure. The results show significant improvements in resource circulation efficiency and network synergy. This study provides an intelligent, analytically rigorous governance framework that equips decision-makers to navigate uncertainty and enhance collaborative outcomes in modern industrial ecosystems.
In this paper, we introduce a Euclidean path integral control approach to determine optimal strategies for firms operating under a Walrasian system, Pareto optimality, and a non-cooperative feedback Nash equilibrium. Our framework formulates a Lagrangian control problem with forward-looking stochastic dynamics, eliminating the need for a value function to derive optimal strategies. The method relies on a continuously differentiable It & ocirc; process generated by integrating factors, providing a computationally feasible alternative to solving complex market dynamics. Our approach facilitates the analysis of generalized nonlinear market dynamics, where constructing a Hamilton-Jacobi-Bellman (HJB) equation is particularly challenging. Similar to the Feynman-Kac approach, our solutions are not unique. Given the large number of firms considered, our method draws comparisons with mean-field game approach. The primary contribution of this work is the derivation of a non-cooperative feedback Nash equilibrium, offering a comparative perspective against solutions generated by mean-field interactions. We illustrate the effectiveness of our approach through various examples, contrasting it with the Pontryagin maximum principle.
In recent years, with the rapid growth of China's e-commerce economy, complaints about illegal content posted on platforms have also increased significantly. How to effectively regulate the behaviors of influencers is a key issue in the regulatory management of e-commerce platforms (ECPs). This study uses evolutionary game theory and prospect theory to conduct theoretical research and modeling on the regulatory behaviors of ECP and the content production behaviors of the influencers. The evolutionary dynamic system is numerically simulated and analyzed using phase diagrams and time series diagrams. The evolutionary system stability and impact relationship of game behavior interaction between ECP and influencers are studied in various scenarios, and some suggestions for ECP's regulation and influencers' producing behaviors are proposed.
Detecting malicious users or unauthorized activities is a critical challenge in dynamic spectrum access. Traditionally, in such problems, an intrusion detection system (IDS) aims to maximize detection probability. Meanwhile, in networks or radio spectrum problems with multiple nodes or bands, respectively, a protocol that maximizes detection probability might lead to focusing on scanning the most plausible nodes or bands for intrusion and neglecting to scan less plausible ones due to limited scanning resources. To address this challenge, we propose a protocol that maximizes the fairness of detection probabilities across all bands within the bandwidth. We consider alpha-fairness as a fairness criterion. By using a game-theoretical approach, we model the IDS, which has to decide which of the bands to scan and how long to do it when the IDS faces an adversary who endorses artificial intelligence (AI), enabling the adversary not only to infiltrate the bandwidth without being detected but also to do so in a less predictable manner for the IDS. The equilibrium strategies of the IDS and adversary are derived. An advantage of the fairness detection probability protocol in comparison with the maximizing detection probability protocol is illustrated.
Partnerships represent strategic alliances where two or more entities collaborate by pooling resources to achieve mutual economic benefits. However, the uncertainty surrounding the return on investment (ROI) poses significant challenges in designing optimal partnership contracts. This paper develops a game-theoretic model to structure partnership contracts under uncertain ROI, where the final investment outcome is stochastic and ex-ante unknown to both partners. The model analyzes the contract design from one partner's perspective, considering the possibility that the other partner may face future market shocks that could affect its ability to honor its commitments to the partnership. We characterize the equilibrium of the game and propose strategies that the primary partner can adopt to mitigate risks and safeguard its interests. The findings provide insights into how strategic contract design can enhance the stability, cooperation, and efficiency of partnerships operating under uncertain market conditions.
