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on Game Theory |
| By: | Claus-Jochen Haake (Paderborn University); Thomas Streck (Paderborn University) |
| Abstract: | We study the impact on outcomes from modeling asymmetric bargaining power in two-person bargaining problems in two different ways. For the Nash and the Kalai-Smorodinsky solutions, we compare application of the asymmetric version of the solution to the outcome from the symmetric version with an upfront modification of the disagreement point. We identify a systematic distortion of the final payoff for each bargaining solution, which is different across the two solutions. While for the Kalai-Smorodinsky solution a player with small power always benefits from modifying the disagreement point, the situation is reversed for the Nash bargaining solution. There, weak players are better off in the asymmetric bargaining solution. When comparing the application of the asymmetric versions of the Nash and the Kalai-Smorodinsky solutions, we demonstrate that there is a threshold weight for a player to be better off with the Nash bargaining solution. This threshold is determined by the relative utilitarian bargaining solution. |
| Keywords: | Asymmetric bargaining power, Nash bargaining solution, Kalai-Smorodinsky bargaining solution |
| JEL: | C78 D63 |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:dispap:143 |
| By: | Shitong Wang |
| Abstract: | This paper investigates the implementation and performance of a decentralized information transmission mechanism in complete information games. We propose a mediator-free mechanism that realizes mediator-free irrational correlated equilibria through a finite sequence of cheap talk. Designed for environments with at least five players, the mechanism leverages encryption techniques to safeguard private information and strategic choices. The core procedure involves three players decomposing and encrypting the equilibrium, while two other players securely randomize and deliver the encrypted recommendations to designated players. Our results demonstrate that all irrational correlated equilibria can be achieved through this mechanism, which is both strategically robust and practically implementable. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.01841 |
| By: | Thomas Streck (Paderborn University) |
| Abstract: | This paper studies the distortion of the asymmetric Nash and Kalai-Smorodinsky bargaining solutions that arise from differences in the shape of the bargaining set. In a two-person bargaining framework, we compare outcomes across different feasible sets for fixed bargaining power and repeat this for all possible power constellations between the players. Two arbitrary bargaining sets are selected, and the distortion of the asymmetric Nash solution, the symmetric Kalai-Smorodinsky solution, and the Nash solution with a shifted disagreement point is measured relative to the asymmetric Kalai-Smorodinsky solution, which serves as a reference. We compare pairs of bargaining problems that differ only in curvature and analyze how outcomes vary across solutions. This yields a quantitative measure of relative distortion and shows how sensitive bargaining solutions are to changes in set structure. For all solutions under observation, a weaker (stronger) player always prefers the more (less) curved bargaining set, as the distortion increases (decreases) in their favor. Indifference between two sets occurs when the distortion is equal for a given power constellation. For the asymmetric Nash and Kalai-Smorodinsky solutions, indifference occurs exactly when the solution points exhibit the same slope on their respective Pareto frontiers. Finally, the number of indifference points is always odd if one bargaining set contains the other. The results highlight how the shape of the Pareto frontier can introduce additional distortion in already unequal situations, suggesting that the structure of the bargaining set plays a crucial role in determining the fairness of outcomes. |
| Keywords: | Asymmetric bargaining power, Nash bargaining solution, Kalai-Smorodinsky bargaining solution |
| JEL: | C78 D63 |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:dispap:145 |
| By: | Giorgio Ferrari; Anna Pajola |
| Abstract: | We study a mean-field game of optimal stopping and investigate the existence of strong solutions via a connection with the Bank-El Karoui's representation problem. Under certain continuity assumptions, where the common noise is generated by a countable partition, we show that a strong randomized mean-field equilibrium exists, in which the mean-field interaction term is adapted to the common noise and the stopping time is randomized. Furthermore, under suitable monotonicity assumptions and for a general common noise, we provide a comparative statics analysis of the set of strong mean-field equilibria with strict equilibrium stopping times. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.19123 |
| By: | Zorana Grbac; Simone Pavarana; Thorsten Schmidt; Peter Tankov |
| Abstract: | We introduce a new mean-field game framework to analyze the impact of carbon pricing in a multi-sector economy with defaultable firms. Each sector produces a homogeneous good, with its price endogenously determined through market clearing. Firms act as price takers and maximize profits by choosing an optimal allocation of inputs-including labor, emissions, and intermediate goods from other sectors-while interacting through the endogenous sectoral price. Firms also choose their default timing to maximize shareholder value. Formally, we model the economy as an optimal stopping mean-field game within each sector. The resulting system of coupled mean-field games admits a linear programming formulation that characterizes Nash equilibria in terms of population measure flows. We prove the existence of a linear programming Nash equilibrium and establish uniqueness of the associated price system. Numerical illustrations are presented for firms with constant elasticity of substitution (CES) production functions. In a stylized single-sector economy, carbon price shocks induce substitution between emissions and labor. In a three-sector economy, the manufacturing sector faces consumer demand and requires inputs from a brown sector, which can be increasingly replaced by green-sector goods as carbon prices rise. These experiments reveal that carbon price shocks can generate substantial spillover effects along the value chain, underscoring the importance of sectoral interdependencies in shaping effective decarbonization pathways. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.11353 |
| By: | Hyeonggyun Ko |
| Abstract: | We study a long-run persuasion problem where a long-lived Sender repeatedly interacts with a sequence of short-lived Receivers who may adopt a misspecified model for belief updating. The Sender commits to a stationary information structure, but suspicious Receivers compare it to an uninformative alternative and may switch based on the Bayes factor rule. We characterize when the one-shot Bayesian Persuasion-optimal (BP-optimal) structure remains optimal in the long run despite this switching risk. In particular, when Receivers cannot infer the state from the Sender's preferred action, they never switch, and the BP-optimal structure maximizes the Sender's lifetime utility. In contrast, when such inference is possible, full disclosure may outperform BP-optimal. Our findings highlight the strategic challenges of information design when the Receivers' interpretation of signals evolves over time. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.01662 |
| By: | Michele Aleandri; Francesco Ciardiello; Andrea Di Liddo |
| Abstract: | We introduce and analyze a novel family of power indices tailored for sharing networks in technological markets, where firms operate competitively within, but not across, distinct industrial sectors. In these settings, inter-firm collaboration structures emerge from formal technology licensing agreements. The proposed indices are defined over graphs with a priori unions and combine two key centrality measures - degree-based and rescaled eigenvector centrality - modulated by positive market coefficients that reflect sectoral dynamics. We first explore the monotonicity properties of these indices, highlighting their responsiveness to local changes in network structure. Interestingly, major economic actors exhibit structural stability when inter-sectoral technological spillovers are minimal. Building on these findings, we provide theoretical underpinnings by characterizing the indices as the Shapley values of a family of coherent and economically interpretable transferable utility (TU) games defined over such graphs. However, for a broad class of network structures, the core of these TU games is often empty, signaling inherent instability in technological sharing arrangements. Finally, we offer an axiomatic foundation for this family of indices, proving independence of the proposed axioms. This axiomatization extends naturally to exchange networks, even when stage-propagation coefficients are not positive. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.13272 |
| By: | Claus-Jochen Haake (Paderborn University); Thomas Streck (Paderborn University) |
| Abstract: | Since Nash's (1950) seminal paper on the cooperative bargaining problem, the discipline has concentrated on the design of and solutions for bargaining problems. Nothing was said about how simple or difficult it is to find an agreement. We consider two-person bargaining problems and provide axioms for a mapping that assigns to each bargaining problem a number that quantifies the severeness of the conflict. We term this number the contestedness of a bargaining problem and show that there is one and only one mapping satisfying the axioms. Moreover, the axioms are shown to be logically independent, so that none of them can be dismissed. The contestedness is a normalized version of the standard traveling time introduced by Perles and Maschler (1981) to define a superadditive bargaining solution. Recognizing the payoff set reflects players' preferences our approach can also be utilized to measure similarity of diversity of preferences. |
| Keywords: | Bargaining problem, Contestedness, Perles-Maschler bargaining solution |
| JEL: | C78 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:dispap:144 |
| By: | Papatya Duman (Universität Bielefeld); Claus-Jochen Haake (Universität Paderborn); Alexander Koch (Universität Paderborn); Sarah Kühn (Universität Paderborn); Simon Hemmrich (Universität Paderborn); Daniel Beverungen (Universität Paderborn) |
| Abstract: | We examine the problem faced by a buyer seeking to purchase an experience good without prior knowledge of its stochastic quality. An expert who owns the product can be paid to provide a signal about its quality. Our analysis explores the impact of introducing a credible signaling mechanism for the buyer. Specifically, we propose using blockchain technology, which ensures immutability, decentralization, privacy, and transparency, to store the signal. Our findings reveal that this approach reduces the number of possible equilibria while preserving the “good equilibrium”, in which information is both acquired and accurately transmitted. Consequently, the use of blockchain tech-nology mitigates the equilibrium coordination problem and improves the provision of credible information. |
| Keywords: | Blockchain, Signaling, Asymmetric Information |
| JEL: | C72 D82 D47 |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:dispap:152 |
| By: | Pawe{\l} Niszczota; Tomasz Grzegorczyk; Alexander Pastukhov |
| Abstract: | Machines driven by large language models (LLMs) have the potential to augment humans across various tasks, a development with profound implications for business settings where effective communication, collaboration, and stakeholder trust are paramount. To explore how interacting with an LLM instead of a human might shift cooperative behavior in such settings, we used the Prisoner's Dilemma game -- a surrogate of several real-world managerial and economic scenarios. In Experiment 1 (N=100), participants engaged in a thirty-round repeated game against a human, a classic bot, and an LLM (GPT, in real-time). In Experiment 2 (N=192), participants played a one-shot game against a human or an LLM, with half of them allowed to communicate with their opponent, enabling LLMs to leverage a key advantage over older-generation machines. Cooperation rates with LLMs -- while lower by approximately 10-15 percentage points compared to interactions with human opponents -- were nonetheless high. This finding was particularly notable in Experiment 2, where the psychological cost of selfish behavior was reduced. Although allowing communication about cooperation did not close the human-machine behavioral gap, it increased the likelihood of cooperation with both humans and LLMs equally (by 88%), which is particularly surprising for LLMs given their non-human nature and the assumption that people might be less receptive to cooperating with machines compared to human counterparts. Additionally, cooperation with LLMs was higher following prior interaction with humans, suggesting a spillover effect in cooperative behavior. Our findings validate the (careful) use of LLMs by businesses in settings that have a cooperative component. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.18639 |
| By: | E. Emanuel Rapsch |
| Abstract: | In this work, an abstract and general language for the fundamental objects underlying dynamic games under probabilistic uncertainty is developed. Combining the theory of decision trees by Al\'os-Ferrer--Ritzberger (2005) and a Harsanyian notion of exogenous uncertainty, the concept of stochastic decision forests is introduced. Exogenous information is modelled via filtration-like objects providing dynamic updates on the "realised tree", and an abstract decision-theoretic model of adapted choice is formulated. Based on this, a consistent model of "rules" is introduced, leading to the notion of stochastic extensive forms, generalising Al\'os-Ferrer--Ritzberger (2008, 2011). Well-posedness is completely characterised in terms of order-theoretic properties of the underlying forest. Moreover, the language of stochastic extensive forms addresses a vast class of dynamic decision problems formulated in terms of time-indexed paths of action -- a first step towards an approximation theory of continuous-time games based on stochastic processes. In this formulation, a well-posed theory obtains if and only if the time half-axis is essentially well-ordered. Therefore, a relaxed game-theoretic model of "extensive form characteristics" is introduced: the stochastic process form. Its action processes arise from well-posed action path stochastic extensive forms under tilting convergence, which is introduced in order to faithfully describe accumulating reaction behaviour. The problem of instantaneous reaction and information about it is tackled by introducing vertically extended continuous time, for which a suitable stochastic analysis is developed. Stochastic process forms admit a natural notion of information sets, subgames, and equilibrium. The theory applies to stochastic differential and timing games, e.g., addressing issues in Fudenberg--Tirole (1985) and Riedel--Steg (2017) . |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.04752 |
| By: | Alexander Egberts (Max Planck Institute for Research on Collective Goods, Bonn); Christoph Engel (Max Planck Institute for Research on Collective Goods, Bonn); Joshua Fairfield (Max Planck Institute for Research on Collective Goods, Bonn) |
| Abstract: | Many social ills can be modelled as a public bad. In such scenarios, private benefit is often immediate while the public damage takes some time to materialize. In this experiment, we investigate the behavioral effects caused by such delays in the realization of collective harm. By manipulating the weight with which the damages caused by group contributions are carried over to the next round, we alter the number of periods required for the social damage to fully unfold. We keep constant the economic consequences of contributions between treatments (by introducing a multiplier for the damage) and between periods (by deducting all unrealized harm at the end of the game) to avoid multiple equilibria. In a second treatment dimension, we isolate the cognitive challenges of this experiment by replacing human group-members with “computerized players†which perfectly copy each subject’s previous behavior. We find that participants’ behavior is less cooperative over time when harm is deferred into the future. Our results also suggest that the driving mechanism behind this effect is not insufficient anticipation, but the lack of having experienced the negative consequences of the public damage. |
| Keywords: | public bad; dynamically developing social harm; cognitive and motivational challenge; experiment |
| JEL: | C91 D62 D91 H41 K24 K32 |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:mpg:wpaper:2024_16 |
| By: | Yuhang Guo; Dong Hao; Bin Li; Mingyu Xiao; Bakh Khoussainov |
| Abstract: | Strategyproofness in network auctions requires that bidders not only report their valuations truthfully, but also do their best to invite neighbours from the social network. In contrast to canonical auctions, where the value-monotone allocation in Myerson's Lemma is a cornerstone, a general principle of allocation rules for strategyproof network auctions is still missing. We show that, due to the absence of such a principle, even extensions to multi-unit network auctions with single-unit demand present unexpected difficulties, and all pioneering researches fail to be strategyproof. For the first time in this field, we identify two categories of monotone allocation rules on networks: Invitation-Depressed Monotonicity (ID-MON) and Invitation-Promoted Monotonicity (IP-MON). They encompass all existing allocation rules of network auctions as specific instances. For any given ID-MON or IP-MON allocation rule, we characterize the existence and sufficient conditions for the strategyproof payment rules, and show that among all such payment rules, the revenue-maximizing one exists and is computationally feasible. With these results, the obstacle of combinatorial network auction with single-minded bidders is now resolved. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.14472 |
| By: | Natalia Montinari; Matteo Ploner; Veronica Rattini |
| Abstract: | Immigration has shaped many nations, posing the challenge of integrating immigrants into society. While economists often focus on immigrants' economic outcomes compared to natives (such as education, labor market success, and health) social interactions between immigrants and natives are equally crucial. These interactions, from everyday exchanges to teamwork, often lack enforceable contracts and require cooperation to avoid conflicts and achieve efficient outcomes. However, socioeconomic, ethnic, and cultural differences can hinder cooperation. Thus, evaluating integration should also consider its impact on fostering cooperation across diverse groups. This paper studies how priming different identity dimensions affects cooperation between immigrant and native youth. Immigrant identity includes both ethnic ties to their country of origin and connections to the host country. We test whether cooperation improves by making salient a specific identity: Common identity (shared society), Multicultural identity (ethnic group within society), or Neutral identity. In a lab in the field experiment with over 390 adolescents, participants were randomly assigned to one of these priming conditions and played a Public Good Game. Results show that immigrants are 13 percent more cooperative than natives at baseline. Natives increase cooperation by about 3 percentage points when their multicultural identity is primed, closing the initial gap with immigrant peers. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.02511 |
| By: | Lichen Wang; Shijia Hua; Yuyuan Liu; Zhengyuan Lu; Liang Zhang; Linjie Liu; Attila Szolnoki |
| Abstract: | The frequent occurrence of natural disasters has posed significant challenges to society, necessitating the urgent development of effective risk management strategies. From the early informal community-based risk sharing mechanisms to modern formal index insurance products, risk management tools have continuously evolved. Although index insurance provides an effective risk transfer mechanism in theory, it still faces the problems of basis risk and pricing in practice. At the same time, in the presence of informal community risk sharing mechanisms, the competitiveness of index insurance deserves further investigation. Here we propose a three-strategy evolutionary game model, which simultaneously examines the competitive relationship between formal index insurance purchasing (I), informal risk sharing strategies (S), and complete non-insurance (A). Furthermore, we introduce a method for calculating insurance company profits to aid in the optimal pricing of index insurance products. We find that basis risk and risk loss ratio have significant impacts on insurance adoption rate. Under scenarios with low basis risk and high loss ratios, index insurance is more popular; meanwhile, when the loss ratio is moderate, an informal risk sharing strategy is the preferred option. Conversely, when the loss ratio is low, individuals tend to forego any insurance. Furthermore, accurately assessing the degree of risk aversion and determining the appropriate ratio of risk sharing are crucial for predicting the future market sales of index insurance. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.02684 |
| By: | Johannes Johnen; Shiva Shekhar |
| Abstract: | This paper proposes a simple yet useful framework for evaluating vertical mergers in digital markets by distinguishing between product-specific and ecosystem-specific network effects. Vis-a-vis no network effects, product-specific network effects amplify foreclosure and steering incentives, as a rival’s growth directly undermines the platform’s product value. Conversely, ecosystem-specific effects dampen foreclosure incentives, since rivals contribute to the overall value of the platform ecosystem. We develop a formal model illustrating how this distinction shapes platform behavior and competitive outcomes. We apply this distinction to real-world examples to illustrate its potential usefulness. Our distinction implies that regulators may want to adopt a stricter standard with no presumption of efficiencies where product-specific effects dominate. In contrast, when ecosystem-specific effects prevail, merger evaluation should mirror traditional vertical merger analysis. Thus, offering a more nuanced approach to merger evaluation by presenting a practical screening tool to identify problematic vertical mergers in markets featuring network effects. |
| Keywords: | network externalities, platforms, vertical integration |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12040 |
| By: | Yiling Chen; Tao Lin; Wei Tang; Jamie Tucker-Foltz |
| Abstract: | The optimal signaling schemes in information design (Bayesian persuasion) problems often involve non-explainable randomization or disconnected partitions of state space, which are too intricate to be audited or communicated. We propose explainable information design in the context of information design with a continuous state space, restricting the information designer to use $K$-partitional signaling schemes defined by deterministic and monotone partitions of the state space, where a unique signal is sent for all states in each part. We first prove that the price of explainability (PoE) -- the ratio between the performances of the optimal explainable signaling scheme and unrestricted signaling scheme -- is exactly $1/2$ in the worst case, meaning that partitional signaling schemes are never worse than arbitrary signaling schemes by a factor of 2. We then study the complexity of computing optimal explainable signaling schemes. We show that the exact optimization problem is NP-hard in general. But for Lipschitz utility functions, an $\varepsilon$-approximately optimal explainable signaling scheme can be computed in polynomial time. And for piecewise constant utility functions, we provide an efficient algorithm to find an explainable signaling scheme that provides a $1/2$ approximation to the optimal unrestricted signaling scheme, which matches the worst-case PoE bound. A technical tool we develop is a conversion from any optimal signaling scheme (which satisfies a bi-pooling property) to a partitional signaling scheme that achieves $1/2$ fraction of the expected utility of the former. We use this tool in the proofs of both our PoE result and algorithmic result. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.14196 |
| By: | Gamal Atallah; Aggey Simons (Department of Economics, University of Ottawa, Canada) |
| Abstract: | We analyze innovation incentives under price cap regulation by examining scenarios with endogenous price caps, both with and without regulatory commitment. In a setting without informational imperfections, our analysis reveals two principal conclusions. First, there is no trade-off between static and dynamic efficiency. Strengthening firm incentives by allowing it to charge higher prices, and thus realize greater profits, leads to less innovation because it reduces output. The optimal strategy to boost innovation and maximize welfare is to set a low price (and thus, a low profit) target, as innovation incentives are proportional to output. Second, the benefits of regulatory commitment for innovation and welfare are not unambiguously clear: commitment neither consistently outperforms nor underperforms non-commitment. Under demand uncertainty, when the firm is risk-averse, the static-dynamic efficiency trade-off reappears, and the firm may prefer non-commitment due to risk-shielding. Under asymmetric information about firm demand type, the trade-off between static and dynamic efficiency becomes inherent (due to information rents and contract distortions), and commitment becomes unambiguously crucial for fostering innovation by preventing the ratchet effect. |
| Keywords: | Price cap regulation; Regulation, Innovation, R&D, Dynamic efficiency; Commitment. |
| JEL: | D42 L12 L43 L51 O31 O38 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ott:wpaper:2504e |
| By: | Jugal Garg; Yixin Tao; L\'aszl\'o A. V\'egh |
| Abstract: | The Probabilistic Serial (PS) mechanism -- also known as the simultaneous eating algorithm -- is a canonical solution for the assignment problem under ordinal preferences. It guarantees envy-freeness and ordinal efficiency in the resulting random assignment. However, under cardinal preferences, its efficiency may degrade significantly: it is known that PS may yield allocations that are $\Omega(\ln{n})$-worse than Pareto optimal, but whether this bound is tight remained an open question. Our first result resolves this question by showing that the PS mechanism guarantees $(\ln(n)+2)$-approximate Pareto efficiency, even in the more general submodular setting introduced by Fujishige, Sano, and Zhan (ACM TEAC 2018). This is established by showing that, although the PS mechanism may incur a loss of up to $O(\sqrt{n})$ in utilitarian social welfare, it still achieves a $(\ln{n}+2)$-approximation to the maximum Nash welfare. In addition, we present a polynomial-time algorithm that computes an allocation which is envy-free and $e^{1/e}$-approximately Pareto-efficient, answering an open question posed by Tr\"obst and Vazirani (EC 2024). The PS mechanism also applies to the allocation of chores instead of goods. We prove that it guarantees an $n$-approximately Pareto-efficient allocation in this setting, and that this bound is asymptotically tight. This result provides the first known approximation guarantee for computing a fair and efficient allocation in the assignment problem with chores under cardinal preferences. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.03359 |
| By: | Thomas Hazenberg; Yao Ma; Seyed Sahand Mohammadi Ziabari; Marijn van Rijswijk |
| Abstract: | This study investigates how Multi-Agent Reinforcement Learning (MARL) can improve dynamic pricing strategies in supply chains, particularly in contexts where traditional ERP systems rely on static, rule-based approaches that overlook strategic interactions among market actors. While recent research has applied reinforcement learning to pricing, most implementations remain single-agent and fail to model the interdependent nature of real-world supply chains. This study addresses that gap by evaluating the performance of three MARL algorithms: MADDPG, MADQN, and QMIX against static rule-based baselines, within a simulated environment informed by real e-commerce transaction data and a LightGBM demand prediction model. Results show that rule-based agents achieve near-perfect fairness (Jain's Index: 0.9896) and the highest price stability (volatility: 0.024), but they fully lack competitive dynamics. Among MARL agents, MADQN exhibits the most aggressive pricing behaviour, with the highest volatility and the lowest fairness (0.5844). MADDPG provides a more balanced approach, supporting market competition (share volatility: 9.5 pp) while maintaining relatively high fairness (0.8819) and stable pricing. These findings suggest that MARL introduces emergent strategic behaviour not captured by static pricing rules and may inform future developments in dynamic pricing. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.02698 |