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on Game Theory |
| By: | Stefan Mladenoski (Faculty of Economics, American University of Europe-FON, North Macedonia) |
| Abstract: | Game theory is considered a key framework in understanding the market economy. That is exactly why the comparison between cooperative and non-cooperative games and their outcomes is significant. Namely, when it comes to what constitutes a cooperative game, as the name suggests, it is a game in which two or more players make decisions together. In contrast, a non-cooperative game is one in which each player independently decides how to play their move. The aim of this paper is to compare the solutions and implications of cooperative and non-cooperative games, which will be explained through theory and practical examples. The methodological approach used in this paper is based on theoretical analysis, modeling of games, and examining the solutions obtained from the structure of the games. Cooperative and non-cooperative games both involve strategic decision-making by rational players, but they differ fundamentally in the role of communication and the possibility of binding agreements. While cooperative games allow for coalition formation and the achievement of efficient outcomes, non-cooperative games focus on individual strategies in conditions of limited trust, which often lead to less optimal but more realistic equilibria. The results of this comparison highlight the importance of selecting the appropriate game model when analyzing strategic situations, depending on the level of trust, the potential for cooperation, and the nature of interests among players. This opens space for further research toward the development of hybrid models and their practical application in areas such as economic markets or international relations. |
| Keywords: | Cooperative games, Non-cooperative games, Nash equilibrium |
| JEL: | C71 C72 D43 |
| Date: | 2025–12–15 |
| URL: | https://d.repec.org/n?u=RePEc:aoh:conpro:2025:i:6:p:356-366 |
| By: | Vasilios Kanellopoulos |
| Abstract: | This paper examines a competition game whose key variables are the R&D efforts (e.g. R&D expenditures) and accumulated knowledge of firms located in a specific region. The most significant element of accumulated knowledge is knowledge spillovers. These are considered intra-industry as it is assumed that the firms operate within the same industry (i.e. similar types of firms) and competitors offer similar products. The present study identifies a Nash equilibrium based on firm cost minimisation. This is derived under the assumption that the firms under examination act rationally and are primarily concerned with achieving optimal outcomes - specifically, by minimising their total costs. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.13282 |
| By: | Nicholas H. Kirk |
| Abstract: | We study dynamic games with hidden states and absorbing failure, where belief-driven actions can trigger irreversible collapse. In such environments, equilibria that sustain activity generically operate at the boundary of viability. We show that this geometry endogenously reverses the value of information: greater informational precision increases the probability of collapse on every finite horizon. We formalize this mechanism through a limit-viability criterion, and model opacity as a strategic choice of the information structure via Blackwell garbling. When failure is absorbing, survival values become locally concave in beliefs, implying that transparency destroys equilibrium viability while sufficient opacity restores it. In an extended game where agents choose the information structure ex ante, strictly positive opacity is necessary for equilibrium survival. The results identify irreversible failure--not coordination, misspecification, or ambiguity--as a primitive force generating an endogenous demand for opacity in dynamic games. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.12046 |
| By: | Federico Echenique; Mat\'ias N\'u\~nez |
| Abstract: | We propose a solution and a mechanism for two-agent social choice problems with large (infinite) policy spaces. Our solution is an efficient compromise rule between the two agents, built on a common cardinalization of their preferences. Our mechanism, the multimatum, has the two players alternate in proposing sets of alternatives from which the other must choose. Our main result shows that the multimatum fully implements our compromise solution in subgame perfect Nash equilibrium. We demonstrate the power and versatility of this approach through applications to political economy, other-regarding preferences, and facility location. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.21275 |
| By: | Nabil I. Al-Najjar (Northwestern University); Harald Uhlig (University of Chicago - Department of Economics) |
| Abstract: | We propose rational disagreement as a formal framework for analyzing seemingly irrational behavior that can persist despite the wide availability of objective information in a steady-state. Agents are rational in that they correctly anticipate the distribution of aggregate outcomes, yet disagree about which specific individuals perform better than others. Notably, the subjective belief of any individual may be objectively correct. We illustrate the key concepts with a simple entry game. We show how unordered individual outcome distributions can be identified solely from aggregate statistics. We then characterize the resulting game, define its Nash equilibria, and develop a statistical test for the null hypothesis of agreement. Finally, we situate our framework within the broader literature on Bayesian games, behavioral biases, and the rational expectations hypothesis. |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:bfi:wpaper:2026-15 |
| By: | Zongxia Liang; Jiayu Zhang; Zhou Zhou; Bin Zou |
| Abstract: | This paper develops a dynamic insurance market model comprising two competing insurance companies and a continuum of insureds, and examines the interaction between strategic underreporting by the insureds and competitive pricing between the insurance companies under a Bonus-Malus System (BMS) framework. For the first time in an oligopolistic setting, we establish the existence and uniqueness of the insureds' optimal reporting barrier, as well as its continuous dependence on the BMS premiums. For the 2-class BMS case, we prove the existence of Nash equilibrium premium strategies and conduct an extensive sensitivity analysis on the impact of the model parameters on the equilibrium premiums. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.12655 |
| By: | Esmat Sangari; Rajni Kant Bansal |
| Abstract: | We study mixed bundling and competitive price-matching guarantees (PMGs) in a duopoly selling complementary products to heterogeneous customers. One retailer offers mixed bundling while the rival sells only a bundle. We characterize unique pure-strategy Nash equilibria across subgames and compare them to a no-bundling benchmark. Mixed bundling strictly dominates whenever an equilibrium exists. Conditional on bundling, PMG adoption trades off strategic demand capture against margin losses on loyal customers and varies systematically with relative demand responsiveness to prices and complementarities. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.15350 |
| By: | Hanchao Liu; Dena Firoozi |
| Abstract: | We extend the results of (Liu and Firoozi, 2025), which develops the theory of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces, by incorporating a common noise. This common noise is modeled as an infinite-dimensional Wiener process affecting the dynamics of all agents. In the presence of common noise, the mean-field consistency condition is characterized by a system of coupled forward-backward stochastic evolution equations (FBSEEs) in Hilbert spaces, whereas, in its absence it is represented by coupled forward-backward deterministic evolution equations. We establish the existence and uniqueness of solutions to the coupled linear FBSEEs associated with the LQ MFG framework for small time horizons and prove the $\epsilon$-Nash property of the resulting equilibrium strategy. Furthermore, we establish the well-posedness of these coupled linear FBSEEs for arbitrary finite time horizons. Beyond the specific context of MFGs, our analysis also yields a broader contribution by providing, to the best of our knowledge, the first well-posedness result for a class of infinite-dimensional linear FBSEEs, for which only mild solutions exist, over arbitrary finite time horizons. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.13493 |
| By: | Masaki Miyashita |
| Abstract: | Building on the generalized hedonic-linear model of Pellegrino (2025), this paper studies optimal product differentiation when a representative consumer has preferences over product characteristics. Under multiproduct monopoly, the monopolist's choice of product characteristics is always aligned with the social planner's optimum, despite underproduction. By contrast, under oligopoly, multiple equilibria can arise that differ qualitatively in their patterns of characteristics design. We show that, while oligopoly equilibria exhibiting product differentiation yield higher welfare than those with product concentration, the degree of product differentiation under oligopoly remains below the socially optimal level. As a result, social welfare under oligopoly is typically lower than under monopoly, highlighting a key advantage of coordination in characteristics design. We extend the analysis to settings with overlapping ownership structures and show that common ownership can improve welfare by inducing firms to soften competition through increased product differentiation rather than output reduction. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.21573 |
| By: | Brian C. Albrecht; Mark Whitmeyer |
| Abstract: | How do cost shocks pass through to prices in markets with price dispersion? Pass-through analysis typically assumes a single equilibrium price, but empirical studies consistently document substantial price variation, even for homogeneous products. This paper develops a tractable framework that decomposes the pass-through problem into two distinct tiers. The first is a competition layer where consumers' \textit{consideration sets} determine equilibrium distributions of normalized margins. The second is a curvature layer where demand elasticity determines how these margins translate into prices and pass-through rates. The key theoretical innovation is showing that the strategic pricing game with arbitrary downward-sloping demand is order-isomorphic to a baseline unit-demand game once reformulated in terms of normalized effective margins. This decomposition yields closed-form pass-through formulas, robust bounds across demand specifications, and clear comparative statics linking market structure to incidence. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.17964 |
| By: | Brown, Tarnell |
| Abstract: | Individuals released from jails and prisons face extremely high risks of fatal overdose and reincarceration, yet many jurisdictions continue to underprovide medications for opioid use disorder (MOUD), recovery housing, and supervised consumption services. At the same time, recovery residences and diversion courts are expanding without a clear framework for institutional design. This paper develops a mechanism-design model of harm-reduction policy at the interface of criminal justice and community treatment. A public funder chooses a funding regime and certification rules, diversion judges set the stringency of supervision and treatment conditions, recovery residence providers decide whether to operate abstinence-only or MOUD-inclusive housing, and high-risk individuals choose whether to comply or relapse. The model yields a punitive equilibrium, supported by abstinence-only funding and strict conditions, and a harm-reduction equilibrium under MOUD-inclusive funding and flexible conditions. Using effect sizes from Rhode Island’s statewide corrections MOUD program, Massachusetts’ jail-based MOUD pilots, and recent recovery housing evaluations, we show that the harm-reduction equilibrium is Pareto-superior for funders, judges, providers, and high-severity residents, yet the punitive equilibrium can remain risk-dominant because of political and informational frictions. We then embed the game in a computational social choice framework: stakeholders hold multi-dimensional preferences over policy bundles—combinations of funding rules, certification standards, diversion guidelines, and overdose prevention interventions such as supervised consumption sites—and social choice is constrained by justice-based requirements that rule out policies generating avoidable lethal risk or systematic exclusion of MOUD patients from housing and treatment. The analysis characterizes which harm-reduction mechanisms are implementable as equilibrium outcomes of the institutional game while respecting these constrained social preferences, and it identifies simple instruments—MOUD-inclusive funding commitments, performance-based transparency, and structured diversion defaults—that can move jurisdictions from punitive to harm-reduction equilibria within existing legal constraints. |
| Date: | 2026–02–03 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:wrkj3_v1 |
| By: | Elisa Botteghi; Martino S. Centonze; Davide Pastorello; Daniele Tantari |
| Abstract: | Cyber risk has become a critical financial threat in today's interconnected digital economy. This paper introduces a cyber-risk management framework for networked digital systems that combines the strategic behavior of players with contagion dynamics within a security game. We address the problem of optimally allocating cybersecurity resources across a network, focusing on the heterogeneous valuations of nodes by attackers and defenders, some areas may be of high interest to the attacker, while others are prioritized by the defender. We explore how this asymmetry drives attack and defense strategies and shapes the system's overall resilience. We extend a method to determine optimal resource allocation based on simple network metrics weighted by the defender's and attacker's risk profiles. We further propose risk measures based on contagion paths and analyze how propagation dynamics influence optimal defense strategies. Numerical experiments explore risk versus cost efficient frontiers varying network topologies and risk profiles, revealing patterns of resource allocation and cyber deception effects. These findings provide actionable insights for designing resilient digital infrastructures and mitigating systemic cyber risk. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.16805 |
| By: | Samkova, Mascha |
| Abstract: | This paper employs a novel approach in applying the cheap talk signalling game to study the EU accession game of the 10 Central and Eastern European states that joined the European Union in 2004 and 2007. The interdisciplinary application of a Bayesian game to international relations reveals the strategic interactions between the Union and applicant states in the light of the Copenhagen criteria and the unprecedented challenges countries faced during the post-Communist transition since 1989. The paper first presents the historical background about the EU accession process, debates on EU conditionality and existing game-theoretical approaches, before presenting the timeline and data on accession and reform speed of applicant states from 1989 to 2007. The model applies a signalling game to the negotiations process where the European Commission’s annual progress reports are seen as costless, unverifiable and observable signals to the applicant states about their final EU accession speed. It is demonstrated that possible equilibria outcomes can be uninformative or informative, depending on the players’ divergence of interests with regards to reform speed. Furthermore, the model is used to explain the outcomes seen in three ex-post case studies, taking into account additional domestic and external factors that shaped the varying outcomes of accession and reform speeds in the two EU enlargement waves in the 2000s. |
| Date: | 2026–02–03 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:43bwe_v1 |
| By: | Zhuo Chen; Yun Liu |
| Abstract: | We study optimal dynamic persuasion in a bandit experimentation model where a principal, unlike in standard settings, has a single-peaked preference over the agent's stopping time. This non-monotonic preference arises because maximizing the agent's effort is not always in the principal's best interest, as it may lead to a dead end. The principal privately observes the agent's payoff upon success and uses the information as the instrument of incentives. We show that the optimal dynamic information policy involves at most two one-shot disclosures: an accelerator before the principal's optimal stopping time, persuading the agent to be optimistic, and a brake after the principal's optimal stopping time, persuading the agent to be pessimistic. A key insight of our analysis is that the optimal disclosure pattern -- whether gradual or one-shot -- depends on how the principal resolves a trade-off between the mean of stopping times and its riskiness. We identify the Arrow-Pratt coefficient of absolute risk aversion as a sufficient statistic for determining the optimal disclosure structure. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.13686 |
| By: | Lang, Xu (Tilburg University, School of Economics and Management); Talman, A.J.J. (Tilburg University, School of Economics and Management) |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:tiu:tiutis:ba028add-c3b1-4de4-bfc6-0cb6a1e05c0c |
| By: | Mark Whitmeyer |
| Abstract: | I study symmetric competitions in which each player chooses an arbitrary distribution over a one-dimensional performance index, subject to a convex cost. I establish existence of a symmetric equilibrium, document various properties it must possess, and provide a characterization via the first-order approach. Manifold applications--to R&D competition, oligopolistic competition with product design, and rank-order contests--follow. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.22112 |
| By: | Sander Onderstal (University of Amsterdam and Tinbergen Institute); Ruben van Oosten (University of Amsterdam) |
| Abstract: | We analyze vertical integration in auction markets using a symmetric independent private-values model where the auctioneer invests in the auctioned object's quality. We find that the auctioneer invests more after integration. The integrated bidder enjoys a bidding advantage over other bidders. The merging parties benefit from integration, while non-merging bidders are worse off. In a platform setting where the auctioneer is an intermediary and the bidders are sellers on her platform, vertical integration has ambiguous effects on consumer surplus and total welfare. Our results contribute to the ongoing policy debate about platforms self-preferencing, effective competition policy, and digital market regulation. |
| JEL: | D44 G34 |
| Date: | 2025–08–26 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250046 |
| By: | Dirk Bergemann; Tibor Heumann; Stephen Morris |
| Abstract: | We develop an integrated framework for information design and mechanism design in screening environments with quasilinear utility. Using the tools of majorization theory and quantile functions, we show that both information design and mechanism design problems reduce to maximizing linear functionals subject to majorization constraints. For mechanism design, the designer chooses allocations weakly majorized by the exogenous inventory. For information design, the designer chooses information structures that are majorized by the prior distribution. When the designer can choose both the mechanism and the information structure simultaneously, then the joint optimization problem becomes bilinear with two majorization constraints. We show that pooling of values and associated allocations is always optimal in this case. Our approach unifies classic results in auction theory and screening, extends them to information design settings, and provides new insights into the welfare effects of jointly optimizing allocation and information. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.17267 |
| By: | Herings, P.J.J. (Tilburg University, School of Economics and Management); Michaelides, Philippos; Seel, Christian |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:tiu:tiutis:39b1b9f1-e6d6-4b83-9330-bc8d1dc06632 |