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on Game Theory |
| By: | Maxime Menuet (Université Côte d'Azur, CNRS, GREDEG, France) |
| Abstract: | This paper studies how the temporal structure of adjustment shapes evolutionary dynamics in symmetric games. We introduce a fractional replicator dynamic that modifies the classical replicator only through the time operator, replacing the ordinary derivative with a fractional derivative of order α ∈ (0, 1]. This formulation preserves payoff monotonicity, feasibility, and the equilibrium set, while allowing past payoff differences to affect current behavior through long memory with power-law decay. We show that fractional time fundamentally alters local stability and equilibrium selection. While evolutionarily stable strategies remain locally asymptotically stable, equilibria that are unstable under the classical replicator can become locally stable when memory is sufficiently persistent, generating stability switching and purely temporal bifurcations without any change in payoffs or strategic interaction. Moreover, convergence toward stable equilibria becomes polynomial rather than exponential, implying slow adjustment even in simple games. As a consequence, equilibrium selection may fail to be completed over economically relevant horizons despite being guaranteed asymptotically. Finally, we provide a microfoundation based on standard payoff-monotone revision processes with heterogeneous and asynchronous revision opportunities. Fractional dynamics thus offer a parsimonious way to incorporate persistent memory into evolutionary models while preserving their core economic structure. |
| Keywords: | Fractional replicator dynamics; Evolutionary game theory; Fractional calculus; Long memory; Stability switching; Equilibrium selection |
| JEL: | C72 C73 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:gre:wpaper:2026-05 |
| By: | Patrice Pieretti; Giuseppe Pulina; Benteng Zou |
| Abstract: | We study dynamic fiscal competition when mobile capital responds to the stock of public infrastructure, not contemporaneous expenditure flows. Two governments choose taxes and public investment in a differential game with gradual accumula tion and investment frictions. In the unique Nash equilibrium, long-run dynamics depend on discounting, erosion of advantages, the share of public investment that effectively adds to infrastructure, the private productivity effects of infrastructure, and adjustment/acquisition costs on public investment. The model delivers conver gence to a symmetric steady state, and “invest–then–stop” behavior. Large initial gaps can rationally delay the laggard’s investment, generating distinct transition paths and persistent asymmetries. |
| Keywords: | Fiscal competition; public capital stock; infrastructure investment; differential games; mobile capital. |
| JEL: | F21 F23 H25 H54 H73 C73 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:bcl:bclwop:bclwp204 |
| By: | Tarush, Akshat (Daikin India) |
| Abstract: | India’s online food delivery market has consolidated into a stable duopoly following the exits of Uber Eats and Amazon Food. Standard Bertrand competition predicts that such a market structure should result in aggressive price discounting and persistent margin erosion. However, the observed trajectory of Zomato and Swiggy diverges from this prediction. This paper argues that the Indian food delivery duopoly is better understood through the framework of Nash equilibrium and repeated game theory rather than static price competition. Drawing on financial disclosures, regulatory developments and strategic investments across adjacent verticals, the analysis shows that both firms have shifted capital allocation toward quick commerce and dining and entertainment services. These investments reduce direct confrontation in the core food delivery segment and function as a structural analogue to mixed strategy behavior. Instead of committing exclusively to price based competition, each firm distributes resources across multiple business lines, generating strategic unpredictability and limiting profitable unilateral deviation. The stability of this equilibrium is reinforced by public market discipline that constrains explicit coordination while allowing tacit adjustment. The paper contributes to the understanding of platform competition in emerging digital markets by demonstrating how vertical differentiation can stabilize outcomes in environments where pure price rivalry would otherwise destroy value. |
| Date: | 2026–03–03 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:4m7yr_v1 |
| By: | Stark, Oded; Kosiorowski, Grzegorz |
| Abstract: | We establish a new approach to the modeling of cooperation, and we formulate a new solution concept for cooperative games. We do this by constructing a game of cooperation between individuals who exhibit distaste for relative deprivation, RD, in the sense that they experience stress when their income is lower than that of their comparators. In such a game, the sharing out of the jointly earned income between these individuals when they cooperate, as prescribed by standard solutions of cooperative games, might not be acceptable to the individuals. The stress from RD may have the upper hand. Measuring stress by RD, we thus model a setting in which two individuals who are concerned with being relatively deprived need to decide whether or not to cooperate. We term this setting an RD cooperative game, and we design a rule, the RD solution, for the distribution of the income yielded in this game. The RD solution prescribes cooperation in spite of cooperation-induced stress and preserves the spirit of standardness (an equal sharing of the gain that accrues from cooperation) for two-player games (a property shared by the main solution concepts for cooperative games). |
| Keywords: | Institutional and Behavioral Economics |
| Date: | 2026–03–17 |
| URL: | https://d.repec.org/n?u=RePEc:ags:ubzefd:396310 |
| By: | Wei Liang (China Economics and Management Academy, Central University of Finance and Economics, Beijing, 100081, China); Heng-fu Zou (The World Bank, Washington, D. C., 20433, USA) |
| Abstract: | This paper develops a dynamic mean field game model of capital accumulation and militarization among symmetric countries facing stochastic shocks. Each country optimizes consumption, productive investment, and military spending while responding to the average militarization level of others. We derive the coupled Hamilton-Jacobi-Bellman and Fokker-Planck equations governing equilibrium, and prove existence and unique ness under strategic externalities. A linear-quadratic-Gaussian version yields closed-form feedback rules and forward dynamics. Simulations reveal that low internalization of global militarization leads to arms traps and stagnation, while stronger externality awareness supports growth and restraint. The model offers a rigorous framework to study decentralized militarization externalities (a tragedy of the commons) and their macroe conomic consequences without assuming hierarchy or conflict. |
| Keywords: | Mean Field Games; Militarization; Strategic Externalities; Capital Accumulation; Arms Race |
| Date: | 2026–03–15 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:807 |
| By: | Wei Liang (China Economics and Management Academy, Central University of Finance and Economics, Beijing, 100081, China); Heng-fu Zou (The World Bank, Washington, D. C., 20433, USA) |
| Abstract: | We develop a continuous-time principal-agent model with mean-field interactions to study optimal incentive design in large economies. We extend Sannikov's recursive contracting framework to a setting where a single principal manages a continuum of heterogeneous agents whose behaviors are interdependent through aggregate effort externalities. Each agent's hidden efort affects their stochastic output, while the principal designs state-contingent contracts that must account for both individual moral hazard and collective behavior effects. The model generates a coupled system of forward-backward stochastic differential equations: a backward Hamilton-Jacobi-Bellman equation characterizing the principal's value function and optimal contracts, and a forward Fokker-Planck equation governing the evolution of the agent distribution. We establish conditions for mean-field equilibrium where the aggregate effort assumed by the principal when designing contracts coincides with the aggregate effort induced by agents following these contracts. Our numerical implementation reveals that despite complex state-dependent individual con tracts, the aggregate effort remains approximately stable over the contract horizon, while the distribution of continuation values exhibits increasing dis persion. Applications include compensation design in large frms, platform economies, and public incentive programs where individual actions generate aggregate externalities. |
| Keywords: | Mean field games, Principal-agent problem, Continuous-time contracting, Moral hazard, Fokker-Planck equation, Dynamic incentives |
| JEL: | C63 C73 D86 G32 J33 |
| Date: | 2026–03–15 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:806 |
| By: | Holmberg, Pär; Ruddell, Keith; Willems, Bert (Université catholique de Louvain, LIDAM/CORE, Belgium) |
| Abstract: | We characterize Nash equilibria in multi-product markets in which producers commit to vectors of supply functions contingent on all prices. The framework accommodates (dis)economies of scope in production, and goods may be substitutes or complements in demand. We show that equilibrium allocations of underlying goods and payoffs are invariant under bundling. With quadratic costs and linear demand, this invariance reduces the multi-product problem to an equivalent set of single-product markets that can be analyzed independently. We introduce Lerner and pass-through matrices to capture markups and welfare losses; their eigenvalues summarize fundamental market properties, remain invariant under bundling, and lend themselves to comparative statics analysis. |
| Keywords: | Supply function equilibrium ; multi-product pricing ; divisible-good auction ; bundling ; pass-through ; welfare |
| JEL: | C62 C72 D43 D44 L94 |
| Date: | 2025–09–24 |
| URL: | https://d.repec.org/n?u=RePEc:cor:louvco:2025018 |
| By: | Catherine Bobtcheff (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Raphaël Lévy (HEC Paris - Ecole des Hautes Etudes Commerciales); Thomas Mariotti (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) |
| Abstract: | Firms receiving independent signals on a common‐value risky project compete to be the first to invest. When firms are symmetric and competition is winner‐take‐all, rents are fully dissipated in equilibrium and the extent to which signals are publicly disclosed is irrelevant for welfare. When disclosure of signals is asymmetric, welfare is highest when firms are most asymmetric, and policies that uniformly promote disclosure may backfire, especially when competition is severe. When firms strategically select their disclosure policies, a moderate subsidy for disclosure induces a low correlation between firms' policies, and thus maximizes welfare. |
| Date: | 2025–02–18 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05475414 |
| By: | Natalia Montinari; Matteo Ploner; Veronica Rattini |
| Abstract: | This paper studies whether alternative integration-policy framings affect cooperation in ethnically diverse groups. We conduct a lab-in-the-field experiment with 390 adolescents in mixed classrooms in Italy. Within each class, students were randomly assigned to small groups that received either a neutral condition, a common-identity framing emphasizing shared school belonging, or a multicultural framing highlighting family origins and local cultural diversity, and then played a repeated public goods game with and without punishment. In the neutral condition, students with an immigrant background contributed about 17 percent more than natives. Framing diversity through a multicultural lens increased natives' contributions by about 13 percent relative to their baseline level, nearly eliminating the initial cooperation gap, whereas the common-identity framing had no detectable effect. When punishment was introduced, treatment effects on contributions became small, but multicultural framing increased the sanctioning of free riders, particularly among natives. The results suggest that cooperation in diverse settings depends not only on minority integration but also on how majority-group members respond to diversity. Policies that recognize multicultural identities, rather than emphasizing generic shared belonging alone, can strengthen cooperative norms in heterogeneous environments. |
| JEL: | C93 D91 J15 Z13 |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:bol:bodewp:wp1219 |
| By: | Chen, Xuyang (Université catholique de Louvain, LIDAM/CORE, Belgium); Sun, Rui |
| Abstract: | This paper investigates how the OECD’s global minimum tax (GMT) affectsmultinational enterprises (MNEs) behavior and countries’ corporate taxes. We consider both profit shifting and capital investment responses of the MNE in a formal model of tax competition between asymmetric countries. The GMT reduces the true tax rate differential and benefits the large country, while the revenue effect is generally ambiguous for the small country. In the short run where tax rates are fixed, due to tax deduction of the substance-based income exclusion (SBIE), a higher minimum rate exerts investment incentives but also incurs a larger revenue loss for the small country. We show that under high (low) profit shifting costs the former (latter) effect dominates so that the small country’s revenue increases (decreases). In the long run where countries can adjust tax rates, the GMT reshapes the tax game and the competition pattern. In contrast to the existing literature, we reveal that the minimum rate binds the small country only if it is low. With the rise of the GMT rate, countries will undercut the minimum to boost real investments and collect top-up taxes. Our simulations show that introducing a GMT with moderate minimum rate raises both countries’ revenues and the large country’s welfare. However, it may reduce the small country’s welfare if the welfare weight of private income is high. |
| Keywords: | Corporate taxes, Global minimum tax, Profit shifting, SBIE, Tax competition |
| JEL: | F21 F23 H25 H73 H87 |
| Date: | 2025–09–01 |
| URL: | https://d.repec.org/n?u=RePEc:cor:louvco:2025019 |
| By: | Huan Cai; Ziqing Lu; Catherine Xu; Weiyu Xu; Jie Zheng |
| Abstract: | With recent development of artificial intelligence, it is more common to adopt AI agents in economic activities. This paper explores the economic actions of agents, including human agents and AI agents, in an economic game of trading products/services, and the equilibria in this economy involving multiple agents. We derive a range of equilibrium results and their corresponding conditions using a Markov chain stationary distribution based model. One distinct feature of our model is that we consider the long-term utility generated by economic activities instead of their short-term benefits. For the model consisting of two agents, we fully characterize all the possible economic equilibria and conditions. Interestingly, we show that unless each agent can at least double (not merely increase) its marginal utility by purchasing the other agent's products/services, purchasing the other agent's products/services will not happen in any economic equilibrium. We further extend our results to three and more agents, where we characterize more economic equilibria. We find that in some equilibria, the ``more powerful'' AI agents contribute zero utility to ``less capable'' agents. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2603.00858 |
| By: | Barbara Antonioli; Federico Trombetta |
| Abstract: | Executives may implement legally contestable policies aggressively before courts reach a final legality determination, creating reliance and other sunk effects that make reversal costly. We study a complete-information sequential game in which an executive chooses policy aggressiveness and a court then decides whether to uphold the policy or strike it. If reversal costs increase sufficiently convexly in aggressiveness, the court strikes mild policies but upholds sufficiently aggressive ones to avoid disruption. Anticipating this, the executive overreaches—choosing a policy more extreme than its ideal point—to deter full reversal, yielding inefficient excess implementation relative to a commitment benchmark. Institutions that limit pre-review sunk effects (stays, phased implementation, expedited review) mitigate this distortion. |
| JEL: | D72 D74 K23 K40 P16 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:dis:wpaper:dis2602 |
| By: | Mercy, Phil (Freelance); Neil, Martin |
| Abstract: | The theory of microeconomics is revisited to gain insight into the underlying mechanics of sub-optimal systems in general. It challenges the prevailing view that efficient markets naturally arise from free competition and instead reformulates the market to reveal mechanisms whereby inefficient operation can naturally emerge. In particular, it shows how individual influence or power, and market scarcity inevitably lead to biased markets for emergent system operation that is anything but efficient. The paper concludes by incorporating these insights into a game-theoretic treatment of market interactions and proves this is simply a special case of the biased interaction game. |
| Date: | 2026–03–14 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:qge3k_v1 |
| By: | Sarah Jacobson (Williams College); John Spraggon (University of Massachusetts Amherst); ; |
| Abstract: | "We use a lab experiment to study a combined linear-threshold public good game, with linear returns to contributions and an additional higher return if a threshold is met. We experimentally vary handling of contributions that do not meet the threshold. Contributions are high, with almost all groups reaching the threshold. Refund institutions matter, but only a little: contributions are only weakly higher on average if insufficient contributions are automatically refunded than if they cannot be refunded. However, optional refunds chosen ex post perform relatively poorly. Risk averse people contribute less, but when a refund is possible, more risk tolerant people reduce their contributions relative to risk averse people. An online survey-experiment shows that people perceive refunds in this institution as desirable from a donor’s perspective, though a donor’s taking advantage of a threshold is perceived as non-normative, especially in a naturalistic charity context." |
| Keywords: | public goods games, threshold public goods, lab experiment, social preferences, risk preferences |
| Date: | 2025–08–01 |
| URL: | https://d.repec.org/n?u=RePEc:wil:wileco:2025_114 |
| By: | Jin Yeub Kim (Yonsei University); Wooyoung Lim (The Hong Kong University of Science and Technology) |
| Abstract: | Mediation is a key strategic instrument for managing conflicts in bargaining scenarios with incomplete information. This paper reports the first systematic laboratory investigation into the informed principal problem concerning mediator selection. The theory of neutral optimum predicts that, in our environment, the informed principal's most reasonable choice is not the mediator that maximizes the ex-ante probability of peace; rather, the one preferred by the stronger type alone constitutes a credibly justifiable compromise between the conflicting interests of different types. We find that subjects do not choose the neutral mediator more often than the peace-maximizing one. Different principal types recognize the need for inscrutable selection and form intertype compromises, and they systematically view the peace-maximizing mediator as the more compelling compromise. The strategic reasoning underlying the neutral optimum fails to materialize in the lab. |
| Keywords: | Informed Principal Problems, Mechanism Selection, Mediation, Inscrutability, Neutral Optimum, Laboratory Experiments |
| JEL: | C72 C91 D82 |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:yon:wpaper:2026rwp-283 |
| By: | Johnen, Johannes (Université catholique de Louvain, LIDAM/CORE, Belgium); Shekhar, Shiva |
| 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 |
| JEL: | L22 L41 L51 |
| Date: | 2025–07–30 |
| URL: | https://d.repec.org/n?u=RePEc:cor:louvco:2025015 |
| By: | Conte, Anna; D'Ippoliti, Carlo; Temperini, Jacopo |
| Abstract: | Consensus mechanisms are institutional governance structures that coordinate decentralized agents by aligning incentives to sustain agreement on shared outcomes. Many contemporary designs embed efficiency-reducing contingencies, such as reduced rewards or penalties, intended to discipline behaviour after coordination failure. The implicit assumption is that efficiency loss strengthens incentives to restore agreement. We test this assumption in a controlled agreement environment derived from a consensus-like structure. In a two-stage mechanism where coordination failure reduces available surplus but agreement remains individually rational, laboratory data from 716 participants reveal persistent disagreement in reduced-surplus states. Conflict rates range from approximately 20% to over 60%, contradicting standard equilibrium predictions of universal agreement. These results show that efficiency loss does not necessarily discipline behaviour. Instead, reduced-surplus environments are associated with sustained disagreement and amplified inefficiency, highlighting the importance of incorporating behavioural considerations into the design of consensus-based governance systems. |
| Date: | 2026–03–03 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:8b6kf_v1 |
| By: | Evgeny Kagan; Kyle Hyndman; Anyan Qi |
| Abstract: | To grow their businesses, entrepreneurs often rely on equity funding. This paper focuses on two elements of entrepreneur-investor equity negotiations: the number of potential investors and the contractual complexity surrounding investor protection. Our approach involves a theoretical model and a series of laboratory experiments that analyze the effects of different bargaining conditions and contractual terms on the equity (ownership) split between entrepreneurs and their investors. We show that the conventional wisdom that entrepreneurs should seek to negotiate with as many investors as possible, while consistent with the theoretical model, is not true in the data. Indeed, negotiating with multiple investors reduces the entrepreneur's profits under most conditions. We also show that investor downside protections may disadvantage early-stage startups, but can be beneficial to later-stage startups. A refinement of belief modeling in multi-party bargaining, as well as a stylized risk allocation framework, reconcile these results with theory predictions. Our findings provide a decision framework for entrepreneurs to optimize their approach to investors and negotiate favorable contractual terms. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2603.00706 |
| By: | Gokan, Toshitaka; Thisse, Jacques-François (Université catholique de Louvain, LIDAM/CORE, Belgium); Zhu, Xiwei |
| Abstract: | We develop a model in which offline and online transportation costs, online shopping disutility cost and consumer taste heterogeneity, and online and offline retailers' pricing policies interact to determine the equilibrium retail format that emerges from firms' and consumers' choices. This is done by combining spatial pricing and discrete choice theory within a unified game-theoretic framework. We study the industry equilibrium, as well as the corresponding consumer surplus and total welfare. Our results show that firms' choices of a retail format and consumers' decision to buy from an offline or online firm often depend on consumers' locations relative to firms'. Comparing aggregate consumer surpluses shows that consumers prefer online to alternative channels when they are sufficiently heterogeneous, but this need not be so when heterogeneity is weak. When consumers' tastes are heterogenous enough, the retail format maximizing total welfare depends on the value of the distaste costs of online purchase. Thus, the nature of products supplied by retailers is likely to affect the socially desirable retailing system through the degree of product differentiation. |
| Keywords: | Offline retailing ; online retailing ; spatial price policies |
| JEL: | L13 L81 R10 |
| Date: | 2025–03–13 |
| URL: | https://d.repec.org/n?u=RePEc:cor:louvco:2025008 |
| By: | Illing, Gerhard |
| Abstract: | During the last decades, central bank independence proved to be the bedrock of credible and effective monetary policy. Both past and recent history provides plenty of evidence of disastrous outcomes with high inflation and economic stagnation, when central banks - lacking independence - were put under strong political influence. Game theoretic modeling provides valuable insights into the crucial role of independence. In a fiat money economy (with costs for producing additional pieces of paper money being close to zero) a commitment for price stability is key. In the absence of binding rules, it would not be dynamically consistent to stick to the promise to implement price stability. The model by Barro Gordon Model (1982) is the work horse model for game theoretic analysis. It builds on the seminal work of Kydland Prescott (1977) on dynamic inconsistency. The starting point of Barro Gordon is a short run Phillips curve, causing a trade-off between stabilizing inflation and stabilizing output. If there are structural distortions in the economy, the promise to stick to some target rate not credible: There is an incentive to stimulate economy by raising above target rate of inflation to raise output. Private agents anticipate this incentive; they raise expected inflation ex ante. So the optimal policy is not dynamic consistent (in game theoretic terms: not subgame perfect). This leads to an inflation bias: Inflation being too high, without any gain in output and employment. So ex post, discretionary policy ends up in an inferior outcome. |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:imfswp:338105 |
| By: | Dehez, Pierre (Université catholique de Louvain, LIDAM/CORE, Belgium) |
| Abstract: | Billot and Thisse's article is placed in the context of past and recent literature on Harsanyi's dividend distribution. A number of shortcomings and errors are highlighted. |
| Keywords: | Harsanyi dividends ; value |
| JEL: | C71 |
| Date: | 2026–02–01 |
| URL: | https://d.repec.org/n?u=RePEc:cor:louvco:2026005 |