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on Game Theory |
| By: | Yao, Shunxin |
| Abstract: | This paper uses the Sydney railway workers’ strike from 2024 to 2025 as a backdrop, employing game theory models to analyze the strategic interactions between unions and the government in labor negotiations. By constructing both static and dynamic game models, the study reveals the decisive impact of game structure on equilibrium outcomes. Under the static game framework, the lack of coordination mechanisms may lead both sides into suboptimal strategy combinations. In contrast, in dynamic games, the union can take the initiative and issue credible strike threats, guiding the government to make concessions, thus forming a subgame perfect Nash equilibrium (SPNE). This equilibrium is not only stable but also likely to be Pareto optimal compared to potential escalation scenarios. The research indicates that in modern labor relations, the order of actions, the credibility of threats, and institutional response mechanisms have critical impacts on negotiation outcomes. |
| Date: | 2025–05–09 |
| URL: | https://d.repec.org/n?u=RePEc:osf:osfxxx:tmcfq_v1 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a dynamic game-theoretic framework to model global arms races in a multipolar world using mean field game (MFG) theory. We analyze the strategic behavior of a continuum of minor countries influenced by the military decisions of three major powers—the United States, China, and Russia — who engage in a finite-player differential game. Each country chooses its military expenditure over time to minimize a cost function that reflects internal costs and strategic positioning relative to others. We derive both general nonlinear and linear-quadratic-Gaussian (LQG) formulations, solve the coupled HJB–FPK systems, and simulate both time-dependent and stationary equilibria. Our results show how strategic interdependence, peer pressure, and deterrence incentives drive excessive militarization in decentralized equilibrium. We compare decentralized and centralized outcomes and analyze policy interventions such as caps and taxes. The framework offers a rigorous foundation for understanding military competition and evaluating arms control policies under uncertainty. |
| Keywords: | Mean Field Games, Arms Race, Strategic Competition, Militarization, Linear-Quadratic-Gaussian Control, Decentralized Equilibrium |
| Date: | 2025–05–15 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:756 |
| By: | Heng-fu Zou |
| 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 security dilemmas and their macroeconomic consequences without assuming hierarchy or conflict. |
| Keywords: | Mean Field Games, Militarization, Strategic Externalities, Capital Accumulation, Arms Race |
| Date: | 2025–05–03 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:761 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a dynamic mean field game model in which a superpower emerges endogenously from stochastic regime shifts in capital productivity and military effectiveness. Starting from a symmetric population, countries accumulate capital and arms under strategic external ities. Rare transitions into high-productivity regimes generate sustained divergence, concentrating power in a single dominant actor. We derive the coupled Hamilton-Jacobi-Bellman and Fokker-Planck equations, simulate closed-form solutions, and illustrate how asymmetry arises without exogenous advantage. The framework provides a tractable foundation for analyzing unipolarity, arms races, and welfare divergence in decentralized strategic environments. |
| Keywords: | Mean Field Games, Superpower Emergence, Militarization, Capital Accumulation, Strategic Externalities, Regime Switching |
| Date: | 2025–05–02 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:762 |
| By: | de Vos, Wout (Tilburg University, Center For Economic Research); Borm, Peter (Tilburg University, Center For Economic Research); Hamers, Herbert (Tilburg University, Center For Economic Research) |
| Keywords: | opinion dynamics; networks; influence; precision targeting; nash equilibria |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:tiu:tiucen:b21371ea-a12a-4e8d-8b21-f60eb10b6a03 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a dynamic mean field game model of global arms races and capital accumulation among heterogeneous nations. Each country allocates its output among consumption, capital investment, and military spending, optimizing against an evolving global militarization level. Strategic interdependence is modeled through forward–backward stochastic differential equations, combining individual HJB equations, Population-level Fokker–Planck dynamics, and a mean field consistency condition. Closed-form solutions are derived under a linear–quadratic benchmark, and steady-state distributions are simulated for major powers including the U.S., China, Russia, and the EU. Results reveal how cross-country differences in productivity, military efficiency, and volatility lead to divergent long-run equilibria and global militarization traps. The model captures strategic path dependence and hysteresis, showing how shocks or preemptive arming can entrench high-arms outcomes. Policy implications include the importance of disarmament mechanisms, transparency, and coordinated institutions to escape inefficient militarized equilibria. The framework offers a robust tool for analyzing geopolitical dynamics under uncertainty. |
| Keywords: | arms race, capital accumulation, mean field games, global militarization, Hamilton–Jacobi–Bellman equation, Fokker–Planck equation, strategic interdependence, geopolitical equilibrium |
| Date: | 2025–05–15 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:755 |
| By: | Michiko Ogaku |
| Abstract: | This paper investigates whether an ex-ante welfare-maximising risk allocation rule can be implemented among many participants. Specifically, we investigate the applicability of the price and choose mechanism proposed by Echenique and N\'u\~nez(2025) to risk allocation problems. While their mechanism implements Pareto optimal allocations in finite choice sets, we consider extending it to an infinite choice set of feasible risk-sharing allocations. This paper asks whether an ex-ante welfare-maximising risk allocation rule can indeed be implemented for a large group. Specifically, we study the price and choose (P&C) mechanism of Echenique and N\'u\~nez(2025) in a risk-sharing setting. In P&C, players sequentially set prices for each possible alternative; the last player chooses an alternative, provided that all previous players receive the prices they set. Echenique and N\'u\~nez(2025) show that, for finite choice sets, the mechanism implements any Pareto optimal allocation in the subgame-perfect Nash equilibrium. Our setting differs in one crucial respect: the choice set is infinite. Each alternative is a feasible allocation of total risk, and each player sets a Lipschitz-continuous price function on this infinite set. We show that the P&C mechanism can still be extended to implement the allocation that maximises the sum of players' utilities, even with an infinite choice set. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.04122 |
| By: | Ferrari, Giorgio (Center for Mathematical Economics, Bielefeld University); Tzouanas, Ioannis (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an Itô-diffusion via onesided singular stochastic control, aiming to maximize a long-term average expected profit criterion. The mean-field interaction is of scalar type through the stationary distribution of the population. Due to the presence of uncertainty, the problem involves the study of a stochastic (zero-sum) game, where the decision maker chooses the ‘best’ singular control policy, while the adversarial player selects the ‘worst’ probability measure. Using a constructive approach, we prove existence and uniqueness of a stationary mean-field equilibrium. Finally, we present an example of mean-field optimal extraction of natural resources under uncertainty and we analyze the impact of uncertainty on the mean-field equilibrium. |
| Keywords: | stationary mean-field games, singular control, model uncertainty, ergodic criterion, freeboundary problem, shooting method |
| Date: | 2025–05–21 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:706 |
| By: | Isa Hafalir (University of Technology Sydney); Onur Kesten (University of Sydney); Katerina Sherstyuk (University of Hawaii at Manoa); Cong Tao (University of Technology Sydney) |
| Abstract: | We study a remarkable auction used in several fish markets around the world, notably in Honolulu and Sydney, whereby high-quality fish are sold fast through a hybrid auction that combines the Dutch and the English formats in one auction. Speedy sales are of essence for these perishable goods. Our theoretical model incorporating Òtime costsÓ demonstrates that such Honolulu-Sydney auction is preferred by the auctioneer over the Dutch auction when there are few bidders or when bidders have high time costs. Our laboratory experiments confirm that with a small number of bidders, Honolulu-Sydney auctions are significantly faster than Dutch auctions. Bidders overbid in Dutch, benefiting the auctioneer, but bidding approaches risk-neutral predictions as time costs increase. Bidders fare better in the Honolulu-Sydney format compared to Dutch across all treatments. We further observe bidder attempts to tacitly lower prices in Honolulu- Sydney auctions, substantiating existing concerns about pricing in some fish markets. |
| Keywords: | auction theory, time costs, laboratory experiments |
| JEL: | C7 C92 D02 D44 L0 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:hai:wpaper:202502 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a dynamic, multi-country model in which governments strategically set import tariffs to fund national defense, and representative agents derive utility from consumption, capital, foreign asset holdings, and publicly financed military strength. The model embeds mercantilist-nationalist preferences within a linear-quadratic-Gaussian (LQG) framework, allowing closed-form solutions for optimal consumption, savings, and trade behavior. We extend the model to a mean field game, where each government optimizes its tariff policy in response to the aggregate tariff behavior of all other countries. The equilibrium is characterized by a Hamilton-Jacobi-Bellman-Fokker-Planck system and features endogenously determined global interest rates, cross-country capital flows, and securitized trade patterns. Simulations reveal a structural mercantilist trap: globally depressed interest rates, strategic reserve ac cumulation, and persistent trade imbalances. The model explains how decentralized, rational policy behavior under sovereignty and security concerns gives rise to systemic instability and geopolitical fragmentation in today's global economic order. |
| Keywords: | Mercantilism, Strategic Trade Policy, Mean Field Games, National Defense, Foreign Asset Accumulation |
| Date: | 2025–05–03 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:760 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a dynamic model of power accumulation and inequality using the framework of mean field games. Agents optimize intertemporally over consumption while accumulating power as a capital stock, subject to idiosyncratic productivity shocks. Power yields direct utility and enhances future accumulation. In equilibrium, the joint distribution of power and productivity evolves endogenously via a coupled Hamilton-Jacobi-Bellman and Fokker-Planck system. We prove that - even absent initial heterogeneity-persistent inequality and elite dominance emerge as stable outcomes. The stationary distribution exhibits fat tails and high Gini coefficients, consistent with empirical observations of power concentration in historical empires and modern regimes. The model offers a structural explanation for the recurrent emergence of dominant elites under decentralized, rational decision-making. |
| Keywords: | power accumulation, inequality, mean field games, elite dominance, stochastic dynamics |
| Date: | 2025–05–15 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:759 |
| By: | Keith Paarporn; Adel Aghajan; Jason R. Marden |
| Abstract: | The allocation of resources plays an important role in the completion of system objectives and tasks, especially in the presence of strategic adversaries. Optimal allocation strategies are becoming increasingly more complex, given that multiple heterogeneous types of resources are at a system planner's disposal. In this paper, we focus on deriving optimal strategies for the allocation of heterogeneous resources in a well-known competitive resource allocation model known as the General Lotto game. In standard formulations, outcomes are determined solely by the players' allocation strategies of a common, single type of resource across multiple contests. In particular, a player wins a contest if it sends more resources than the opponent. Here, we propose a multi-resource extension where the winner of a contest is now determined not only by the amount of resources allocated, but also by the composition of resource types that are allocated. We completely characterize the equilibrium payoffs and strategies for two distinct formulations. The first consists of a weakest-link/best-shot winning rule, and the second considers a winning rule based on a weighted linear combination of the allocated resources. We then consider a scenario where the resource types are costly to purchase, and derive the players' equilibrium investments in each of the resource types. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.02860 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a dynamic mean field game model to explain the emergence of heavy-tailed city size distributions and persistent urban inequality. Each city optimizes intertemporal consumption and investment in infrastructure to maximize utility from both consumption and population scale. City size follows a stochastic process with investment-driven drift, while productivity evolves as a mean-reverting diffusion. We derive the equilibrium using the Lasry–Lions Master Equation and simulate the resulting stationary distribution. The model generates high Gini coefficients and Pareto-like upper tails, consistent with Zipf’s law and Gibrat’s law. These patterns arise endogenously through capital accumulation, productivity shocks, and scale feedbacks, offering a unified framework to understand urban size inequality. |
| Keywords: | City size distribution, Zipf's law, Gibrat's law, Mean field games, Urban inequality, Capital accumulation |
| Date: | 2025–05–15 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:757 |
| By: | Zaccaria, Niccolò (Tilburg University, Center For Economic Research) |
| Keywords: | Overconfidence; beauty contest games; imperfect information; strategic complementarity |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:tiu:tiucen:7ac7f3a2-0a15-4d18-b645-6e600cfcdf91 |
| By: | Kyohei Okumura |
| Abstract: | This paper investigates the robustness of online learning algorithms when learners possess private information. No-external-regret algorithms, prevalent in machine learning, are vulnerable to strategic manipulation, allowing an adaptive opponent to extract full surplus. Even standard no-weak-external-regret algorithms, designed for optimal learning in stationary environments, exhibit similar vulnerabilities. This raises a fundamental question: can a learner simultaneously prevent full surplus extraction by adaptive opponents while maintaining optimal performance in well-behaved environments? To address this, we model the problem as a two-player repeated game, where the learner with private information plays against the environment, facing ambiguity about the environment's types: stationary or adaptive. We introduce \emph{partial safety} as a key design criterion for online learning algorithms to prevent full surplus extraction. We then propose the \emph{Explore-Exploit-Punish} (\textsf{EEP}) algorithm and prove that it satisfies partial safety while achieving optimal learning in stationary environments, and has a variant that delivers improved welfare performance. Our findings highlight the risks of applying standard online learning algorithms in strategic settings with adverse selection. We advocate for a shift toward online learning algorithms that explicitly incorporate safeguards against strategic manipulation while ensuring strong learning performance. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.05341 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a dynamic stochastic model of state formation from an anarchic condition, integrating insights from Hobbes, Nozick, and Tilly within a mean field game framework. A continuum of agents, each equipped with capital and arms, optimize consumption, investment, and military spending while facing externalities from the militarization of others. Recursive military advantage allows some agents to defeat ri- vals, seize resources, and transition into dominant protective agencies— emergent states. We formalize war as a capital transfer mechanism and taxation as a means of fiscal consolidation. The model produces endoge- nous divergence in coercive and productive capacity, demonstrating how military asymmetries, recursive violence, and fiscal extraction lead to the birth and persistence of centralized authority. |
| Keywords: | State formation, mean field games, military asymmetry, capital accumulation, war and taxation, dynamic political economy |
| Date: | 2025–05–15 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:754 |
| By: | Ori Haimanko (BGU) |
| Keywords: | Simple Games, Shapley-Shubik Power Index, Consistency, Subgames, Transfer, Dummy |
| JEL: | C71 D72 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:bgu:wpaper:2502 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a continuous-time mean field game model of capital accumulation with heterogeneous agents facing idiosyncratic stochastic productivity. Agents optimize infinite-horizon consumption under linear production and quadratic utility. The model yields a coupled Hamilton-Jacobi-Bellman and Fokker-Planck system, whose stationary solution ex hibits a Pareto-tailed wealth distribution. We derive the Pareto exponent analytically and show it depends on productivity and volatility. Numerical simulations confirm that realistic parameter values generate Gini coeffcients exceeding 0.7, consistent with empirical inequality. We evaluate the effectiveness of wealth taxation, consumption subsidies, and productivity equalization, finding these policies have limited long-run impact. Inequal ity emerges as a structural property of decentralized optimization under uncertainty, offering a micro-founded explanation for persistent wealth Concentration in capitalist economies. |
| Keywords: | Mean field games, wealth inequality, capital accumulation, Pareto distribution, stochastic dynamics, policy robustness |
| Date: | 2025–05–15 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:758 |
| By: | Yevgeny Mugerman; Eyal Winter; Tomer Yafeh |
| Abstract: | We explore strategic betting in competitive environments with multiple participants and potential winners. We examine two scenarios: an “inclusive†low-competition scenario with many winners and an “exclusive†high-competition scenario with few winners. Using a simple model, we illustrate the strategic insights in these scenarios and present experimental results that align with our predictions. In the experiment, participants made repeated bets with feedback on past results and their payoffs. In the inclusive scenario, all but the worst guessers were rewarded, while in the exclusive scenario, only the top guessers received rewards. Our findings show that in the inclusive scenario, participants exhibit herding behavior by coordinating their bets, while in the exclusive scenario, they diversify their bets across multiple options. The main general insight of our findings is that in moderate competitions, one tends to join the majority to avoid standing out in case of failure, whereas in intense competitions, one tends to differentiate oneself from one’s peers to ensure that success stands out. This insight is relevant for a broad domain of strategic interactions. |
| Keywords: | Experimental Economics, Competitive Decision-Making, Herding Behavior, Divergence Strategy, Inclusive vs. Exclusive Scenarios, Multi-Winner Competition |
| JEL: | C9 D7 D8 L1 M3 G1 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:lan:wpaper:423283787 |