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on Game Theory |
| By: | Heng-fu Zou |
| Abstract: | We develop a dynamic differential game model of strategic arms accumulation between two rival states, reflecting the security dilemma of major geopolitical adversaries such as the United States and China or the United States and the former Soviet Union. The model features both determinis tic and stochastic formulations, where each country maximizes intertem poral utility over its own military stock while negatively internalizing the rival's arms buildup. We derive Markov-Perfect Nash equilibrium strate gies in both open-loop and feedback forms, with special emphasis on the characterization and solution of the coupled Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck-Kolmogorov (FPK) partial diferential equa tions. In the linear-quadratic case, we solve the time-consistent Riccati equations and analyze the elasticity of optimal strategies with respect to changes in strategic preferences, investment costs, and external threats. The model is extended to include regime shocks-discontinuous jumps in threat perception or strategic aggressiveness-which may destabilize de terrence and trigger explosive arms escalation. Comparative statics from Riccati dynamics reveal thresholds beyond which deterrence collapses and feedback control solutions blow up in finite time. We also explore welfare trade-offs, deterrence sustainability, and policy implications of dynamic treaties. The mathematical framework developed here provides a foun dation for modeling arms races as nonlinear stochastic systems under en- dogenous expectations, belief dynamics, and political instability. |
| Keywords: | Strategic arms race, differential games, Nash equilibrium, feedback strategy, Riccati equation, Fokker–Planck equation, HJB equation, stochastic dynamics, regime shocks, deterrence collapse, Markov–Perfect equilibrium, dynamic stability, military investment, geopolitical competition, arms control treaties |
| Date: | 2025–07–08 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:773 |
| By: | Guanxing Fu (The Hong Kong Polytechnic University); Ulrich Horst (Humboldt University Berlin) |
| Abstract: | We study mean field portfolio games under Epstein-Zin preferences, which naturally encompass the classical time-additive power utility as a special case. In a general non-Markovian framework, we establish a uniqueness result by proving a one-to-one correspondence between Nash equilibria and the solutions to a class of BSDEs. A key ingredient in our approach is a necessary stochastic maximum principle tailored to Epstein-Zin utility and a nonlinear transformation. In the deterministic setting, we further derive an explicit closed-form solution for the equilibrium investment and consumption policies. |
| Keywords: | epstein-zin utility; mean field game; stochastic maximum principle; |
| Date: | 2025–07–27 |
| URL: | https://d.repec.org/n?u=RePEc:rco:dpaper:540 |
| By: | Heijmans, Roweno; Suetens, Sigrid (University of Groningen) |
| Abstract: | We use experiments to systematically test the performance of subsidies aimed atinducing efficient coordination in a coordination game. We consider two classesof policies: those based on divide-and-conquer (i.e. iterated dominance) and thosemaking the efficient Nash equilibrium of the game risk dominant. Cost-efficientpolicies from both classes are equally expensive but differ in the distribution ofsubsidies among agents. Our results show that risk dominance subsidies increasecoordination more effectively or at a lower cost than divide-and-conquer subsidies. |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:gro:rugfeb:2025004-eef |
| By: | Elgersma, Simon (University of Groningen) |
| Abstract: | Facing possible disaster, countries can mitigate the risk of disaster or invest inadaptation to lower the impact of disaster. Contrary to a cooperative outcome, under non-cooperation the possibility to adapt can affect incentives to mitigate.We model this tradeoff in a transboundary pollution game where countries face anendogenous regime shift. We study a cooperative outcome and a non-cooperativeMarkov Perfect Nash Equilibrium. We find that mitigation efforts are reduced bythe possibility to adapt, but this reduction is larger in a non-cooperative than acooperative outcome. Furthermore, free-riding becomes more intense when eitherthe impact of the disaster or the sensitivity of the hazard rate to the pollution stockincreases. Finally, the gains from cooperation increase heavily when adaptation ispossible. |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:gro:rugfeb:2024008-eef |
| By: | Markus Dertwinkel-Kalt; Vincent Eulenberg; Christoph Feldhaus; Jonas Frey; Kevin Breuer; Ben Bruske; Flynn Fehre; Penelope Hoffmann; Cederik Höfs; Nico Klocke; Lucas Schnack; Florian Strunk; Moritz Thiele; Annika Walter; Julia Weinberg; Konstantin Zörner |
| Abstract: | In social dilemmas, cooperation failures often arise due to the absence of mechanisms that prevent free-riding and enhance cooperation. Given the critical role these mechanisms play in sustaining cooperation, why are they so frequently missing? To explore this, we conducted an online experiment testing whether individuals choose to implement such cooperation-inducing mechanisms and why they might refrain from doing so. Participants were introduced to the rules of two public goods games, one of which includes a cooperation-inducing mechanism, while the other does not. Regarding the likelihood of successful cooperation, we found that participants were overly optimistic in the absence of the mechanism and overly pessimistic in its presence. As a result, a majority of subjects preferred the game without the cooperation-inducing mechanism. However, when we corrected participants' beliefs about the actual payoffs obtained in the two games, a majority shifted their preference toward the game with the cooperation-inducing mechanisms in place. |
| Keywords: | free riding, equilibrium effects, misspecified beliefs, spectator design |
| JEL: | D90 D01 C91 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11999 |
| By: | David Lagziel; Ehud Lehrer; Tao Wang |
| Abstract: | We analyze incomplete-information games where an oracle publicly shares information with players. One oracle dominates another if, in every game, it can match the set of equilibrium outcomes induced by the latter. Distinct characterizations are provided for deterministic and stochastic signaling functions, based on simultaneous posterior matching, partition refinements, and common knowledge components. This study extends the work of Blackwell (1951) to games, and expands the study of Aumann (1976) on common knowledge by developing a theory of information loops. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.15955 |
| By: | Philippe Jehiel; Giacomo Weber |
| Abstract: | Normal-form two-player games are categorized by players into K analogy classes so as to minimize the prediction error about the behavior of the opponent. This results in Clustered Analogy-Based Expectation Equilibria in which strategies are analogy-based expectation equilibria given the analogy partitions and analogy partitions minimize the prediction errors given the strategies. We distinguish between environments with self-repelling analogy partitions in which some mixing over partitions is required and environments with self-attractive partitions in which several analogy partitions can arise, thereby suggesting new channels of belief heterogeneity and equilibrium multiplicity. Various economic applications are discussed. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.13022 |
| By: | Bradley J. Ruffle; William B. Zhang |
| Abstract: | Social dilemmas with a shared resource pool and privately observed entitlements are susceptible to overclaiming. A dishonest claim that exceeds one’s true entitlement imposes a negative externality on others. To explore such social dilemmas, we introduce a novel four-player game where each player rolls a die in private and earns their die report, subject to budget availability. We vary the timing of players’ reporting (simultaneous vs sequential moves) and the available budget (limited vs excess). When resources are limited, mean reports do not differ significantly between simultaneous and sequential treatments. However, simultaneous reporting promotes greater equity under scarcity and reduces dishonesty when resources are plentiful. Frequent displays of virtue signaling take place whereby Player 4 chooses to earn zero by reporting more than the remaining budget. Our results demonstrate that these social dilemmas can be better managed by promoting simultaneous reporting structures, which obscure in formation about individual claims. |
| Keywords: | experimental economics; cheating externalities; budget constraint; virtue signaling |
| JEL: | C90 D91 H80 |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:mcm:deptwp:2025-05 |
| By: | Allen Vong |
| Abstract: | I study a setting where a sender communicates her information about a hidden state with a receiver who wants to match his action with that state. The sender strives to appear informed at the receiver's expense. I characterize the receiver's tradeoff between relying on the sender or on prior information about the state when picking his action in all informative equilibria. I show that the receiver relies only on prior information, irrespective of how informed the sender may be, if and only if prior information is neither sufficiently noisy nor sufficiently informative. My results highlight a complementarity that informative prior information facilitates high-quality communication under reputation concern. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.11877 |
| By: | Kailin Chen |
| Abstract: | This paper analyzes a cheap talk model with one receiver and multiple senders. Each sender observes a noisy signal regarding an unknown state of the world. Existing literature (e.g., Levit and Malenko, 2011; Battaglini, 2017) focuses on scenarios where the receiver and senders have aligned preferences in each state. We further explore situations with disagreement states in which the receiver and the senders have misaligned preferences. We first show that, when the number of senders grows large, each sender's message must convey almost no information to the receiver. Furthermore, we identify a discontinuity in information transmission: with moderate conflict between the receiver and the senders, introducing an arbitrarily small probability of disagreement states causes complete unraveling, contrary to full learning predicted by the literature. Finally, we demonstrate that the receiver cannot fully learn the state even when receiving messages from arbitrarily many senders. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.14639 |
| By: | Alessandro Spiganti (University of Genoa); Francesco Trevisan (Ca' Foscari University of Venice) |
| Abstract: | We provide a micro-founded dynamic framework to analyse the effects of inequality on social competition, mobility, and welfare. We consider an infinitely repeated Tullock contest in which players with concave utility allocate resources between consumption and costly effort, and the prizes from the current competition determine the players' endowments in the subsequent period. We characterize the unique pure-strategy Markov Perfect Equilibrium, proving that the highly endowed player exerts more effort and has a higher probability of winning. Social competition is maximized at an intermediate level of inequality, whereas utilitarian social welfare is maximized under full equality. Assuming non-increasing absolute risk aversion preferences, we find that greater inequality monotonically reduces social mobility (a pattern consistent with the Great Gatsby curve) and lowers the welfare of the lowly endowed player. By contrast, the welfare of the highly endowed player is non-monotonic when the discount factor is sufficiently high. Thus, being richer in a more unequal society does not necessarily imply higher individual welfare. For example, under logarithmic utility and beta = 2/3, an individual must control over 88% of total resources to strictly prefer inequality over full equality. |
| Keywords: | Contests, Social Competition, Social Mobility, Great Gatsby curve |
| JEL: | D63 D82 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ven:wpaper:2025:09 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a unified theoretical and historical framework to explain the cyclical structure of political purging and institutional collapse in totalitarian regimes, with a focus on the Chinese Communist Party(CCP) from 1942 to the present. We introduce three formal models: a dynamic signaling game with time-inconsistent punishment, a modified epidemic model of political participation and removal, and a quota driven reinterpretation game that captures the regime's shifting definition of guilt. These models reveal a structural logic in which early-stage partic ipation is incentive-compatible but later becomes retroactively incriminating as political needs evolve. Simulations demonstrate how participation spreads rapidly, trust deteriorates, and long-run strategy space collapses under coercive reinterpretation. By mapping these models onto major Chinese political campaigns-from the Yan'an Rectification and the Anti Rightist purge to the Cultural Revolution and Xi Jinping's anti-corruption drive -- we show that totalitarian governance operates through sequential betrayal of compliance. The regime manufactures loyalty, rewards it in the short term, then redefines it as disloyalty to fulfill ideological or factional quotas. This dynamic creates a system where no strategy ensures safety and all signals become vulnerable to reinterpretation. We conclude that this self-consuming logic of incentive collapse is not an aberration but a mathematically demonstrable feature of totalitarianism itself. |
| Keywords: | Chinese Communist Party, totalitarianism, political purges, game theory, incentive compatibility, signaling games, reinterpretation of guilt, quota systems, Cultural Revolution, authoritarian collapse |
| Date: | 2025–05–22 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:769 |
| By: | Vincent Meisner (HU Berlin); Pascal Pillath (HU Berlin) |
| Abstract: | We design profit-maximizing mechanisms to sell an excludable and non-rival good with positive and/or negative network effects. Buyers have heterogeneous private values that depend on how many others also consume the good. In optimum, an endogenous number of the highest types consume the good, and we can implement this allocation in dominant strategies. We apply our insights to digital content creation, and we are able to rationalize features seen in monetization schemes in this industry such as voluntary contributions, community subsidies, and exclusivity bids. |
| Keywords: | mechanism design; non-rival goods; club goods; network effects; digital content; creator economy; |
| JEL: | D82 |
| Date: | 2025–07–30 |
| URL: | https://d.repec.org/n?u=RePEc:rco:dpaper:541 |
| By: | Lijun Wu; Dong Hao; Zhiyi Fan |
| Abstract: | Graph Neural Networks (GNNs) have achieved outstanding performance across a wide range of graph-related tasks. However, their "black-box" nature poses significant challenges to their explainability, and existing methods often fail to effectively capture the intricate interaction patterns among nodes within the network. In this work, we propose a novel explainability framework, GraphEXT, which leverages cooperative game theory and the concept of social externalities. GraphEXT partitions graph nodes into coalitions, decomposing the original graph into independent subgraphs. By integrating graph structure as an externality and incorporating the Shapley value under externalities, GraphEXT quantifies node importance through their marginal contributions to GNN predictions as the nodes transition between coalitions. Unlike traditional Shapley value-based methods that primarily focus on node attributes, our GraphEXT places greater emphasis on the interactions among nodes and the impact of structural changes on GNN predictions. Experimental studies on both synthetic and real-world datasets show that GraphEXT outperforms existing baseline methods in terms of fidelity across diverse GNN architectures , significantly enhancing the explainability of GNN models. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.17848 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a dynamic two-country differential game model to examine the long-term economic and geopolitical implications of the trade war between the United States and China. Departing from classical com parative advantage theory, the model incorporates national preferences for industrial self-sufficiency, trade balance, and strategic power accumulation. Each country is represented as a national agent optimizing intertem poral welfare based on consumption, production, trade, and geopolitical rivalry. Endogenous capital accumulation, productivity growth through learning-by-doing, and disutility from foreign dependence are central to the analysis. Strategic power is derived from both capital stock and trade surpluses, reflecting their role in underwriting technological leadership and military influence. Through simulations, we demonstrate how persistent trade surpluses allow China to accumulate strategic advantage, while sustained U.S. deficits weaken industrial capacity and global leverage. The framework challenges the orthodoxy of free trade and provides a basis for evaluating nationalist economic strategies and decoupling policies in a multipolar world. |
| Keywords: | Trade war, U.S.–China rivalry, differential game, capital accumulation, strategic power, tariffs, industrial policy, geopolitical economy, learning-by-doing, reindustrialization, dynamic optimization, economic nationalism |
| Date: | 2025–06–10 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:774 |
| By: | Zhicheng Du; Wei Tang; Zihe Wang; Shuo Zhang |
| Abstract: | In digital advertising, online platforms allocate ad impressions through real-time auctions, where advertisers typically rely on autobidding agents to optimize bids on their behalf. Unlike traditional auctions for physical goods, the value of an ad impression is uncertain and depends on the unknown click-through rate (CTR). While platforms can estimate CTRs more accurately using proprietary machine learning algorithms, these estimates/algorithms remain opaque to advertisers. This information asymmetry naturally raises the following questions: how can platforms disclose information in a way that is both credible and revenue-optimal? We address these questions through calibrated signaling, where each prior-free bidder receives a private signal that truthfully reflects the conditional expected CTR of the ad impression. Such signals are trustworthy and allow bidders to form unbiased value estimates, even without access to the platform's internal algorithms. We study the design of platform-optimal calibrated signaling in the context of second-price auction. Our first main result fully characterizes the structure of the optimal calibrated signaling, which can also be computed efficiently. We show that this signaling can extract the full surplus -- or even exceed it -- depending on a specific market condition. Our second main result is an FPTAS for computing an approximately optimal calibrated signaling that satisfies an IR condition. Our main technical contributions are: a reformulation of the platform's problem as a two-stage optimization problem that involves optimal transport subject to calibration feasibility constraints on the bidders' marginal bid distributions; and a novel correlation plan that constructs the optimal distribution over second-highest bids. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.17187 |
| By: | Alonso, Ricardo; Padró i Miquel, Gerard |
| Abstract: | Two opposed interested parties (IPs) compete to influence citizens with heterogeneous priors which receive news items produced by a variety of sources. The IPs fight to capture the coverage conveyed in these items. We characterize the equilibrium level of capture of item as well as the equilibrium level of information transmission. Capture increases the prevalence of the ex ante most informative messages and can explain the empirical distribution of slant at the news‐item level. Opposite capturing efforts do not cancel each other and instead undermine social learning as rational citizens discount informative messages. Citizen skepticism makes efforts to capture the news strategic substitutes. Because of strategic substitution, competition for influence is compatible with horizontal differentiation between successful media. In equilibrium, rational citizens choose to consume messages from aligned sources despite knowledge of the bias in a manner consistent with recent empirical evidence. |
| Keywords: | collective action; communication technology;; media bias; lobbying; public opinion |
| JEL: | D72 |
| Date: | 2025–07–31 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:127777 |
| By: | D\'ora Gr\'eta Petr\'oczy |
| Abstract: | In a weighted majority voting game, the players' weights are determined based on the decision-maker's intentions. The weights are challenging to change in numerous cases, as they represent some desired disparity. However, the voting weights and the actual voting power do not necessarily coincide. Changing a decision threshold would offer some remedy. The International Monetary Fund (IMF) is one of the most important international organisations that uses a weighted voting system to make decisions. The voting weights in its Board of Governors depend on the quotas of the 191 member countries, which reflect their economic strengths to some extent. We analyse the connection between the decision threshold and the a priori voting power of the countries by calculating the Banzhaf indices for each threshold between 50% and 87\%. The difference between the quotas and voting powers is minimised if the decision threshold is 58% or 60%. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.16654 |