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on Game Theory |
| By: | Mauro Bambi; Ehud Lehrer; Eilon Solan |
| Abstract: | This paper investigates the strategic and welfare properties of endogenous population partitioning (secession) within large-population anonymous games featuring strategic heterogeneity. We consider a continuum-player framework with a binary action space where players are categorized either as fol- lowers, who experience positive network externalities from conformity, or as contrarians, who seek distinctiveness via anti-conformism. We fully characterize the set of Nash equilibria and establish con- ditions under which costless secession yields structural Pareto improvements. We demonstrate that in any strategically mixed society, every mixed-strategy Nash equilibrium admits a Pareto-improving se- cession. With finitely many types, secession systematically mitigates coordination frictions, enhancing both individual payoffs and aggregate utility. Furthermore, we characterize social planner configura- tions optimizing weighted aggregate utility, establishing a formal mathematical isomorphism between optimal jurisdictional design and the theory of Bayesian persuasion solved via concavification. Finally, we derive the structural conditions governing migration stability when subgroups can unilaterally re- locate across distinct societies. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.06092 |
| By: | Yukihiko Funaki; Yukio Koriyama; Matias Nunez; Giacomo Rostagno |
| Abstract: | Extending the Price-and-Choose (P&C) mechanism of Echenique and Nunez (2025), we propose the Price-Accept-and-Choose (PA&C) mechanism, which preserves efficiency while eliminating P&C's first-mover advantage. We then analyze randomized and bidding variants and show that the resulting equilibrium payoffs correspond to standard solutions in transferable utility games: the Center of the Imputation Set value for P&C and the Shapley value for PA&C. In the randomized variants, these solutions arise in expectation; in the bidding variants, they are implemented on every equilibrium path. We further relate other efficient designs, such as balanced VCG payments, to additional solution concepts, forging an interpretable bridge between implementation theory and cooperative game theory. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.02773 |
| By: | Itai Arieli; Jo\~ao Correia-da-Silva; Wade Hann-Caruthers; Anna Rubinchik |
| Abstract: | We study a network formation game in which agents sponsor links at a linear cost in order to maximize centrality, defined as a weighted sum of walk counts with positive and weakly decreasing weights. This class includes Katz Bonacich centrality and total communicability and captures environments in which access decays with distance. Our main result is a sharp equilibrium characterization: every Nash equilibrium network is core periphery, meaning there exists a set $C$ such that every node is linked to every node in $C$, and there are no other edges. The driving force is that linking to better connected agents generates many additional short connections at once, so incentives concentrate links on a dense subset. Finally, we show that the welfare maximizing network is always either empty or complete. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.02357 |
| By: | Furkan Sezer |
| Abstract: | Bergemann and Morris (2016) show that one information structure is more informative than another exactly when it induces a smaller set of Bayes correlated equilibrium outcomes in every game. We build the quantum analogue. An information structure becomes a family of density operators indexed by the payoff state, which the mediator observes. We show that obedience is equivalent to a Loewner domination between operators on one player's subsystem. The equilibrium set is then a nonempty compact spectrahedron computable by semidefinite programming, classical structures embed exactly, and under quantum individual sufficiency more information shrinks the equilibrium set in every game. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.04973 |
| By: | Mira Frick; Ryota Iijima; Daisuke Oyama |
| Abstract: | We study the strategic impact of ambiguity through the channel of higher-order beliefs. We show that even small amounts of prior ambiguity about game payoffs can generate arbitrarily large amounts of higher-order ambiguity. This gives rise to a novel form of contagion: vanishingly small payoff ambiguity can select ``secure'' actions (e.g., non-participation) as the unique equilibrium outcome even when those actions are almost dominated. We highlight two main implications. First, classical robustness results under probabilistic uncertainty break down under ambiguity when players can deviate to secure actions. Second, if a designer can introduce small amounts of payoff ambiguity into a game, this can serve as a powerful tool for unique implementation. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.24560 |
| By: | Zhonghong Kuang; Jingfeng Lu |
| Abstract: | Two contestants with possibly different marginal costs compete across identical battlefields governed by a Tullock technology with discriminatory power at most one. A symmetric schedule divides a fixed prize according to the number of victories. Allowing for inactivity, unequal efforts across battlefields, and arbitrary mixed strategies, we prove the existence and uniformity of equilibrium. Equilibrium may be pure, semi-pure (one contestant mixes), or two-sided mixed; in a two-sided mixed equilibrium, each contestant uses at most countably many positive effort levels. Multiple equilibria with different structures can coexist while generating the same expected effort, prize share, cost, and payoff. For every admissible schedule and cost ratio, equilibrium is unique with six or fewer battlefields, whereas seven first permits multiplicity or two-sided mixing. We also characterize all equilibria under majority rule. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.02031 |
| By: | Zihao Li; Minghao Pan |
| Abstract: | Which social norms are self-correcting under rational learning? We show that conduct sustained by false beliefs cannot persist if a single departure from prevailing behavior generates evidence against those beliefs. We study the overlapping-generations learning model of Fudenberg and Levine (1993), in which finitely lived Bayesian agents are repeatedly and randomly matched with agents in other player roles, observe only their own matches, and learn from experience. In simple extensive-form games with nodewise-independent, nondegenerate priors, as agents live increasingly long lives and become sufficiently patient, every limiting game outcome is path-equivalent to a subgame-confirmed equilibrium. This establishes the converse of Fudenberg and Levine (2006). The mechanism is endogenous experimentation: uncertainty about the consequences of a potentially profitable departure gives patient agents an incentive to test it, generating the observations that correct beliefs and discipline continuation play. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.05380 |
| By: | Mohsen Pourpouneh; Rasoul Ramezanian; Arunava Sen; Vilok Taori |
| Abstract: | We consider a variant of the Assignment Game of Shapley and Shubik (1971), where agents do not observe the assignment or the surplus division of other matched pairs. We propose a set-valued solution concept (Self-Stabilizing Set) and characterize the largest such set. This leads to the formulation of the Stable Payoff Guarantee (SPG) set, which assumes that agents receive at least their payoff guarantees and that this is common knowledge. Our main result is that, for generic surplus matrices, the SPG set consists only of the efficient assignment. The associated payoff vectors are given by the smallest interval that contains the worker-optimal and firm-optimal stable payoffs. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.03230 |
| By: | Darrell Duffie; Chaojun Wang |
| Abstract: | With complete-information bilateral bargaining in network settings, holdup is eliminated when contracts across the network are agreed atomically (all or none) via a smart contract. Applications include over-the-counter asset trading, third-party-financed purchase agreements, and land assembly. Under a novel extensive-form bargaining protocol, a firm can give a “greenlight” to the terms of a contract proposed to that firm, and the protocol automatically converts those terms into a binding contract if the terms proposed to all other firms are likewise given greenlights. In any Perfect Bayesian Equilibrium with Markov strategies, firms immediately agree on socially efficient contracts. |
| JEL: | C70 D47 D60 D70 |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35678 |
| By: | Igal Milchtaich |
| Abstract: | The paper explores a theoretical freemium model for the sale of information, drawing on mathematical tools used in the study of repeated zero-sum games and Bayesian persuasion. Unlike standard Bayesian persuasion models, the information seller (IS) is indifferent to the actions taken by the information buyer (IB) and is concerned solely with maximizing the revenue from selling information. Offering some information for free may increase the IB's willingness to pay for additional information. The information that the IB seeks is about the state of the world. Initially, the IB only knows the prior distribution over possible states. The IS supplies both free and paid information through signals whose state-dependent distributions determine the IB's posterior via Bayes' rule. The IB's utility is a function of the posterior. An optimal free signal is one that maximizes the IS's expected revenue from the subsequent paid signal. That revenue is equal to the IB's expected utility gain when moving from the posterior induced by the free signal to that induced by the paid signal. The paper characterizes the optimal free and paid signals and derives a formula for the maximal revenue in terms of the IB's utility function. It shows that a revenue gain for the IS from the provision of free information is accompanied by a loss to the IB. Whether free information can increase the IS's revenue depends on the form of the IB's utility function. In the two-state case, that dependence is fully characterized. In the general case, only necessary conditions are obtained. In particular, if the IB's utility function is convex, the IS can never profit from providing free information. This occurs, in particular, when the IB uses the information to solve a decision problem. By contrast, when the IB is engaged in a strategic interaction with a third party, the IS may benefit from providing free information. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.01468 |
| By: | Thomas W L Norman (Magdalen College, Oxford); Tim Willems (Bank of England and Centre for Macroeconomics) |
| Abstract: | The fiscal theory of the price level (FTPL) posits that the price level adjusts to ensure the Government’s budget equation is met in equilibrium, but is silent on the exact adjustment mechanism. By modelling the Government as a large, satiable player in a game with households, we demonstrate that the FTPL’s outcome can be understood as a 'dividend equilibrium', achieved via price level driven revaluation of initial debt. It coincides with the Core (ensuring stability) and the unique outcome consistent with players receiving their Shapley Value. The price level adjustment envisioned by the FTPL thus emerges endogenously as the sole stable outcome when agents are compensated according to their marginal contributions, rather than it being imposed as an assumption. This provides a formal foundation for non-Ricardian fiscal policies, central to the FTPL. |
| Keywords: | The Core;Shapley Value;the fiscal theory of the price level |
| JEL: | D51 E31 E62 |
| Date: | 2025–07–18 |
| URL: | https://d.repec.org/n?u=RePEc:boe:boeewp:023259 |
| By: | Changxia Ke; Greg Kubitz; Yang Liu |
| Abstract: | We study auctions with costly entry in which bidders have incomplete information about their affiliated private valuations prior to entry. We examine whether indicative bidding--a mechanism requiring non-binding preliminary bids before entry--can stimulate participation and improve entrant selection, and we compare its performance with unrestricted and capped entry in a controlled laboratory experiment. When entry costs are high, indicative bidding generates significantly more revenue, primarily by increasing participation beyond theoretical predictions. When entry costs are low, its predicted revenue advantage is attenuated by higher-than-predicted selection inefficiency. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.24457 |
| By: | Mark Whitmeyer |
| Abstract: | I argue that there is a sense in which universal equilibrium (defined loosely) existence in games is incompatible with eschewing strictly dominated strategies and a sense in which it isn't. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.06327 |
| By: | Yu Awaya; Vijay Krishna; Eduard Osipov |
| Abstract: | We study auctions of k identical objects to n bidders, each of whom wants at most one. The objects have a common but unknown value and the bidders receive private signals about this value. The discriminatory price auction and the uniform-price auction are compared in terms of how informative the resulting auction prices (not bids) are in conveying the true value to an outside observer/investor. Since both auctions have symmetric, monotone equilibria, the problem reduces to comparing the informativeness of the highest order statistic of a sample to the (k+1)st highest. We find sufficient conditions under which the highest order statistic is superior---in the sense of Lehmann---in this regard. The sufficient conditions involve the informativeness of high versus low signals and the ratio k/n of objects to bidders. These conditions are also qualitatively necessary. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.04332 |
| By: | Cabau, Noemie; Tenev, Anastas |
| Abstract: | We consider a model of network formation in which agents benefit from intermediation insofar as they are the only bridge between agents who would otherwise be unconnected. Their payoffs depend proportionally on their frequency as intermediaries. We analyze two types of payoffs: global, based on the intermediation across the whole network; and local, based on an agent’s perceived centrality in a subnetwork, measured within a fixed radius around the agent. These capture two measurements of network importance: objective and perceived (subjective). Agents have an incentive to form links so that they become key intermediaries in their (perceived) network and to bypass other key intermediaries in it. However, because payoffs are determined relative to other agents’ contributions, an agent might refrain from forming links if this would expose them to relatively more essential players. In case agents’ payoffs are global, the pairwise stable networks are connected and have at most one (central) agent with a nonzero payoff. In the case where agents’ payoffs are local, we describe the pairwise stable networks and some characteristics of the individual payoffs within them. A class of networks we call augmented stars (stars in which spokes may be connected but no cycle encompasses all spokes) is pairwise stable for both global and all possible local payoffs. |
| Keywords: | social networks, structural holes, network formation, intermediation |
| JEL: | C72 D85 |
| Date: | 2026–08–31 |
| URL: | https://d.repec.org/n?u=RePEc:cvh:coecwp:2026/03 |
| By: | Zhaohan Wang; Mohsen Ramezani; David Levinson (TransportLab, School of Civil Engineering, University of Sydney) |
| Abstract: | This paper proposes a two-dimensional trajectory controller (2DTC) for autonomous vehicles (AVs) operating on a lane-free freeway. Without relying on inter-vehicle communication, each AV independently determines its acceleration and steering in real time. The 2DTC is formulated as a receding-horizon optimal control problem (OCP) with nonlinear dynamics, costs, and constraints. The OCP is discretized and solved using the continuation/GMRES method to obtain the optimal control values. Strategic interactions between AVs are captured through a level-k game theory model. The performance of the 2DTC is evaluated through both microscopic and macroscopic analyses. Microscopic simulations show that the generated trajectories are smooth and compliant with constraints, while macroscopic measures are used to construct fundamental diagrams, demonstrating capacity levels exceeding those typically reported for human-driven freeway traffic. Further experiments show that higher reasoning depth yields reductions in travel time, while increased vehicle size heterogeneity improves traffic efficiency by enabling more compact packing in lane-free flow. In addition, more homogeneous vehicle speeds tend to result in higher average speed, thereby improving efficiency. Comparisons with a similarly defined lane-based controller reveal that lane-free traffic is less efficient when vehicle sizes are uniform but becomes more efficient once size heterogeneity exceeds a critical threshold of roughly 22%. |
| Keywords: | Automated vehicle, Trajectory planning, Model predictive control, Nonlinear control, Game theory |
| JEL: | R40 |
| Date: | 2027 |
| URL: | https://d.repec.org/n?u=RePEc:nex:wpaper:paper-2027-01 |
| By: | Mohlin, Erik (Swedish Defense University); Rigos, Alexandros (University of Copenhagen) |
| Abstract: | We present a model of how an individual’s preference for a specific behaviour can evolve as an adaptation to her social environment. Our key assumptions are that the decision maker (DM) (i) is boundedly rational in her ability to process information and evaluate which actions yield the highest payoff and (ii) can develop a subjective preference for actions. A stronger preference for an action reduces the probability of not taking it when it is optimal (omission error), but it also increases the probability of taking the action when it is suboptimal (commission error). The optimally adapted preference strikes a balance between these errors and depends on the DM’s environment. DMs are typically better off (in objective terms) if they are endowed with subjective preferences that deviate from maximisation of expected objective payoff. Importantly, if DMs can evaluate actions perfectly, they do not develop such biases. The results extend in an intuitive manner to n-player, two-strategy supermodular games. Our framework can be used to interpret preferences for specific actions or strategies (e.g., conditional cooperation, truth-telling, or norm-following) as psychological and cultural consequences of material incentives and social organisation. |
| Keywords: | Preference evolution; Bounded rationality; Culture; Cooperation; Cognitive economics; Logit choice; Monotone comparative statics; Supermodular games |
| JEL: | C72 C73 D01 D83 D91 |
| Date: | 2026–09–09 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:lunewp:2026_008 |
| By: | Joseph Lecl\`ere; Mathieu Rosenbaum |
| Abstract: | Although market participants generally have access to a common information set, they make decisions based on forecasts formed over heterogeneous horizons. Because market impact depends on aggregate positions rather than trader identities, these decisions feed back into prices through their collective effect. We introduce a linear mean-field model of this interaction. The observed price is decomposed into a martingale component, a common predictable signal represented by a Volterra process, and the market impact generated by aggregate positions. Agents take positions according to conditional forecasts of future signal increments and a fraction of anticipated aggregate impact over their respective horizons. Within a Gaussian-Volterra framework, we characterize equilibrium through a linear fixed-point equation for aggregate positions and establish existence and uniqueness under explicit conditions. At equilibrium, we identify a balance condition that cancels the direct transmission of the common signal to the observed price. We then study the limit in which agents fully account for market impact. Along a suitably scaled family of equilibria satisfying explicit conditions, the contributions of the predictable signal and the market impact cancel in the limit, and the observed price converges to its martingale component. For fractional-type signals and Gamma-distributed horizons, we further derive local H\"older bounds and identify the horizon distributions for which the observed price has local regularity compatible with that of Brownian motion. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.03115 |
| By: | Takaaki Abe |
| Abstract: | This paper examines how outside options are incorporated into payoff distributions in games with coalition structures. We introduce and characterize the alpha-value, which "fully" incorporates outside options, and provide a new characterization of the Aumann-Dreze value as an allocation rule that does not incorporate outside options. We show that the chi-value (Casajus, 2009) is a component-wise convex combination of these two values and thus incorporates outside options in a discounted form. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.00799 |
| By: | Seiya Hirano |
| Abstract: | Two-sided markets exhibiting network effects often face coordination problems, which may lead to an inefficient outcome where a lower-quality platform wins the market. Some users make collective decisions as a group, potentially affecting the choices of others. This paper analyzes the impact of group users on two-sided platform competition. We develop a model with two platforms: one with a quality advantage (the higher-quality platform) and the other with a network advantage due to its focality (the lowerquality platform), meaning that users expect others to join it when multiple equilibria exist. There are two types of users: individual users and group users. An individual user makes decisions independently, whereas group users make collective choices that can affect others’ decisions. Our main findings are as follows: First, the group affects individual users’ choices if its size is sufficiently large, meaning it is pivotal. However, even if the group is pivotal, it may join the lower-quality platform unless it is large enough. The group joins the higher-quality platform only when it is both pivotal and sufficiently large. Second, we examine how the group size affects surplus distribution. Increasing group size improves market efficiency but exacerbates the disparity in the surplus between the group users and individual users. Our results highlight the dual role of group users in platform competition: while they can enhance efficiency by steering the market toward the higher-quality platform, they may also contribute to imbalances in surplus distribution. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:dpr:wpaper:1320 |
| By: | Xuan Mei; Junze Lin |
| Abstract: | Forecasting systems used in the Comprehensive Capital Analysis and Review (CCAR) and Current Expected Credit Losses (CECL) processes combine portfolio data, macroeconomic scenarios, model specifications, business assump- tions, and management adjustments. When the forecast changes from one run to the next, practitioners need an attribu- tion that reconciles to the total change without depending on an arbitrary sequence of input replacements. This paper formulates forecast-gap attribution as a cooperative game and examines several approaches: the exact Shapley value, hierarchical or nested Shapley values, Integrated Gradients, Gradient SHAP, Permutation SHAP, and Kernel SHAP. We compare their allocation rules, computational costs, implementation requirements, and limitations in production forecasting systems. The analysis provides a practical framework for choosing an attribution method according to the number and type of inputs, the feasibility of hybrid forecast runs, and the need for interpretability, reproducibility, and governance. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.04547 |
| By: | Igor Cialenco; Mike Ludkovski |
| Abstract: | This non-technical survey introduces the topic of groundwater management to the mathematics and statistics communities. We focus on the emerging marketplaces for groundwater pumping rights, outlining probabilistic and statistical approaches to groundwater dynamics and game equilibria that underpin stakeholder decisions. After discussing rationing schemes and regulatory policies we list a range of open problems that are well suited to be tackled by the mathematical sciences researchers. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.23914 |
| By: | Yutong Zhang; Yangfan Zhou |
| Abstract: | We study robust mechanisms when the designer possesses a Bayesian belief over some components of agents' private information but faces ambiguity over others. The designer evaluates mechanisms by their worst-case performance over all joint distributions consistent with her belief over the Bayesian components. The framework encompasses settings such as multidimensional delegation in which a principal knows the distribution of the state but not the agent's preferences (e.g., his tradeoffs across dimensions), screening in which a seller only has misspecified estimates of buyer preferences, and auction and voting design when agents' beliefs about each other are ambiguous to the designer. We provide conditions under which a \emph{knowledge-based} mechanism---one that conditions only on the Bayesian components but not the ambiguous ones---is robustly optimal. Our results unify earlier work across distinct economic environments and uncover new applications. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.03439 |