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on Game Theory |
| By: | Moeen Nehzati |
| Abstract: | We show that distinct pure-strategy Nash equilibria typically have different utilitarian welfare values in sufficiently rich classes of $C^2$ games with open strategy sets. Here, typical means both generic and finitely prevalent, while rich means that the class admits a finite-dimensional family of perturbations that can independently move payoff values and first derivatives in any direction at any two distinct strategy profiles (for example, polynomial perturbations of degree at most three). Consequently, a welfare-maximizing equilibrium, if one exists, is unique. The result extends to each fixed $C^1$ payoff aggregator whose derivative with respect to the payoff vector is everywhere nonzero. In the full $C^2$ utility space, we also treat scalar criteria depending on strategies, payoffs, and payoff derivatives, subject to a nonvanishing condition in payoff-level or cross-player derivative directions. Finally, adjoining arbitrarily small perturbations from a suitable finite-dimensional space makes welfare separation typical in the augmented family, with separation holding for almost every perturbation of each fixed base game. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.08661 |
| By: | Davit Gondauri |
| Abstract: | We study a fixed-normalization class of symmetric bimatrix games generated by a common kernel and show that it admits efficient approximation despite exact symmetric-equilibrium computation remaining PPAD-hard. For every rational game in the class, a single auxiliary zero-sum saddle computation yields a rational symmetric \(1/5\)-approximate Nash equilibrium in polynomial time. We also give exact recognition and unique kernel recovery, and an exact polynomial-time post-processing algorithm that minimizes regret along the segment joining the selected saddle strategies. For arbitrary rational square games, we formulate the nearest common-kernel projection as a linear program with an explicit dual certificate, obtaining a certified \((1/5+2\eta^*)\)-approximation guarantee. A separate selector result proves a sharp regret-to-uniformity constant for the full-subset construction. The results provide a tractable and certifiable structured-game regime and clarify which common-kernel reduction architectures cannot support certain fine-grained approximation-hardness objectives. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.33471 |
| By: | Gondauri, Davit |
| Abstract: | This paper establishes a strict deterministic polynomial-time approximation guarantee below the one-third frontier for general two-player rational bimatrix games with payoffs normalized to the unit interval. The result addresses the long-standing upper-bound question of whether the universal worst-case approximation guarantee can be separated strictly from one third rather than merely approached from above. Building on the stationary framework of Deligkas, Fasoulakis, and Markakis, the paper introduces an enriched fixed-side completion architecture that extracts additional algorithmic information from the DFM stationary configuration. Each side is augmented by a midpoint best response, producing a three-strategy fixed-side hull over which completion is optimized. The analysis converts the DFM stationary dual certificate into pointwise pure-action inequalities, providing a direct bridge from stationary duality to fixed-anchor regret control. The proof develops a complete quantitative localization of the DFM parameter space. The difficult Case 4.2 equality-set analysis is robustified through explicit threshold-perturbed residual functions, a uniform perturbation envelope, and exact separation margins away from the critical zero sets. Noncentral high-face and asymmetric endpoint configurations are excluded using explicit derivative, denominator, and stationary bounds rather than qualitative continuity arguments. The central obstruction is resolved by a new two-point fixed-anchor completion theorem. After the direct-mixing branch fails, the construction produces a profile with regret below 0.308, eliminating the need for the earlier near-one-twelfth saturation and thirteen-fortieths cross-mixing mechanism. Together with the exhaustive parameter partition, this closes every possible obstruction to a strict improvement below one third. The resulting enriched-hull theorem establishes an explicit universal positive gap below one third at the exact candidate level. A self-contained fixed-side discretization argument then converts the structural theorem into a fully specified deterministic polynomial-time algorithm that, for every normalized rational bimatrix game, returns an approximate Nash equilibrium with a worst-case regret strictly below one third. Consequently, the deterministic polynomial-time approximation threshold is strictly smaller than one third. The significance of the result is qualitative rather than numerical: the explicit constant is deliberately nonoptimized, but its positivity establishes that one third is not a terminal deterministic polynomial-time upper-bound frontier. Beyond the final approximation constant, the paper contributes a reusable methodological framework combining stationary primal-dual certificates, enriched strategy hulls, equality-set localization, fixed-anchor completion, finite candidate extraction, rational linear programming, and controlled discretization. These mechanisms provide concrete directions for sharper approximation constants, automated theorem search, symbolic verification, computational benchmarking, and further investigation of the true approximation threshold for bimatrix Nash equilibria. The result does not determine the exact approximation threshold, establish optimality of the displayed gap, provide a matching hardness lower bound, or solve exact Nash equilibrium computation in polynomial time. Its precise contribution is the strict crossing of the one-third deterministic polynomial-time upper-bound frontier for general normalized rational bimatrix games. |
| Keywords: | Approximate Nash Equilibrium, Bimatrix Games, Algorithmic Game Theory, Polynomial-Time, Approximation, One-Third Approximation Barrier, Computational Complexity |
| JEL: | C72 C61 C63 C62 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:esprep:344039 |
| By: | Yuki Shiomi; Nobuyuki Hanaki |
| Abstract: | We experimentally examine whether partial commitment to the message distribution can substitute for full commitment to the information structure in Bayesian persuasion. Theory predicts that when the players’ marginal incentives are aligned, an equilibrium with the same level of information transmission as under full commitment can be sustained even under partial commitment, whereas when marginal incentives are misaligned, no information can be credibly transmitted. Our central finding is that, even when marginal incentives are aligned, information transmission is substantially lower under partial commitment than under full commitment: partial commitment does not fully substitute for full commitment in practice. When marginal incentives are misaligned, information transmission declines further under partial commitment, as theory predicts. We also find that misaligned marginal incentives reduce information transmission even under full commitment, where the standard theory predicts no such effect. Our analysis of sender behavior shows that, in all of these cases, senders transmit less information than the theoretical benchmark implies, suggesting that sender undercommunication plays an important role in the lower information transmission we observe. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:dpr:wpaper:1322 |
| By: | Dongshuang Hou (School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, China); Aymeric Lardon (Université Jean Monnet Saint-Etienne, Université Lumière Lyon 2, emlyon business school, GATE UMR 5824, F-42023 Saint-Etienne, France) |
| Abstract: | We introduce similarity Gaussian games, transferable-utility games in which the worth of a coalition is the total pairwise similarity among its members, measured by a Gaussian kernel. Similarity Gaussian games are convex weighted graph games, so the Shapley value is always a core allocation; it also has two complementary interpretations: it is weighted degree centrality in the associated similarity network and, up to a common factor, a Gaussian kernel density estimate evaluated at each player’s characteristic. We derive the Shapley value in closed form and study how it changes with the bandwidth. For large bandwidths, we establish an exact asymptotic affine relationship between the Shapley values of similarity Gaussian games and squared deviations games, providing a precise link between local similarity and dispersion. |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:gat:wpaper:2609 |
| By: | Ola Andersson; Carlos Kurschilgen; Michael Kurschilgen; Daniel Spiro |
| Abstract: | Rotating leadership is prevalent in international relations. Examples include the presidencies of the EU Council, the G7, and the African Union. Why would self-interested actors take turns rather than, for instance, have a permanent leader? We study this question in a repeated three-player coordination game of conflicting interests, where agents want to coordinate on a common action (leadership), but disagree on what is the best action to coordinate on (who should lead at any point in time). Standard subgame perfection provides no answer to the research question since it allows for many leadership arrangements, including a permanent leader, or the exclusion of one agent from leadership, or fully rotating leadership. We show, however, that they differ in robustness to coalitional deviations. Asymmetric arrangements give disadvantaged players persistent incentives to form a breakaway coalition against the incumbent. By evenly distributing leadership opportunities, full rotation emerges as the most stable self-enforcing institution. Results from a preregistered laboratory experiment support the relevance of this mechanism also to interpersonal relations: rotations predominate when interests are highly heterogeneous, while permanent leadership arises mainly when interests are relatively aligned. Refuting predictions from inequality aversion, rotations remain predominant even when one player receives an additional choice-independent lump-sum income, while strategies aimed at reducing this payoff gap remain rare. This suggests that the risk of coalitional breakdown is an important driver of why also individuals – not just nations – share decision making evenly. |
| Keywords: | turn-taking, rotations, coalition proofness, inequality aversion, coordination, experiment |
| JEL: | C72 C92 D71 D74 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_13027 |
| By: | Hinata Kurashita |
| Abstract: | We study object reallocation problems with single-peaked preferences. On the unrestricted domain of strict preferences, top trading cycles (TTC) is the unique rule that satisfies efficiency, individual rationality, and strategy-proofness. On the single-peaked preference domain, the crawler introduced by Bade (2019) satisfies the same properties. We show that the Nash equilibrium allocations of the crawler's direct revelation game form a complete lattice under weak Pareto dominance. The truthful allocation is the greatest element of this lattice, while the initial endowment allocation is its least element. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.08096 |
| By: | Vladimir Asriyan; William Fuchs; Caio Lorecchio |
| Abstract: | We study dynamic monopoly pricing with multiple buyers whose valuations are privately known and correlated, so that one buyer 's purchase reveals information about the valuations of others. Without seller commitment, these information spillovers alter future pricing incentives and feed back into current demand. We show that they generate strategic complementarities in buyers' purchase decisions, making demand non-monotone and giving rise to equilibrium multiplicity. Information spillovers can either strengthen or weaken the seller 's effective commitment power, implying that seller revenue, buyer surplus, and total welfare are generically non-monotonic in the strength of spillovers. We characterize when these spillovers encourage data investment and experimentation, as well as facilitate coordination that mitigates hold-up. |
| Keywords: | commitment, dynamic monopoly pricing, equilibrium multiplicity, information spillovers, strategic complementarities |
| JEL: | D42 D82 D83 |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:bge:wpaper:1598 |
| By: | Marcus Gawronsky; Chun-Sung Huang |
| Abstract: | Firms follow changing economic opportunities, but rivalry changes their response. We develop ESCAPE, a rational-share game of distribution-valued positioning with heterogeneous capability costs, establish a unique equilibrium, and derive an exact reallocation restriction separating opportunity and crowding contributions. Competition need not push firms apart: rational firms can enter increasingly crowded regions, because the full reallocation gain can be positive even when its crowding component is negative. Rivalry instead changes how differently firms respond to the same opportunity shift. In the benchmark many-firm economy, the relative-response component accounts for 90.5% of the weighted squared composition-response contrast between strategic and independent firms; it is numerically zero under identical capabilities. The contrast remains distinguishable under corpus-scale measurement. Corporate news distributions document persistent but changing peer structure: optimized peer reconstructions retain 86.5% of their aggregate validation advantage one year later even as absolute distance to both frozen reconstructions increases. Peer structure is persistent without being a fixed destination, so current similarity can remain informative without fixing firms' future relative positions. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.37820 |
| By: | Ingrid Ott; Susanne Soretz |
| Abstract: | Rapid technological change can generate risks that extend beyond the actors creating them, while institutional capacity to contain these risks adjusts only gradually. Strategic rivalry can reinforce this mismatch by sustaining incentives for technological acceleration even as risk increases. The interaction of endogenous risk creation with institutional inertia can therefore transform a quantitative imbalance between risk creation and governance-capacity formation into a qualitative viability problem: beyond a critical boundary, a low-risk equilibrium ceases to exist. We develop a differential game in which countries choose technological acceleration and governance mobilization. These flows accumulate into technological capability, a common risk stock, and effective governance capacity. Technological capability has productive and strategic value, whereas aggregate acceleration generates risk that is only partially internalized. Rising risk strengthens incentives for containment but can simultaneously increase the strategic value of relative technological capability. Governance mobilization responds to risk but becomes effective only as it is gradually converted into governance capacity. Relative to a multilateral cooperative benchmark, the non-cooperative equilibrium features excessive technological acceleration and insufficient governance mobilization. We map these equilibrium responses into a two-dimensional risk--governance system, which yields an endogenous viability frontier. "Low-risk'' denotes an equilibrium in which accumulated governance capacity is sufficient to balance endogenous risk creation; it does not imply intrinsically low or socially optimal risk. Institutional delay can therefore shift the policy problem from correcting an externality toward preserving a dynamically sustainable balance between risk creation and governance capacity. We apply the framework to current AI policy configurations and AI-enabled synthetic biology. Rapid and increasingly distributed technological capability raises informational, monitoring, and coordination requirements for effective safeguards and can narrow the margin within which risk creation remains dynamically containable. |
| Keywords: | dynamic risk externalities, institutional inertia, nonlinear dynamics, viability frontier, strategic technological competition, artificial intelligence |
| JEL: | D62 O33 H41 C73 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_13024 |
| By: | Stefanie S Baumgartner (UNIFR - Université de Fribourg = University of Fribourg); Fabio Galeotti (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne - UJM EPE - Université Jean Monnet (EPSCPE) - EM - EMLyon Business School - CNRS - Centre National de la Recherche Scientifique); Thierry Madiès (UNIFR - Université de Fribourg = University of Fribourg); Marie Claire Villeval (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne - UJM EPE - Université Jean Monnet (EPSCPE) - EM - EMLyon Business School - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | Trust plays a crucial role in refugees' integration. This study examines how social information about trust levels among peers from home and host countries affects non-Western refugees' trust. Using a trust game, we experimentally measured trust levels among Swiss citizens, Turkish refugees, and Afghan refugees. We found that Turkish refugees exhibited higher trust levels than Afghan refugees, but no significant differences in trust were observed between Swiss participants and either refugee group. Turkish refugees adjusted their trust to match Swiss levels when receiving social information, but observation by compatriots reduced this effect. By contrast, Afghan refugees exhibited a more limited response to social information, except when told their behavior would be revealed, which led them to align more closely with Swiss trust levels. These findings highlight the complex impact of social information on refugee trust behavior and suggest that trust can be a social norm. |
| Keywords: | Social norms, Lab-in-the-field experiment, Social information, Trust, Refugees |
| Date: | 2026–09–28 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05001907 |
| By: | Olivier Bos; Martin Pollrich |
| Abstract: | We study mechanisms in which agents' preferences depend both on an object allocation and on a third party's beliefs about private information. A mechanism determines an allocation, transfers, and sends signals to the aftermarket. We compare two informational environments: (i) private transfers, where the aftermarket observes allocations and signals, and (ii) public transfers, where transfers are publicly observable. Our main result shows that any equilibrium outcome implementable with hidden transfers can be approximated arbitrarily well with public transfers. Thus, transfer observability generates at most a vanishing informational distortion and helps rationalize the common assumption that transfers remain hidden from aftermarkets. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.03146 |
| By: | Parinaz Naghizadeh; Jingyan Wang |
| Abstract: | In school choice, a lottery number is often used by the matching mechanism to break ties when there are more students who prefer the same school than the number of seats available. There has been growing theoretical and empirical interest in understanding the impact of revealing the lottery number to students. In practice, in recent years, the NYC Public Schools started revealing the lottery number to students to improve transparency. Theoretical findings from prior literature also suggest that revealing the lottery number strictly improves the number of matches under the deferred acceptance algorithm. However, these theoretical results are based on the over-simplifying assumption that all students share the same preference ranking for schools. In this work, we relax this assumption and allow students to have heterogeneous preference rankings. Under a game-theoretic model where student strategies form a Bayesian Nash equilibrium, we characterize scenarios where revealing the lottery number can either improve or worsen the matching outcome, measured by two metrics of match rate and social welfare. We further consider revealing partial information about the lottery, and demonstrate non-monotonic effects in the amount of information available to students. These results together illustrate complex tradeoffs induced by the lottery revealing policy. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.34074 |
| By: | Takashi Shimizu (Graduate School of Economics, Kobe University) |
| Abstract: | We study information transmission within organizations, focusing on how biased Subordinates should be combined to elicit truthful information. We assume that the directions of the Subordinates’ biases are common knowledge, whereas their magnitudes are privately known to each Subordinate. We show that a homogeneous composition of Subordinates is preferable to a heterogeneous one. The intuition is that, under a homogeneous composition, the effect of an individual false report is amplified by false reports from other Subordinates. Anticipating this amplification effect reduces each Subordinate’s incentive to misreport and thereby promotes truthful information transmission. |
| Keywords: | Cross-holdings: Organization; Information transmission; Cheap talk; Bias; Homogeneous mode; Heterogeneous mode |
| JEL: | D23 D82 |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:koe:wpaper:2614 |
| By: | Tingyi Lin; Shawn Yu; Ruoran Lai; Huanxi Zhang |
| Abstract: | A coalition that deviates once can profit many times when what it sells keeps working. In a threshold-encrypted mempool, a leading defense against maximal extractable value (MEV), a quorum of the decryption committee that sells its decryption capability to a front-runner exposes every later block that the capability still decrypts. We ask how large a penalty, such as slashable stake, deters this kind of collusion. In our repeated game, a single leak by any coalition in a monotone family of authorized coalitions (for example, any $k$ of the $n$ committee members) unlocks a set of future rounds, costs a one-time penalty, and ends the coalition's participation. We show that every dynamic deviation reduces to choosing a leak time, so deterrence holds if and only if each coalition's penalty covers the largest discounted value that a single leak reaches. Without discounting, over $T$ rounds of unit value full reuse needs a penalty of $T$ while binding each leak to its own round needs $1$, so no penalty that is constant in the horizon deters unbounded reuse; a reuse window of $w$ rounds costs at most $w$ times the largest per-round value. The cheapest profile of per-party stakes that deters every coalition solves a covering linear program. For blockchain design, per-epoch keys cut the required stake from the value of a key's lifetime to the value of one epoch; we calibrate the gap on Ethereum front-running data and place Ferveo and Shutter in the model. The analysis extends to sealed-bid auctions, multi-authority voting, and federated learning under a shared key. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.36667 |
| By: | Siu Tung Wong (Institute of Finance and Technology, University College London); Carlo Campajola (Institute of Finance and Technology, University College London; UZH Blockchain Center) |
| Abstract: | Reinforcement learning (RL) is increasingly used for financial optimal-control problems when complex dynamics make analytical strategies difficult to obtain. There are financial mathematics literactures which provides many solved models whose equations and controls could evaluate and guide learning; we ask whether RL can exploit these results. We place a proximal policy optimisation (PPO) agent in an analytically solved continuous-time broker--trader game. PPO replaces the broker and chooses its trading speed while interacting with an informed trader and stochastic uninformed order flow. We derive a finite-step reward from the broker's continuous-time payoff and verify its discrete implementation through grid refinement and an exact one-step identity. With zero uninformed flow, a validation-selected PPO--FFNN approaches the reference action. With stochastic uninformed flow, the tested PPO--FFNN and PPO--LSTM remain inaccurate, although supervised learning confirms that their actors can represent the action. Monte Carlo diagnostics show that their critics do not reliably rank nearby actions; potential-based reward shaping also gives no reliable improvement. Under partial information, a causal certainty-equivalent controller based on the broker's observable history remains close to the reference, while PPO has larger errors and lower payoffs. Finally, we freeze the analytical policy and train PPO to adjust it after the execution cost changes. Halving the cost yields a repeatable improvement that closes \(2.22\%\) of the gap to the changed-cost reference. The analytical solution therefore provides both a benchmark for diagnosing RL and a useful starting policy for adaptation. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.03598 |