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on Game Theory |
| By: | Benjamin Marsh |
| Abstract: | A single auction can have both a shill-proof equilibrium and a non-shill-proof equilibrium in the model of Komo, Kominers, and Roughgarden. We give an explicit single item example with three bidder positions, publicly observed actions, positive winning prices, and a strictly regular i.i.d.\ value distribution. Real bidders have strict incentives in both equilibria. An initial public action conveys information about whether the final position is real. The resulting belief changes the middle bidder's response and reverses the first shill's strict preference between two actions. We verify both equilibria and compute their expected revenues. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.06262 |
| By: | Jason Shachat (Center for Intelligence Economic Science, Southwestern University of Finance and Economics and Chapman University); J. Todd Swarthout (Department of Economics, Georgia State University); Yun Wang (School of Economics, Renmin University of China) |
| Abstract: | We examine how competitive allocation of scarce participation rights shapes behavior in a Berg-style trust game. Trustor and trustee roles are allocated through multi-unit uniform-price English auctions with varying scarcity, alongside a matched-fee random-assignment control treatment. Positive transfers and returns persist, but behavior lies near the low-trust, low-reciprocity end of comparable benchmarks. Tighter scarcity accelerates the decline in trustor transfers, while trustee returns show no monotonic pattern. Scarcity strongly raises auction prices without comparably raising participants’ gross trust-game earnings, thereby lowering net earnings. Exit bids adjust to past game profitability, indicating adaptive learning about the value of participation. |
| Keywords: | Trust Game; trust game; Scarcity; Market Allocation; Participation Rights |
| JEL: | C91 D82 D83 D84 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:chu:wpaper:26-12 |
| By: | Galit Ashkenazi-Golan; Edward Plumb; Clemens Possnig; Yufei Zhang |
| Abstract: | We study the strategic design of learning algorithms in a canonical continuous-time pricing game. We introduce a meta-game in which firms select learning rates for a gradient dynamic, evaluating payoffs as the discounted sum of profits accrued along the entire learning path. We uncover a fundamental dichotomy driven by stage-game incentives: if the stage game exhibits strategic substitutability, firms unambiguously prefer the fastest possible algorithms to rapidly exploit a gradually adjusting opponent. Under strategic complementarity, however, an excessively fast algorithm accelerates the rival's competitive response, destroying transitional profit margins. Even though the competitive price is a strictly dominant action in the underlying stage game, we prove that firms optimally design sluggish algorithms, extracting surplus during a prolonged convergence to the competitive equilibrium. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.11675 |
| By: | Ezra Einy; Ori Haimanko |
| Abstract: | It is known that completeness of the coalitional ($C$-)desirability relation in a simple game does not imply the existence of a weighted-majority representation. We show that weightedness is implied in an approximate sense. Call an $n$-player simple game $\varepsilon$-weighted if, for some weight vector in the $(n-1)$-simplex, any losing coalition weight exceeds any winning coalition weight by at most $\varepsilon$; let $\varepsilon^{\ast}$ be the smallest such $\varepsilon$. We establish an upper bound on $\varepsilon^{\ast}$ in a general $C$-complete game, and deduce that, if all classes of equally desirable players become large asymptotically but the number of classes is bounded, then $\varepsilon^{\ast}=O(1/n_{\min})$ for the minimal player class size $n_{\min}$, and the bound is tight. Importantly, the minimal attainable fraction $\delta$ of coalitions mislabeled by a weighting rule also tends to $0$ when $n_{\min}\rightarrow\infty$ and the number of player classes is bounded, with $\delta=O(1/\sqrt{n_{\min}})$. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.08968 |
| By: | Sinan Ertemel |
| Abstract: | Weighted Shapley values represent asymmetry through positive weights and ordered priority classes. We give these parameters a preference interpretation in Roth's framework of lotteries over positions in transferable-utility games. Under common calibration, nullity, ordinary risk neutrality, unanimity efficiency, and unanimity positivity, position values in unanimity games are probability equivalents. Luce conditioning of these probabilities characterizes the Kalai-Samet family and is equivalent to partnership consistency. We separate conditioning into transitivity of revealed priority, pairwise determination of support, and invariance of positive odds. Two-player observations admit a weighted Shapley extension exactly when revealed priority is transitive and within-class odds satisfy a product rule. The extension is unique: pairwise comparisons identify the priority classes and weight ratios within each class. Larger unanimity games provide additional restrictions on supports and shares. We give constructive proofs, establish independence of the five axioms, and explain the scope and limits of the elicitation interpretation. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.09899 |
| By: | Yuta Nakamura; Noriaki Okamoto |
| Abstract: | A second-price auction must determine its price but need not learn how far losing values lie below it. We show that protecting this information from the seller conflicts with auction credibility. In deterministic protocols with private communication, lower-tail privacy forces the first informative question to reveal whether a bidder has the highest possible value. The seller can then manipulate the winner's payment without any bidder detecting the deviation, increasing revenue at some valuation profiles and never reducing it. A descending protocol conceals losing values below the price but permits manipulation; with mandatory sale, a credible ascending protocol reveals them. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.12204 |
| By: | Joshua S. Gans |
| Abstract: | An advertiser in a second-price auction sees what it paid, not the rival bids that supposedly set the price. Akbarpour and Li (2020) show that an auctioneer can therefore charge a winner up to its bid undetected. The Federal Trade Commission alleges that Amazon’s advertising auctions, described as second-price, used soft reserves that did this. We ask whether repeated bidding exposes such charges and what adjustment does to welfare. If each charge equal to the bid is flagged, the soft reserve is exposed quickly, however much the advertiser trusted the description. If reports show only win rates and expected charges, it is indistinguishable from a second-price auction at any fixed bid: an advertiser that trusts the description and bids its value never learns, and one that doubts it but bids for current profit needs a number of auctions at least inversely proportional to its doubt before it considers a soft reserve more likely than not. The second-price description and aggregate reporting are complements. Among informed, symmetric advertisers, the soft reserve raises no more revenue than a second-price auction, and when only some advertisers adjust, placements are misallocated. Disclosure returns surplus to advertisers; removing the surcharge also restores efficiency. |
| JEL: | D44 D83 L86 |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35841 |
| By: | Lijian Lu; Ce Zhang |
| Abstract: | When auction bidders misperceive their rivals, a seller can change not only the amount of information rent but also the states in which it is delivered. We ask when this payment-design opportunity survives a finite bidding interface, nonnegative-payment restrictions, and comparison with conventional auctions under the same beliefs. We formulate payment design as a linear program in nonnegative bidder rents. A single state can safely carry a report's rent when it is both cheapest for its intended type and least attractive to potential mimics. We characterize this alignment, bound the cost of a restricted payment architecture when alignment is imperfect, and use shadow prices when the rankings conflict. Own-type projection yields a unique optimal expected-payment rule for a fixed allocation. Contiguous bid bands implement truthful reporting at every value, but create pooling losses and within-band surplus. Under a separate smooth-belief model, feasible truthful rules and revenue upper bounds support comparisons with a first-price equilibrium under the same beliefs. A calibration using 1, 000 eBay proof-set auction records illustrates a partition-dependent reversal: first price dominates all exactly truthful, no-subsidy rules on ten equal-probability bands in one scenario, while a richer contingent rule on ten equal-dollar bands outperforms it. An operator should choose interface resolution, payment dependence, and integrity tolerances jointly. Validate the probabilities that support incentives, compare formats under the same beliefs, and distinguish redesign from deployment. Any receipt advantage must cover implementation costs before it can imply a profit advantage. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.05650 |
| By: | Ratna K. Shrestha (University of British Columbia); Gaurav Subedi (RALP Technologies); Ayush Shrestha (Global Relay Communications Inc) |
| Abstract: | Standard theories trace information asymmetry to privately held information, heterogeneous signals, or costly information acquisition. We identify a distinct mechanism: otherwise identical rational agents observing a common Markov state at asynchronous times can hold different predictive distributions because their information differs in age. When the transition kernel separates information ages, independent Bernoulli observation arrivals make such divergence recur infinitely often almost surely, even with identical arrival probabilities. When agents instead choose costly updating intensities, independent update realizations can regenerate heterogeneous information ages among ex ante identical agents. In a stationary Gaussian AR(1) environment, the consequences depend on common staleness as well as the age gap: holding the gap fixed, older information raises individual uncertainty while reducing expected squared forecast disagreement and the value of certifying relative freshness. This generates stale consensus: low disagreement despite high uncertainty. With multiple ordered ages, costly certification supports partial-unraveling equilibria in which fresher types certify and sufficiently stale types pool. Under geometric information ages, more frequent updating weakly lowers the smallest and largest equilibrium disclosure cutoffs wherever positive-certification equilibria exist. The framework has implications for credit, insurance, financial markets, and multi-agent AI. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.11200 |
| By: | Robin Ng; Greg Taylor |
| Abstract: | We study how content moderation facilitates communication on online platforms. A sender transmits information to a receiver, exerting effort to signal their truthfulness. Communication fails without moderation because the effort required is prohibitive. Moderation resolves this problem by making effort a more powerful signal of veracity. However, moderation crowds out sender effort, decreasing engagement value of content on the platform. A socially optimal policy may therefore involve limited moderation, but platforms often have an incentive to allow too much false content. We study the interaction between moderation and other strategic platform choices, including a platform’s decision to share revenue with creators, the decision to be a content-hosting platform, and the enablement of AI features. |
| Keywords: | user-generated content, content moderation, creator economy, media platforms, misinformation |
| JEL: | D83 L82 L86 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_698v4 |
| By: | Volker Nocke; Nicolas Schutz |
| Abstract: | We derive closed-form expressions for the welfare distortions arising from oligopolis tic market power. Our analysis covers competition among multiproduct firms facing constant elasticity of substitution (CES) or multinomial logit demand. The derived formulas rely solely on observed (oligopolistic) firm-level market shares and, under CES demand, the elasticity of substitution. Under CES demand, we fully character ize resource misallocation and extend the analysis to general oligopolistic equilibrium, decomposing welfare losses into within- and between-industry components. Taylor ap proximations connect these losses to standard concentration indices: within-industry misallocation is proportional to the difference between the cubic Hannah–Kay index and the squared Herfindahl index, while between-industry misallocation is proportional to the variance of the Herfindahl index across industries. |
| Keywords: | Market power, oligopoly pricing, misallocation, industry concentration, Herfindahl index, Hannah-Kay indices, sufficient statistics |
| JEL: | L13 D43 D61 E23 |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_669v2 |
| By: | Qi-Qing Song; Jia-Lin Liu; Jia-Yu Cui |
| Abstract: | This paper investigates the non-emptiness of the fuzzy core and introduces the notion of the TU-fuzzy core for pure exchange economies with discontinuous utility functions. We propose two stability conditions: local fuzzy-coalition stability and local TU-fuzzy-coalition stability. We also introduce an independent-$\pi$-balanced family of subsets of the agent set to construct two payoff-dependent NTU games. These constructions serve as bridges linking the fuzzy core, the TU-fuzzy core, and NTU games. Under the proposed stability conditions, we establish the non-emptiness of the fuzzy core for economies with quasi-concave utility functions and the non-emptiness of the TU-fuzzy core for economies with concave utility functions. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.06572 |
| By: | David J. Jin |
| Abstract: | An agent learns from data that many parameters of her model explain equally well. Berk's theorem states that her belief concentrates on the parameters that best fit the data, but does not select between them. We show that, with a continuum of parameters, the posterior concentrates on the best-fitting parameters with the smallest local learning coefficient. We propose a definition of narratives, subsets of the best-fitting parameters on which the learning coefficient is constant. Narratives are characterized by the number of coincidences they require (complexity) and how exactly each must hold (robustness). When the agent's actions affect her data, every long-run action is a singular equilibrium, a best reply to a belief supported on the least complex and most robust narratives. Singular equilibrium refines Berk-Nash and self-confirming equilibrium by restricting overly complex or knife-edge off-path beliefs, and its strict uniform version characterizes uniformly stable actions. |
| Date: | 2026–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.11615 |
| By: | Kurt R. Brekke; Odd Rune Straume; Lars Sørgard |
| Abstract: | Book markets are characterised by common distribution through competing bookstores and vertical integration between publishers and bookstore chains, and in many countries publishers are allowed to set fixed book prices (FBP) in the bookstores. Under vertical separation, FBP can reduce retail prices when publishers have sufficiently strong bargaining power, as the elimination of double marginalisation outweighs the loss of intra-brand competition. We show that vertical integration fundamentally changes this trade-off. It eliminates double marginalisation inside the chain, thereby substantially reducing the scope for FBP to lower retail prices. But since FBP eliminates retail price differences on the same title, the allocative distortions are reduced when imposing FBP and consumer welfare and total welfare are no longer aligned. We find that, in the presence of vertical integration, the introduction of FBP is less likely to benefit consumers and more likely to benefit publishers than in an industry with vertical separation. |
| Keywords: | fixed book prices, vertical integration, double common agency |
| JEL: | D43 K21 L42 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_13042 |