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on Game Theory |
| By: | Mingyang Liu; Gabriele Farina; Asuman Ozdaglar |
| Abstract: | Nash equilibrium (NE) arises from selfish utility maximization, yet its social welfare can be arbitrarily far from optimal. Moreover, computing an NE is intractable in general. We study augmented game models in which players use budget-balanced internal transfers to improve incentives before play. We first introduce \emph{Self-Enforcing Transfer Equilibrium} (SETE), where players commit to nonnegative peer-to-peer transfers that are paid only if the recipient does not deviate from a prescribed strategy. For polymatrix games, we show that every stationary point of the social welfare function, in particular any socially optimal strategy profile, can be sustained as a SETE. This induces a Nash equilibrium in the agent normal form of the corresponding augmented game. We further propose a polynomial-time algorithm and a decentralized learning dynamic to compute such product-form equilibria. We then introduce \emph{Mediated Self-Enforcing Transfer Equilibrium} (M-SETE), where a mediator makes both the payment schedule and the prescribed strategies binding offers. This additional enforcement resolves the agent-normal-form limitation: an M-SETE is a Nash equilibrium of the augmented game itself, not merely of its agent normal form, and any socially optimal strategy profile can be supported as an M-SETE in any finite game while preserving budget balance. Thus, internal transfers improve welfare and computation while preserving independent play on the equilibrium path. When full sequential-game stability is required, binding mediation provides the corresponding implementation. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.20960 |
| By: | Delgado-Vega, Alvaro; Lee, Barton |
| Abstract: | Individuals often face a tradeoff between cooperating to expand a collective good (the “pie†) or competing to expand their share of it. We study this tradeoff as a dynamic public goods problem where the pie's size and its shares can only be gradually changed and contributions to the pie are irreversible. In the unique subgame perfect equilibrium, growth of pie occurs but halts at an inefficiently low level, at which point perpetual conflict over the shares ensues. Growth ultimately leads to a prisoner's dilemma stage game, but cooperation is unsustainable for any discount factor. We also explore the dynamics of growth and conflict and empirical relevance of our results. |
| Keywords: | zero-sum conflict; Growth; Dynamic games |
| JEL: | D72 D74 D78 P00 |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21010 |
| By: | Lahiri, Somdeb |
| Abstract: | We introduce multi-attribute bi-matrix games and show that a strategy profile is an equilibrium strategy profile with respect to a preference relation satisfying additivity with respect to the zero vector for an arbitrary finite set of such games having the same number of attributes if and only if it solves a bi-linear programming problem and the value of the objective function at this solution is zero. An immediate consequence of this result, is that if the outcome matrix for the row player is a convex combination of its outcome matrices in the finite collection and the outcome matrix for the column player is a (possibly different) convex combination of its outcome matrices in the finite collection, then a strategy profile is an equilibrium strategy profile for the game associated with pair of matrices if and only if it satisfies the same two conditions. |
| Keywords: | multi-attribute outcomes, preference relation, additivity with respect to the zero vector, equilibrium strategy profile, finite set of bi-matrix games, bi-linear programming problem, value of objective function, convex hull |
| JEL: | C61 C72 D81 |
| Date: | 2026–07–01 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:129920 |
| By: | Hattori, Keisuke |
| Abstract: | Leadership is usually understood as a means of influencing followers. Can it also discipline the leader herself? In an infinitely repeated team-production game where the leader moves first, sequential timing creates an enforcement asymmetry: a shirking leader is punished within the same period, whereas a follower can free ride on the leader's sunk effort and is punished only later. Full exposure removes the leader's dynamic incentive constraint and turns role assignment into a choice of whom to discipline. Holding the other dimension fixed, the less patient member should lead, whereas the more able member should follow, because ability relaxes the only remaining constraint. When high ability and low patience coincide in one person, task complementarity favors keeping that person as a productive follower, while substitutability favors assigning her to lead. This pure-exposure benchmark is sharply overturned once a leader's traits spill over to followers: above a single assimilation threshold, the conventional assignment of the high-ability, patient leader becomes superior on both output and enforcement grounds. Greater transparency of the leader's effort strengthens this disciplinary mechanism, and costly supervision can substitute for that discipline. The model implies that promoting the best worker can undermine team cooperation even when that worker would make a competent leader. |
| Keywords: | leadership, repeated games, team production, cooperation, promotion, supervision |
| JEL: | C72 C73 D23 J24 M51 M54 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:esprep:341546 |
| By: | Dirk Bergemann (Yale University); Kevin Breuer; Peter Cramton (Max Planck Institute for Research on Collective Goods and University of Maryland); Jack Hirsch (Harvard University); Yero S. Ndiaye (University of Cologne and Max Planck Institute for Behavioral Economics); Axel Ockenfels (Adenauer School of Government and Department of Economics, University of Cologne; Max Planck Institute for Behavioral Economics) |
| Abstract: | A soft-floor auction asks bidders to accept an opening price to participate in a second-price auction. If no bidder accepts, lower bids are considered using first-price rules. Soft floors are common despite being irrelevant with standard assumptions. When bidders regret losing, soft-floor auctions are more efficient and profitable than standard optimal auctions. Revenue increases as bidders are inclined to accept the opening price to compete in a regret-free second-price auction. Efficiency improves because a soft floor allows for a lower hard reserve, reducing the frequency of no sale. Theory and experiment confirm these motivations from practice. |
| Date: | 2026–04–02 |
| URL: | https://d.repec.org/n?u=RePEc:cwl:cwldpp:2512 |
| By: | Kováč, Eugen; Schmidt, Robert |
| Abstract: | The timing of actions is ubiquitous in economic decision-making. This research project aimed to improve our understanding of the timing of actions across various economic environments. We introduced a novel framework of strategic interaction in continuous time, where players choose both an action as well as its timing. Departing from much of the existing literature, which either imposes a certain sequence of actions or focuses on timing games with trivial action sets, our results offer new insights in the interaction of action choices and their timing. Apart from providing a greater level of realism, we developed new methods for the analysis of timing games. This addresses short-comings of existing frameworks, including finite action sets or difficulties with accommodating both impatience and sequential actions. Our results establish a close connection between continuous time games with infinite action sets and related games played on discrete time grids, generalizing well-known results of Si-mon and Stinchcombe (1989). Our methodology combines rigor with a wide range of applica-tions, including price competition games. In some cases, we find similar results as authors who used other setups (e.g., two-period settings) to endogenize the order of moves. In other cases, our results differ markedly. We find that the stronger firm often leads, but the possibility to deter entry may reverse the order of moves. Our methodology allows us to analyze games in continuous time that were previously not con-sidered as dynamic. We embedded electoral competition in our framework, thus opening up a novel aspect of strategic interaction also here. The order of candidates' policy announcements becomes an integral part of their strategic interaction. We find that candidates who differ in their valences or in their competence never choose to announce their platforms simultaneous-ly when they are free to decide when to make their choices. Imposing an order of moves can thus be restrictive. Using our methodology, we endogenized the order of candidates' moves, along with their policy platforms. We also analyzed patent races as timing games, focusing on the trade-off between keeping an innovation secret or revealing it to a rival. Such disclosures may be purely informational or involve patenting. In one study, we identify how private information about research progress influences disclosure strategies. We find that firms reveal breakthroughs primarily to discour-age rivals when research is difficult, but keep them secret when rapid innovation is expected. A second study evaluates how the choice between patenting and secrecy depends on the market structure. In markets with complementary products, firms benefit from patenting to facil-itate coordination and patent pools, whereas in markets with substitutes, secrecy serves as a strategic tool to prevent competition. Overall, our results indicate that firms have greater incen-tives to patent when they are impatient and when technological spillovers are low. Last but not least, we brought our continuous-time analysis to the lab and confirmed some of our theoretical predictions. We used state-of-the art experimental methods (e.g., the "freeze time protocol" of Calford and Oprea 2017), and expanded these to include non-trivial action choices of the players. Specifically, we analyzed a variant of Matching Pennies in continuous time with an endogenous order of players' action choices. |
| Abstract: | Das "Timing" von Aktionen ist allgegenwärtig in ökonomischen Entscheidungen. Dieses Pro-jekt trug zu unserem Verständnis der Interaktion von Aktionen und ihrem Timing in verschie-denen ökonomischen Umfeldern bei. Wir entwickelten einen neuen Modellrahmen strategi-scher Interaktion in stetiger Zeit, in dem Spieler ihre Aktionen und deren Timing wählen. Ab-weichend von einem Großteil der bestehenden Literatur, wo entweder eine bestimmte Reihen-folge der Spielzüge vorgegeben wird oder Spiele mit trivialen Aktionsmengen betrachtet wer-den, liefern unsere Ergebnisse neue Einblicke in die Interaktion von Aktionen und ihrem Ti-ming. Dies bietet ein höheres Maß an Realismus. Zudem entwickelten wir neue Methoden für Timing-Spiele, mit denen Schwächen anderer Ansätze überwunden werden, wie z.B. endliche Aktionsmengen oder Schwierigkeiten mit dem gleichzeitigen Einbetten von Ungeduld und sequenziellen Spielzügen. Unsere Ergebnisse zeigen eine enge Verbindung auf von Spielen in stetiger Zeit mit unendli-chen Aktionsmengen und verwandten Spielen in diskreter Zeit. Dazu verallgemeinerten wir Ergebnisse von Simon und Stinchcombe (1989). Unsere Methodik kombiniert Stringenz mit einer Vielzahl von Anwendungen. So haben wir Preiswettbewerbs-Spiele in stetiger Zeit ana-lysiert. In manchen Fällen finden wir ähnliche Ergebnisse wie Autoren, die andere Modellrah-men (z.B. 2-Periodenmodelle) verwenden, um die Reihenfolge der Spielzüge zu endogenisie-ren. In anderen Fällen unterscheiden sich unsere Ergebnisse stark. Während eine dominante Firma oft zuerst zieht, kann die Möglichkeit, den Markteintritt eines Konkurrenten zu verhin-dern, die Reihenfolge der Spielzüge umkehren. Unsere Methodik gestattet es, Spiele in stetiger Zeit zu analysieren, die zuvor nicht dynamisch betrachtet wurden. So haben wir Wahlwettbewerb in stetiger Zeit analysiert, und auch hier neue Aspekte strategischer Interaktion beleuchtet. Die Reihenfolge der Bekanntgabe von Wahlprogrammen wird zu einem integralen Bestandteil strategischer Interaktion. Kandidaten, die sich in ihren "Wertigkeiten" oder ihrer Kompetenz unterscheiden, geben ihre Programme niemals gleichzeitig bekannt, wenn sie über das Timing frei entscheiden können. Eine exoge-ne Reihenfolge von Spielzügen kann somit restriktiv sein. Mit unserer Methodik können so-wohl die Reihenfolge der Züge als auch die Aktionen endogenisiert werden. Darüber hinaus haben wir Patentrennen als Timing-Spiele analysiert. Dabei haben wir uns auf Zielkonflikte zwischen der Offenlegung von Innovationen und deren Geheimhaltung fokussiert. Solche Offenlegungen können rein informativen Charakter tragen oder über Patentierung er-folgen. In einer Studie analysieren wir, wie private Information über den Forschungsfortschritt die Offenlegungsstrategien beeinflussen kann. Firmen veröffentlichen ihre Durchbrüche vor allem, um Wettbewerber abzuschrecken, wenn die Forschung schwierig ist, und halten sie geheim, wenn schnelle Innovation zu erwarten ist. Eine zweite Studie untersucht, wie die Wahl zwischen Patentierung und Geheimhaltung von der Marktstruktur abhängt. In Märkten mit komplementären Produkten nutzen Firmen die Patentierung, um die Koordination und ei-nen Patentpool zu fördern. In Märkten mit Substituten dient Geheimhaltung als strategisches Instrument, um Wettbewerb zu verhindern. Insgesamt zeigen unsere Ergebnisse, dass größe-re Anreize zur Patentierung bestehen, wenn Firmen ungeduldig sind und bei geringen techno-logischen Spillover-Effekten. Schließlich haben wir Spiele in stetiger Zeit im Labor analysiert und einige unserer zentralen theoretischen Vorhersagen bestätigt. Wir verwendeten moderne Methoden (z.B. das "freeze time protocol" von Calford und Oprea 2017), und erweiterten diese um nicht-triviale Aktionen der Spieler. Dabei analysierten wir eine Variante von Matching Pennies in stetiger Zeit mit einer endogenen Reihenfolge der Spielzüge. |
| Keywords: | continuous-time game, timing, second-mover advantage, electoral competition, price competition, R&D, patent race, information revelation, matching pennies, coordination |
| JEL: | C72 C73 D72 D43 O30 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:esrepo:341725 |
| By: | Corneo, Giacomo |
| Abstract: | NATO enlargement and Russian annexation of Crimea marked crucial turning points. According to one narrative, the Russian occupation was part of a plan to re-establish dominion over Eastern Europe. According to a rival view, it was an attempt to counter a U.S. plan to subjugate Russia. I scrutinize the logical requirements of those narratives in a multi-stage game of incomplete information that produces equilibrium play such that first NATO is enlarged and then Russia attacks Ukraine. The two competing narratives correspond to two different separating equilibria. Conditions for their existence inform about the consistency and plausibility of the associated narratives. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21183 |
| By: | Hattori, Keisuke |
| Abstract: | Teamwork can either cure or create procrastination. We trace this to guilt: present-biased members who break a joint plan feel guilt that is largest when one shirks alone and smallest when failure is shared-an ordering we derive from a single monotonicity of second-order beliefs rather than impose. The resulting coordination game traps the team in collective procrastination only under symmetry. Two kinds of member break the symmetry and lead the team out, both by acting as a self-starter-one who acts whatever the partner does. The first has the disposition by type: enough follow-through to act unconditionally, she does exactly what a committed visible leader would. The second acquires it by foresight: a sophisticated member who anticipates her own delay pays to commit, making herself a self-starter where her type alone would not. A self-starter is thus an endogenous leader, supplied by heterogeneity when present bias differs across members and by self-commitment when it does not. |
| Keywords: | procrastination, present bias, guilt aversion, teams, coordination, leadership |
| JEL: | C72 D23 D91 M54 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:esprep:341671 |
| By: | Zenou, Yves |
| Abstract: | This paper reviews the theoretical and empirical foundations of peer and network effects, aiming to bridge insights from both literatures. We first examine the main identification challenges in linear-in-means models — reflection, correlated effects, and sorting — and show how introducing explicit network structures can help address them. We also review reduced-form strategies based on within-school cohort composition, exposure to peers’ shocks, random assignment, and exogenous variation in network links. The analysis then develops the microfoundations of peer effects through linear–quadratic network games, linking equilibrium behavior to network centrality and highlighting the role of key players. Using this framework, we discuss how structural models of network formation and individual effort choices can resolve endogeneity concerns. The paper concludes with recent advances on non-linear and multiplex interactions, where individuals respond to specific peers and operate across multiple, interdependent layers. |
| JEL: | A14 C57 D85 Z13 |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20814 |
| By: | Emons, Winand; Lenhard, Severin; Parisi, Francesco |
| Abstract: | We study settlement bargaining under three alternative fee-shifting rules: the American Rule, the English Rule, and an optional feeshifting regime in which the defendant chooses whether the case will proceed under the American or the English Rule. The defendant knows whether his conduct gives rise to liability while the plaintiff only has a noisy signal. This two-sided asymmetric information creates scope for strategic misrepresentation: defendants who face liability may try to pass as if they do not, while plaintiffs with weak evidence may act as if they have a strong case. When litigation costs are similar for both parties, optional fee-shifting reduces litigation rates more effectively than either the American or the English Rule alone. |
| JEL: | D41 D82 |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20847 |
| By: | Zenou, Yves |
| Abstract: | This paper examines the behavior of Katz–Bonacich centrality and key-player intercentrality in linear–quadratic network games when spillovers are large. This question is both important and empirically relevant, as it greatly simplifies the empirical testing of peer-effect models. We show that Katz–Bonacich centrality converges (up to scale) to the Perron eigenvector, while intercentrality diverges and loses all discriminatory power across nodes. Consequently, designing key-player policies becomes problematic: key-player rankings collapse, and no agent is more important than another when spillovers are sufficiently large. |
| JEL: | D85 C72 D62 |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20856 |
| By: | Dirk Bergemann (Yale University); Soheil Ghili (Yale University); Xinyang Hu (Yale University); Chuanhao Li (Yale University); Zhuoran Yang (Yale University) |
| Abstract: | Bilateral bargaining under incomplete information provides a controlled testbed for evaluating large language model (LLM) agent capabilities. Bilateral trade demands individual rationality, strategic surplus maximization, and cooperation to realize gains from trade. We develop a structured bargaining environment in which LLMs negotiate via tool calls within an event-driven simulator, separating binding offers from natural-language messages to enable automated evaluation. The environment serves two purposes: as a benchmark for frontier models and as a training environment for open-weight models via reinforcement learning. In benchmark experiments, a round-robin tournament among five frontier models (15, 000 negotiations) reveals that effective strategies implement price discrimination through sequential offers. Aggressive anchoring, calibrated concession, and temporal patience are associated with both the highest surplus share and the highest deal rate. Accommodating strategies that concede quickly disable price discrimination in the buyer role, yielding the lowest surplus capture and deal completion. Strategically competent models scale their behavior proportionally to item value, maintaining consistent performance across price tiers; weaker models perform well only when wide zones of possible agreement compensate for suboptimal strategies. In training experiments, we fine-tune Qwen3 (8B, 14B) via supervised fine-tuning (SFT) followed by Group Relative Policy Optimization (GRPO) against a fixed frontier opponent. The two stages optimize competing objectives: SFT approximately doubles surplus share but reduces deal rates, while RL recovers deal rates but erodes surplus gainsÑa tension traceable to the reward structure. SFT also compresses surplus variation across price tiers, and this compression generalizes to opponents unseen during training, suggesting that behavioral cloning instills proportional strategies rather than memorized price points. |
| Date: | 2026–04–01 |
| URL: | https://d.repec.org/n?u=RePEc:cwl:cwldpp:2514 |
| By: | Ashfaq, Marium; Toxvaerd, Flavio; Wei, Yi |
| Abstract: | We study collusive agreements in an infinite-horizon model in which firms invest in inventories of intermediate goods and compete in quantities of final goods. Stocks of inventories act as capacity constraints at the time of production, but can be replenished for future use through investment. Input stocks simultaneously impact firms’ ability to deviate from collusive agreements and their ability to punish such deviations and therefore have ambiguous effects on the sustainability of collusion. We characterize subgame perfect equilibria in grim trigger strategies in which firms potentially hold asymmetric excess inventories on the collusive path. We show that the sustainability of collusive agreements is non-monotone in inventory stocks. While holding excess capacity is costly and unproductive, the practice can improve firms’ ability to sustain anticompetitive agreements. |
| Keywords: | Collusion |
| JEL: | L13 L41 D25 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21232 |
| By: | Hassan Benchekroun (McGill University); Simon Elgersma (Rijksuniversiteit Groningen); Gerard van der Meijden (Vrije Universiteit Amsterdam); Cees Withagen (Vrije Universiteit Amsterdam) |
| Abstract: | We study how market power, leadership, and commitment affect oil extraction and climate outcomes in a cartel-fringe model with renewables and a backstop technology. Comparing competitive, Nash-Cournot, open-loop, and feedback von Stackelberg equilibria, we show that market power and leadership can either increase or reduce climate damages, depending on commitment, cost and emission factor heterogeneity, and relative resource stocks. In a benchmark with a social cost of carbon of 250 USD/tC, market power without leadership lowers climate damages by 3.9 trillion USD relative to perfect competition. With leadership, these gains fall to 3.1 trillion USD when the leader can commit and to 2.6 trillion USD without commitment. Small changes in resource stocks, cost parameters, or climate policy can trigger regime shifts with discontinuous welfare and climate effects. Carbon taxes and backstop subsidies can remove sequencing distortions but may weaken the conservation effect of market power. When the cartel cannot commit, the second-best carbon tax lies well below the Pigouvian level yet often delivers near-first-best welfare. Finally, we show that market power and leadership may reduce cartel profits. |
| Keywords: | cartel-fringe, climate policy, renewables, dynamic game, von Stackelberg equilibrium |
| JEL: | C72 Q30 Q38 Q42 |
| Date: | 2026–06–11 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20260030 |
| By: | Behnaz Minooei Fard |
| Abstract: | Critical mineral markets over the past decade have exhibited distinctive patterns of nonlinear price adjustment, discontinuous supply responses, and regime dependent behavior. This paper develops a dynamic game theoretical model of strategic extraction in critical mineral markets under a nonlinear supply function. Replacing the linear market reactions standard in the exhaustible resource literature with a partially inverse supply function generates three distinct price-quantity equilibria. Each equilibrium corresponds to a qualitatively different market regime as a constrained low-extraction/high-price state reflecting Chinese supply dominance, an intermediate state of partial Rest of the World (ROW) entry, and a high-extraction/low-price state of full supply diversification. The model is solved using Model Predictive Control (MPC), which parameterizes the degree of strategic foresight. Three scenarios are simulated to assess the effects of policy interventions on extraction dynamics, profitability, and resource depletion. The results show that reducing ROW marginal costs is necessary but not by itself sufficient for supply diversification. Moreover, the results reveal that cost subsidies and support payments have limited impact on depletion speed unless accompanied by a change in market behavior from short-termism to extended decision horizons. |
| Keywords: | Critical minerals, game theory, nonlinear supply function, multiple equilibria, Model Predictive Control, export controls, price jumps, strategic extraction |
| JEL: | C61 C7 Q3 |
| Date: | 2026–06–19 |
| URL: | https://d.repec.org/n?u=RePEc:mpi:wpaper:tax-mpg-rps-2026-08 |
| By: | Jimenez Martinez, Antonio; Melguizo Lopez, Isabel |
| Abstract: | We investigate evidence acquisition and disclosure by a communicator who cares about the distribution of the opinions of an audience. Uncertainty about whether evidence can be obtained allows for selective disclosure. We consider two alternativemotivations for the communicator: (i) to shift the average opinion towards her preferred one and (ii) to raise the dispersion of opinions. Under general structures for evidence provision, we characterize the unique equilibrium disclosure strategy for both motivations. The communicator’s return in equilibrium is linear in a measure of the extent to which the evidence-provision structure could favor her preferred state conditional on a given obtained piece of evidence. In this context, we analyze how certain features of the evidence-provision structure and of the distribution of initial opinions of the audience influence the communicator’s return. The relation between thewelfare of the audience and the acquisition effort depends critically on which of the two motivations yields higher returns to the communicator, an insight useful for policy recommendations. Minimum limits on evidence acquisition benefit audiences only when communicators seek to raise the dispersion of opinions, not when they seek to shift the average opinion. |
| Keywords: | Distributions of Opinions; Evidence Acquisition; Strategic Disclosure; Sanitization Strategies; Hazard Rates |
| JEL: | C72 D72 D83 D84 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:128334 |
| By: | John Cremin (Aix Marseille Univ, CNRS, AMSE, Marseille, France) |
| Abstract: | An agent, Sleeping Beauty, in a game with self-locating uncertainty (i.e. one play of the game visits the same information set multiple times, as in the paradox of the absentminded driver) must select a behavioural strategy that is self-ratifying: a best-response to the belief that her other instances do likewise. When there are multiple such fixed points, the standard treatment of Aumann et al. (1997) assumes that all instances of the agent can simply coordinate. I drop this assumption (supposing that Sleeping Beauty 'lose her magic psychic powers' ), and study said agent iteratively reasoning her way to an equilibrium selection instead. Which strategy other instances select can be seen as ambiguous, so I model Beauty's choice via a response function that encodes her response to ambiguity, and a procedure that describes in what manner she iterates the application of this response function. I consider two response functions, 'Bayesian' and EU-maximin, and two procedures, replacement and accumulation, and characterise in which cases the iterative reasoning converges. For either response function, accumulation always converges, but replacement does so if and only if there are no cycles of length weakly greater than two on a particular finite functional digraph I call the support digraph. |
| Keywords: | Sleeping Beauty Problem; Imperfect Recall; Self-Locating Uncertainty; Decision Instability; Ambiguity; Absent-Minded Driver |
| JEL: | C72 C73 D81 D83 |
| Date: | 2026–06–25 |
| URL: | https://d.repec.org/n?u=RePEc:aim:wpaimx:2620 |
| By: | Masaaki Fujii (Graduate School of Economics, The University of Tokyo) |
| Abstract: | This work solves the equilibrium price formation problem for the risky stock by combining mean-field game theory with the binomial tree framework, adapting the classic approach of Cox, Ross & Rubinstein. For agents with exponential and recursive utilities of exponential-type, we prove the existence of a unique mean-field market-clearing equilibrium and derive an explicit analytic formula for equilibrium transition probabilities of the stock price on the binomial lattice. The agents face stochastic terminal liabilities and incremental endowments that depend on unhedgeable common and idiosyncratic factors, in addition to the stock price path. We also incorporate an external order ow. Furthermore, the analytic tractability of the proposed approach allows us to extend the framework in two important directions: First, we incorporate multi-population heterogeneity, allowing agents to differ in functional forms for their liabilities, endowments, and risk coefficients. Second, we relax the rational expectations hypothesis by modeling agents operating under subjective probability measures which induce stochastically biased views on the stock transition probabilities. Our numerical examples illustrate the qualitative effects of these components on the equilibrium price distribution. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:cfi:fseres:cf630 |
| By: | Achim, Peter; Strausz, Roland |
| Abstract: | In modern information markets, buyers routinely combine signals from multiple sellers. We develop a model of "portfolio competition" to analyze this distinctive feature. We show that the combinability of information overturns standard oligopoly intuition. Unlike traditional markets, competitive pressure does not necessarily protect buyers: when signals are complements, sellers can leverage the buyer's desire for the joint portfolio to extract the full social surplus, regardless of the number of competitors. We characterize the precise conditions for rent extraction, which reduce to a simple geometric test for symmetric sellers. Furthermore, we find that the canonical logic of market entry fails. Entry is never socially excessive because efficient portfolio choices eliminate business-stealing effects. Paradoxically, entry can reduce competitive pressure: when entrants provide strong complementarities, they shift the buyer's threat point, allowing all sellers to extract higher rents. |
| Keywords: | Complementarity |
| JEL: | L13 D43 D83 |
| Date: | 2025–11 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20867 |
| By: | Ennio Bilancini; Leonardo Boncinelli; Pablo Marcos-Prieto; Chiara Nardi |
| Abstract: | Using a one-shot Hawk–Dove game, we experimentally investigate the effect of different cognitive modes—intuitive (induced by Time Pressure), deliberative (by Time Delay), and motivated deliberative (by Time Delay combined with a written motivation)—on the propensity to behave hostilely (i.e., to play Hawk). We also examine whether cognitive modes affect responsiveness to payoff incentives by varying the harshness of conflict. Our results show that intuition significantly increases the likelihood of hostile behavior, while motivated deliberation reduces it. The harshness of conflict does not significantly affect behavior, and we find no evidence that its effect differs across cognitive manipulations. However, when restricting attention to subjects in the pooled delay conditions, the effect of harshness becomes statistically significant, indicating that responsiveness to payoff incentives may require deliberation. Consistently, we find that deliberation increases the likelihood that subjects best respond to their own beliefs |
| JEL: | C72 C90 D91 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:dis:wpaper:dis2603 |
| By: | Kai A. Konrad |
| Abstract: | Why do strong players allow weak players to join their team, even though weak players are notorious for free riding? This paper shows that the dynamic structure of a tug-of-war is suitable for mobilizing efforts by weak players and making the team to become stronger and to succeed. The strategic role of weak players emerges if the dynamics for the team develop unfavorably for the team. If the team falls behind, a discouragement effect sets in for the strong player. The player is inclined to throw the towel. This alarms the weak player. The player hoped to be able to free-ride and gain an expected windfall payoff. This payoff is lost if the strong player gives up. At that point the weak player actively seeks to motivate the strong player to perform at its best. |
| Keywords: | tug-of-war, dynamic contest, teams, team contests, free-riding, discouragement effect, asymmetric teams |
| JEL: | D72 D74 H41 |
| Date: | 2026–06–04 |
| URL: | https://d.repec.org/n?u=RePEc:mpi:wpaper:tax-mpg-rps-2026-07 |
| By: | Jeong, Byeong-hyeon; Pycia, Marek |
| Abstract: | We show that first-price auctions can maximize a wide variety of objectives, including revenue, welfare, bidder surplus, and equality, while second-price (or ascending) auctions do not maximize revenue except in Myerson’s regular case. This stark contrast between canonical auction pricing rules qualifies the celebrated revenue equivalence. Furthermore, the optimality of first-price auctions does not hinge on any distributional assumptions, which enables us to analyze problems that are beyond the scope of Myersonian mechanism design. The resulting optimal auctions might employ not only reserve prices but also bid caps and other exclusions in the space of allowed bids. We also provide tools for the optimal design of first-price auctions and establish conditions for equilibrium existence and uniqueness. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21116 |
| By: | Filipp Ushchev; Guntram Wolff |
| Abstract: | We develop a new model for green investments which blends features of the portfolio choicemodel and the non-cooperative private provision of pubic goods game. Agents differ in timepreference and in economic size. Our model shows that (a) long-term investors tend to have alarger share of their portfolio in green bonds, (b) larger agents/economies tend to invest morein climate mitigation, and (c) more heterogeneity among the types of agent (both in termsof time preference as well as economic size, looking beyond thresholds) increases aggregateclimate investments. We provide empirical evidence for the first two effects. Our model hassignificant implications for climate policy: it points to the importance of long-term investors inthe green transition and to the importance of larger groups of countries agreeing on cooperativeframeworks, for example, in the form of climate clubs, to increase overall investments in climatemitigation. |
| Keywords: | Public goods game; portfolio choice model; green investment; greenium |
| JEL: | H41 C72 Q54 Q58 G11 |
| Date: | 2026–07–08 |
| URL: | https://d.repec.org/n?u=RePEc:eca:wpaper:2013/410034 |
| By: | Gersbach, Hans |
| Abstract: | This paper introduces Propose or Vote (PoV), a democratic procedure for collective decision-making and elections that does not rely on a central mechanism designer. In the first stage, members of a polity choose whether to become proposal-makers or to participate only as voters. In the second stage, voters decide by majority voting over the set of submitted proposals. With appropriately chosen default points, PoV implements the Condorcet winner in a single round of voting whenever one exists. We show that this implementation is globally unique when the number of members is odd; for an even number of members, uniqueness can be restored by adding an artificial agent. PoV can also be applied to elections, where agents decide whether to stand as candidates or vote over the resulting candidate set. |
| Keywords: | proposal-making; Democracy; Majority voting |
| JEL: | C72 D70 D72 |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:21026 |