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on Game Theory |
| By: | Yosuke Hashidate |
| Abstract: | We study a mechanism of cooperation in the Prisoner's Dilemma (PD). Incorporating social preferences as efficiency concerns into the PD game, we study how altruism translates into cooperation. Under complete information, cooperation requires the opponent's altruism to clear a threshold. We then introduce a subjective extension of Bayesian Nash equilibrium that relaxes the Common Prior Assumption, letting players hold heterogeneous, potentially misspecified beliefs about each other's altruistic type. Cooperation then depends on beliefs about altruism rather than altruism itself, and can be sustained even when opponents are, on average, only weakly altruistic. When fear of exploitation dominates the temptation to defect, beliefs about the opponent's cooperation become strategic complements, so a cooperative and an uncooperative equilibrium can coexist under identical payoffs and an identical, correctly specified prior. Using multiplier preferences, we then study how robust this belief-driven cooperation is to model misspecification. Cooperation is fragile: it survives only above a threshold level of confidence in one's own belief, and can unravel even when the belief itself correctly supports cooperation. As a formal extension, the same robust-control apparatus, applied to a player's action choice, nests Nash equilibrium, Bayesian Nash equilibrium, and logit Quantal Response Equilibrium as limiting cases. Cooperation depends less on how altruistic agents are than on what they believe about each other, and how confident they are that this belief is right. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.11374 |
| By: | Chai, Ziyi; Dietzenbacher, Bas (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory) |
| Abstract: | This paper studies classes of two-bound core games with communication restrictions modeled by an undirected graph. We focus on unanimity games, bankruptcy games, 1-convex games, big boss games, clan games, compromise stable games, one-bound core games, and the entire class of two-bound core games. For each of these classes, we characterize all communication graphs that guarantee that the graph-restricted game belongs to the same class as the original two-bound core game. |
| Keywords: | two-bound core games, communication situations, graph-restricted games |
| JEL: | C71 |
| Date: | 2026–09–10 |
| URL: | https://d.repec.org/n?u=RePEc:unm:umagsb:2026008 |
| By: | Igal Milchtaich |
| Abstract: | Agnostic sequential equilibrium (ASE) is a refinement of sequential equilibrium that does not force on the players a single, arbitrary belief system. In addition, whereas sequential equilibrium assumes the players' beliefs to be fully consistent (a notion that is based on perturbations of strategies), ASE employs a novel, simpler and local concept of strong consistency between strategy profiles and off-equilibrium beliefs, which is applicable to a large class of dynamic games, including games with a continuum of actions. In the last respect, the new solution concept is similar to perfect Bayesian equilibrium. It is shown that a strategy profile in an imperfect-information extensive-form game with perfect recall is an ASE precisely when it is a sequential equilibrium with every fully consistent belief system. ASE is generalized by the set-valued solution concept of agnostic sequential polyequilibrium, which allows leaving the players' actions in some information sets partially or completely unspecified. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.25731 |
| By: | Igal Milchtaich |
| Abstract: | In a number of large, important families of finite games, not only is the set of pure-strategy Nash equilibria nonempty but it is also reachable from any initial strategy profile by some sequence of myopic single-player moves to a better or best-reply strategy. This weak acyclicity property is weaker than acyclicity of the game, which requires every such sequence to reach an equilibrium. For example, all perfect-information extensive-form games are weakly acyclic, but they are generally not acyclic as even sequences of best-improvement steps may cycle. Weak acyclicity is equivalent to acyclicity of some priority rule, which is a rule that allows only some improvement moves. It is also equivalent to the existence of a weak potential, which unlike a potential increases along some rather than every sequence as above. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.25966 |
| By: | Philipp Peitler |
| Abstract: | The von Neumann-Morgenstern axioms are uncontroversial desiderata for individual decision-making. We say that a bargaining solution is rational if it can be interpreted as the most preferred alternatives under these axioms. Yet, neither the Nash nor the Kalai-Smorodinsky bargaining solution is rational in this sense. We formalize two consequences of rationality, namely that one can neither be strictly better off nor strictly worse off from randomizing over different actions. These two axioms, together with other standard axioms, characterize the relative utilitarian bargaining solution. We then implement this bargaining solution in sub-game perfect equilibrium. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.19932 |
| By: | Tongseok Lim |
| Abstract: | The random-order interpretation of the Shapley value specifies both a terminal allocation and a payment path: when a player enters, she receives her marginal contribution at that moment. We ask whether players would voluntarily follow this path. A player may prefer to wait if her marginal contribution is expected to rise as the coalition grows. This creates a tension in convex games. The Shapley allocation belongs to the core, but, except in additive games, the associated marginal-contribution payment path does not support voluntary entry. We separate these two objects by introducing payment flows that divide the surplus created at each coalition transition. Every efficient allocation can be implemented by a local, budget-balanced voluntary flow when signed payments are available. We select a canonical implementation by minimizing the distance from the Shapley flow, and show that the problem simplifies sharply in symmetric cardinality games. We then consider equal residual sharing, under which any transition surplus not paid to the entrant is divided equally among incumbents. The closest voluntary flow in this class selects an allocation endogenously. With two player types, the selected allocation is a game-dependent affine combination of the Shapley and equal-division allocations. Examples show both the role of payment restrictions and a possible conflict between voluntary entry and coalitional stability. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.20421 |
| By: | Jeremy Bertomeu; Edwige Cheynel; Peicong Hu |
| Abstract: | We study voluntary disclosure when investors observe firm reports through noisy information intermediaries such as auditors, analysts, rating agencies, or data providers. Any processing noise overturns the standard prediction of a unique partial-disclosure equilibrium. With low disclosure costs, the model unravels to full disclosure despite positive costs. With higher costs, the game admits two threshold equilibria featuring different disclosure probabilities. We characterize how the cost threshold for unraveling and the equilibrium set respond to changes in noise and fundamental uncertainty. In settings with high disclosure, both uncertainty and processing noise reduce disclosure, while higher certification costs can counterintuitively increase it. Endogenizing disclosure costs as optimal fees shows how profit-maximizing intermediaries select among equilibria, potentially generating a high-fee, high-disclosure regime. Extensions with bounded support, uncertain information endowment, endogenous noise, and competing information sources apply the insights to general information environments. The results caution against interpreting greater frictions as necessarily reducing disclosure. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.07898 |
| By: | Sylvain Béal (Université Marie et Louis Pasteur, CRESE UR3190, F-25000 Besançon, France); Emmanuelle Lebeuf (Université Marie et Louis Pasteur, F-25000 Besançon, France); Kevin Techer (Université Marie et Louis Pasteur, CRESE UR3190, F-25000 Besançon, France) |
| Abstract: | We introduce a new allocation rule for network games that combines a local component and a global component. The local component depends only on the links incident to each player, whereas the global component allocates a surplus equally among the members of each connected component. We characterize this allocation rule by three classical axioms together with a new axiom, Fairness under Neighborhood Restriction, which requires that two adjacent players experience the same payoff variation when the network is restricted to their local neighborhoods, that is, to the sets of links incident to each player. We also examine an alternative allocation rule that differs only in its global component, distributing the surplus within each connected component in proportion to players’ degrees in the network. |
| Keywords: | Network games, Fairness under Neighborhood Restriction, Neighborhood Equal Surplus Division, axiomatic characterization |
| JEL: | C71 |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:crb:wpaper:2026-08 |
| By: | Pierre Bernhard (MACBES Team, INRIA Center of Université Côte d’Azur, Sophia Antipolis, France); Marc Deschamps (Université Marie et Louis Pasteur, CRESE UR3190, F-25000 Besançon, France); Alain Bensoussan (University of Texas, Naveen Jindal School of Management, USA.) |
| Abstract: | Low Earth orbits (between 100 and 2, 000 km above sea level) are currently the most congested regions of outer space. This congestion stems also from the presence of space debris, which, once it reaches a certain level, could trigger a chain reaction that would physically prevent the use of these orbits (i.e., the Kessler syndrome). The actual and planned deployment of numerous satellite mega-constellations significantly exacerbates this problem. In addition to minimizing the creation of new space debris, it has become necessary to remove some of the existing debris. To address the issue of funding these removals, we propose the creation of an international tax administered by an international agency. Given the current and future presence of a large number of mega-constellations, we propose a mean-field game model. We then compare two possible taxation systems: one proportional and the other one progressive. Within the framework of this model, we conclude that it is possible to finance the removal of the most dangerous space debris and thereby ensure a sustainable outer space without stopping the contributions and potential of the New Space economy. |
| Keywords: | Mean-field game, linear-quadratic, outer space, space debris, mega constellations |
| JEL: | C72 C61 H23 H32 |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:crb:wpaper:2026-06 |
| By: | Elliot Lipnowski; Doron Ravid |
| Abstract: | Limited attention forces organizations to decide not only how much to discuss, but also which issues merit discussion. We study strategic communication about a multidimensional decision when a receiver can respond only along a few endogenously chosen issues. Players agree on the ideal action but prioritize different errors. In equilibrium, communicated and omitted issues must be statistically unrelated and separable according to the sender's preferences. Thus, the sender's priorities determine the agenda; the receiver's do not. Synchronized priorities raise the receiver's best equilibrium payoff but lower his worst, so he may prefer a less synchronized sender. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.00380 |
| By: | Yackolley Amoussou-Guenou (Université Paris-Panthéon-Assas); Maarten R.C. van Oordt (Vrije Universiteit Amsterdam) |
| Abstract: | Censorship resistance is often considered to be a core attribute of distributed ledgers. Censorship resistance refers to the inability to selectively exclude technically valid but undesirable transactions from the blockchain. We examine blockchain censorship in a game-theoretic framework that allows for both primary and secondary censorship. The analysis identifies scenarios in which both inclusion and censorship equilibria exist. Once an equilibrium with strategic secondary censorship is implemented, it may be hard to revert to inclusion: Censorship equilibria are perfectly coalition-proof if the negative impact of an undesirable transaction on block producers is sufficiently large. These results highlight the growing importance of research into methods shaping censorship resistance at the technical layer. |
| Keywords: | Blockchain, Consensus, Cryptocurrency, Distributed ledger, Game theory |
| JEL: | C72 G2 L86 |
| Date: | 2026–09–13 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20260069 |
| By: | Péter Bayer; Mánuel László Mágó |
| Abstract: | We introduce participation uncertainty to the theory of cooperative TU- games. Under participation uncertainty, each coalition's effective value is an expected value taken over the (full) value of its subsets. We identify 'constant-marginal' participation as a key property for various economic problems to be well-behaved. This class of uncertainty environments is closed for mixing and composition. Under this property, solution concepts are easily calculated, two-sided markets clear and are insurable, and voting power under uncertain participation can be characterized and efficiently computed. |
| Keywords: | cooperative games, matching market, overselling, participation uncertainty, voting power |
| JEL: | C71 C72 D51 D72 D81 |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:bge:wpaper:1590 |
| By: | Gerrit Meyerheim |
| Abstract: | Observed action returns guide decisions: use less of the lower-return action. I show when that rule fails in adversarial environments. A zero-sum envelope validates comparisons. When actions move a persistent defense state, an interior stationary equilibrium equates the net current-return gap to the negative discounted value of the induced path. Observed and decision-relevant return gaps coincide when reallocation has no separate payoff effect. Otherwise, the observed gap must be adjusted. This creates a use-up/return-down inversion: strategic leverage can raise use while lowering the gross return gap. Stronger preparedness incentives and lower adjustment costs preserve this inversion with a forward-looking defender on an open set. A curvature-feedback condition characterizes their signs along an affine-equilibrium branch. A two-state patent model shows lower-return patents can remain privately valuable through diversion and blocking yet be socially overused. Net return gaps identify the continuation wedge, not its decomposition into state values, persistence, and action leverage. |
| Keywords: | dynamic games, post-defense returns, strategic decoys, strategic state dependence |
| JEL: | C73 D21 D43 O34 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12962 |
| By: | Endre Cs\'oka |
| Abstract: | We study the repeated allocation of a single indivisible resource among $n$ strategic players. Each player $i$ has a privately known value distribution $D_i$, and values are drawn independently across players and periods. The goal is to find fair and efficient mechanisms. We apply the repeated first-price auction with equal initial endowments of virtual money. We show that each player can asymptotically secure the same fair-floor guarantee $f(D_i)$ as in Cs\'oka 2026; consequently, the mechanism is $1.283$-optimal. This provides a simpler and more robust alternative mechanism for this special case and may also help derive sharper upper bounds on the price of anarchy. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.05499 |
| By: | Potarca, Matthias |
| Abstract: | The decline of auction-format sales in favor of posted prices on digital marketplaces is commonly attributed to behavioral biases or secular changes in the market environment. This paper examines the latter by jointly modeling two forms of buyer opportunity cost within a standard symmetric independent private values framework: an entry cost sunk upon auction participation, and a mechanism-independent outside option reflecting the surplus a buyer can obtain from a close substitute at a known market price. A seller chooses between a second-price auction and a posted price; potential buyers decide whether to participate after observing their private valuations. The outside option endogenously partitions buyers into low-value types, who bid their full valuation, and high-value types, whose bids are capped at the outside option price, giving rise to qualitatively distinct entry regimes that the seller anticipates and actively shapes. Pressure from either channel strictly erodes the auction's advantage, but the seller's response to the two is asymmetric. The model yields testable implications that qualitatively align well with observed patterns and place weight on the outside option channel as a driver for the shift towards posted prices. |
| Keywords: | auctions, posted prices, entry costs, outside options, mechanism design, e-commerce |
| JEL: | D44 D47 D82 L81 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:kitwps:343538 |
| By: | Buchholz, Wolfgang; Hattori, Keisuke |
| Abstract: | This paper studies how an outsider can strategically induce a merger between rival firms. The outsider's anticipated post-merger output expansion lets it capture part of the gains from the merger but can also make the merger unprofitable for the insiders. We show that the outsider can make the merger profitable by committing in advance to a weaker competitive position, while the softer competition following the merger can more than compensate it for its self-imposed handicap. A general framework identifies conditions under which the outsider optimally chooses the minimum merger-inducing handicap. Three Cournot models show that voluntary capacity reduction, withdrawal from a profitable market, and a credible increase in marginal cost can each strictly raise the outsider's profit above the no-handicap, no-merger benchmark. Merger synergies can also benefit the outsider by reducing the handicap required to induce the merger. The analysis highlights the need to account for endogenous outsider constraints in ex ante assessments of mergers. |
| Keywords: | horizontal mergers, strategic commitment, self-handicapping, merger paradox, Cournot competition |
| JEL: | D43 L13 L41 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:esprep:343613 |
| By: | Ganglmair, Bernhard; Holcomb, Alex |
| Abstract: | Partners in R&D alliances and joint ventures are rarely symmetric, yet whether asymmetry helps or hurts collaboration is not fully understood. We study how asymmetry in competitors' information endowments affects collaborative knowledge exchange. A model of word-of-mouth communication predicts a clean separation: Initiating the knowledge exchange requires that the informational advantage sac rificed be sufficiently small, while the continuation incentive is independent of the initial endowment (and asymmetry). In a laboratory experiment, we confirm the model's comparative-statics predictions and establish three results. First, initiation rates decline as initial asymmetry increases, holding the better-endowed partner's initial endowment constant. Second, conditional on initiation, the initial asymme try does not predict defection later in collaboration. Third, extreme asymmetry reduces match length and joint surplus because initiation fails, not because continu ation breaks down. The initiation-continuation separation implies that governance mechanisms targeting the formation margin (such as pilot projects, phased disclo sure agreements, or credible commitments to reciprocate) can expand the range of asymmetric partnerships that succeed, while continuation requires no special intervention. |
| Keywords: | asymmetric partnerships, cooperation, experimental economics, information sharing, joint ventures, knowledge diffusion, open innovation, R&D collaboration, strategic alliances |
| JEL: | C92 D83 L24 M21 O31 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:zewdip:343045 |
| By: | Alistair Barton |
| Abstract: | I propose a novel, tractable model of pro-social norms in large communities with slightly altruistic agents. Agents participate in the norm to influence others to participate in the norm, influencing further agents. A continuum of equilibria sustain the pro-social norm, varying in the distribution of how much agents are influenced by their observations. If agents' effective altruism $\alpha$ is larger than their impatience $1-\delta$, equilibria exist that are robust to a population of bad actors. Greater strategic homogeneity increases the robustness of the norm. Robustness is not improved by increasing the number of observers of each action beyond 1. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.06151 |
| By: | Dan M. Bernhardt; Laurent Bouton; Stefan Krasa; Francesco Squintani |
| Abstract: | We propose a model of costly voting in a canonical spatial setting that reconciles key empirical features of electoral turnout. We integrate citizens with prosocial voting motives who realize higher payoffs from voting when (i) they expect more fellow supporters to vote, (ii) such votes collectively matter more for winning probabilities, and (iii) they care more about which candidate wins. We establish existence of Nash equilibria satisfying an additional condition that ensures equilibria correspond to those in a finite setting with many voters. We derive how electoral primitives—e.g., voter ideology, voting costs, elite polarization, expected closeness—affect outcomes such as turnout, turnout rates, and winning margins. We relate the predictions to empirical findings both from existing studies and our original data work. With all three prosocial motive components, our model reconciles the empirical regularities qualitatively and quantitatively; while existing models fail on multiple dimensions. |
| JEL: | D7 P0 |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35723 |
| By: | Alessandro Lizzeri; Yichuan Lou; Jacopo Perego |
| Abstract: | We compare verifiable and unverifiable communication in a sender–receiver setting with partially aligned preferences, where the sender knows more than what her evidence can prove. We identify a credibility–flexibility tradeoff: tying the sender’s claims to her evidence enhances her credibility, but limits how flexibly she can communicate when her evidence does not accurately reflect her private information. This tradeoff changes the economics of verifiable disclosure. When preferences are sufficiently aligned, full evidence disclosure is neither sustainable in equilibrium nor efficient. We show that verifiability facilitates communication when preferences are sufficiently misaligned, but hinders it when they are sufficiently aligned, suggesting that institutions that impose verification need not al- ways improve information transmission. Finally, we study how verifiable and unverifiable communication can complement one another when both are available: unverifiable communication can contextualize verifiable evidence when the latter is misleading. |
| JEL: | C72 D83 |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35712 |
| By: | Taiga Saito (Faculty of Economics, Hitotsubashi University); Akihiko Takahashi (The University of Tokyo); Shivam Gupta (Neoma Business School) |
| Abstract: | This study formulates, for the first time, the back-running mechanism in private routing for on-chain cryptocurrency trading as a leader–follower stochastic differential game between a user and a trusted searcher, providing practical implications for the mechanism design of on-chain market infrastructure. We propose a model to investigate the effect of back-running by a trusted searcher in private routing for a user in on-chain cryptocurrency transactions. The continuous-time linear–quadratic (LQ) leader–follower stochastic differential game is solved via a forward–backward stochastic differential equation (FBSDE) approach using the stochastic maximum principle. Numerical examples illustrate how allowing back-running affects the market impact of the cryptocurrency and the user's total purchasing cost under different liquidity conditions in the on-chain market. This helps infrastructure companies design healthier markets by allowing users to choose whether to provide trade information to trusted searchers. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:tky:fseres:2026cf1279 |
| By: | Pham, Ngoc Anh |
| Abstract: | A funder divides a fixed budget between an equal baseline and a merit pool awarded through a contest on a measured signal. Applicants produce the signal with two efforts: research, which the funder values, and polishing, which only raises the measure. The two-effort contest reduces exactly to a one-effort contest governed by two numbers, the signal's cost and its research content, and the design problem runs on the gap between them. Better polishing technology strictly shrinks the optimal pool; costly scrutiny of proposals re-expands it, and full scrutiny is never optimal. Voluntary participation removes researchers first and retains polishers, so the equal baseline is what shelters the research-rich; a shortlist ranked on contest strength admits exactly the entrants that shrink the pool. The same structure appears wherever fixed money is split between a flat share and a contest on a measured signal that mixes valued production with measure-improving effort, from exam-based awards to merit pay and promotion tournaments. The rule is deterministic throughout: merit still decides who wins, and the design decides how much merit pays. |
| Keywords: | contests, grantsmanship, research funding, sharing rules, multitask incentives |
| JEL: | C72 D72 O38 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:qmsrps:202607 |