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on Game Theory |
| By: | Florian Lengyel |
| Abstract: | We study a noncooperative $n$-player game of slack allocation in which each player $j$ has entitlement $L_j>0$ and chooses a claim $C_j\ge0$. Let $v_j=(C_j-L_j)_+$ (overage) and $s_j=(L_j-C_j)_+$ (slack); set $X=\sum_j v_j$ and $I=\sum_j s_j$. At the end of the period an overage-proportional clearing rule allocates cooperative surplus $I$ to defectors in proportion to $v_j$; cooperators receive $C_j$. We show: (i) the selfish outcome reproduces the cooperative payoff vector $(L_1, \dots, L_n)$; (ii) with bounded actions, defection is a weakly dominant strategy; (iii) within the $\alpha$-power family, the linear rule ($\alpha=1$) is the unique boundary-continuous member; and (iv) the dominant-strategy outcome is Strong Nash under transferable utility and hence coalition-proof (Bernheim et al., 1987). We give a policy interpretation for carbon rationing with a penalty collar. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.07145 |
| By: | Georgy Lukyanov; David Li |
| Abstract: | This paper studies a two-player game in which the players face uncertainty regarding the nature of their partner. In this variation of the standard Prisoner's Dilemma, players may encounter an 'honest' type who always cooperates. Mistreating such a player imposes a moral cost on the defector. This situation creates a trade-off, resolved in favor of cooperation if the player's trust level, or belief in their partner's honesty, is sufficiently high. We investigate whether an environment where players have explicit beliefs about each other's honesty is more or less conducive to cooperation, compared to a scenario where players are entirely uncertain about their partner's beliefs. We establish that belief diversity hampers cooperation in environments where the level of trust is relatively low and boosts cooperation in environments with a high level of trust. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.08851 |
| By: | Jacopo Bizzotto; Nathan Hancart |
| Abstract: | We study cheap talk with simple language, where the sender communicates using a score that aggregates a multidimensional state. Both the sender and the receiver share the same payoffs, given by a quadratic loss function. We show that the restriction to scores introduces strategic considerations. First, equilibrium payoffs can be strictly lower than those achievable under commitment to a scoring rule. Second, we prove that any equilibrium score must be either linear or discrete. Finally, assuming normally distributed states, we fully characterize the set of equilibrium linear scores, which includes both the ex-ante best and the worst linear scores. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.09621 |
| By: | Fabian Alex |
| Abstract: | We build a signaling game model of a firm’s decision to acquire a costly green label which enables it to emit a green bond. A greenium may compensate it for the incurred cost. That cost is higher for non-green firms. With an investor that prefers a clean environment and dislikes being fooled into believing in a fabricated green label, there are equilibria featuring green bonds by either both firm types, only the green firm or neither. Allowing side payments undermines stability of all equilibria where a green label is acquired. A neutral rather than a green investor considerably decreases the number of conceivable equilibria, as does uncertainty about the investor type. The equilibria of the baseline model are preserved if we allow two investors, a green and a neutral one, to decide on their respective purchase of the bond sequentially. Lastly, if investors hold all market power, no green labels will be observed at all. |
| Keywords: | Environment, Environmental Economics, Green Economics, Game Theoretic, Game Theory, Two Player, Strategic Game, Signaling Game |
| JEL: | C72 D21 Q5 |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:bav:wpaper:242_alex.rdf |
| By: | Lukasz Balbus; Michael Greinecker; Kevin Reffett; Lukasz Wozny |
| Abstract: | We provide general theoretical foundations for modeling strategic uncertainty in large distributional Bayesian games with general type spaces, using a version of interim correlated rationalizability. We then focus on the case in which payoff functions are supermodular in actions, as is common in the literature on global games. This structure allows us to identify extremal interim correlated rationalizable solutions with extremal interim Bayes-Nash equilibria. Notably, no order structure on types is assumed. We illustrate our framework and results using the large versions of the electronic mail game and a global game. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.18426 |
| By: | Craig Steven Wright |
| Abstract: | This paper develops a formal game-theoretic model to examine how protocol mutability disrupts cooperative mining behaviour in blockchain systems. Using a repeated game framework with stochastic rule shocks, we show that even minor uncertainty in institutional rules increases time preference and induces strategic deviation. Fixed-rule environments support long-term investment and stable equilibrium strategies; in contrast, mutable protocols lead to short-termism, higher discounting, and collapse of coordinated engagement. Simulation results identify instability zones in the parameter space where rational mining gives way to extractive or arbitrage conduct. These findings support an Austrian economic interpretation: calculability requires rule stability. Institutional noise undermines the informational basis for productive action. We conclude that protocol design must be treated as a constitutional economic constraint, not a discretionary variable, if sustainable cooperation is to emerge in decentralised systems. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.20992 |
| By: | Craig Steven Wright |
| Abstract: | This paper integrates Austrian capital theory with repeated game theory to examine strategic miner behaviour under different institutional conditions in blockchain systems. It shows that when protocol rules are mutable, effective time preference rises, undermining rational long-term planning and cooperative equilibria. Using formal game-theoretic analysis and Austrian economic principles, the paper demonstrates how mutable protocols shift miner incentives from productive investment to political rent-seeking and influence games. The original Bitcoin protocol is interpreted as an institutional anchor: a fixed rule-set enabling calculability and low time preference. Drawing on the work of Bohm-Bawerk, Mises, and Hayek, the argument is made that protocol immutability is essential for restoring strategic coherence, entrepreneurial confidence, and sustainable network equilibrium. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.20965 |
| By: | Alejandro Saavedra-Nieves; M. Gloria Fiestras-Janeiro |
| Abstract: | An important operational aspect in airport management is the allocation of fees to aircraft movements on a runway, whether operated by separate operators or under code-sharing agreements. This paper analyses the problem of determining fees under code-sharing of the movements at an airport from a game theoretic perspective. In particular, we propose the configuration value for games with coalition configuration as the mechanism for allocating operating costs. We provide the exact expression of this game-theoretic solution for airport games, which depends only on the parameters of the associated airport problem. For this purpose, we consider a new and natural game-theoretic characterization of the configuration value. Finally, for the specific context of airport games, we apply it to a real case as a mechanism to determine the aircraft fees at a Spanish airport in a code-sharing scenario. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.02894 |
| By: | Shuige Liu; Gabriel Ziegler |
| Abstract: | Interactive decision-making relies on strategic reasoning. Two prominent frameworks are (1) models of bounded reasoning, exemplified by level-$k$ models, which keep reasoning implicit, and (2) epistemic game theory, which makes reasoning explicit. We connect these approaches by "lifting" static complete-information games into incomplete-information settings where payoff types reflect players' reasoning depths as in level-$k$ models. We introduce downward rationalizability, defined via minimal belief restrictions capturing the basic idea common to level-$k$ models, to provide robust yet well-founded predictions in games where bounded reasoning matters. We then refine these belief restrictions to analyze the foundations of two seminal models of bounded reasoning: the classic level-$k$ model and the cognitive hierarchy model. Our findings shed light on the distinction between hard cognitive bounds on reasoning and beliefs about co-players' types. Furthermore, they offer insights into robustness issues relevant for market design. Thus, our approach unifies key level-$k$ models building on clear foundations of strategic reasoning stemming from epistemic game theory. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.19737 |
| By: | Raouf Boucekkine; Giorgio Fabbri; Salvatore Federico; Fausto Gozzi; Ted Loch-Temzelides; Cristiano Ricci |
| Abstract: | In order to investigate strategic interactions between a "global north" and a "global south" we introduce a two-country extension of the model in Golosov et al. (2014). We consider different transfers between the two regions, including transfers that can improve the abatement technology. Our model can accommodate several kinds of heterogeneity, including in preferences, time discount rates, and damages resulting from the stock of accumulated GHG. We solve for both planner’s solutions and non-cooperative equilibria. We then calibrate our model in order to study quantitative differences between these solutions and to quantitatively explore the role of heterogeneity and Knightian uncertainty. We characterize emissions, damages, consumption, transfers, and welfare by computing the Nash equilibria of the associated dynamic game. We then compare these to efficiency benchmarks. Further, we investigate how (deep) uncertainty affects climate outcomes. We develop a general model for the study of optimal control and differential games that are linear-in-state, which we term the Integral Transformation Method (ITM), which encompasses several existing models as special cases. |
| Keywords: | Integral Transformation Method, Analytical Integrated Assessment Model, Differential Game, Climate Policy, Robust Control |
| JEL: | C7 Q5 Q54 D62 H23 |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:gbl:wpaper:2025-04 |
| By: | Georgy Lukyanov; Anastasia Makhmudova |
| Abstract: | We study a regime change game in which the state and an opposition leader both observe the regime's true strength and may engage in costly communication by manipulating the mean of citizens' private signals. Each citizen then decides whether to attack the regime. From the perspective of both the state and the opposition, the size of the attack is uncertain, as the number of committed partisans - those who always attack regardless of their signal - is not observed in advance. We show that a regime on the brink of collapse optimally refrains from propaganda, while the opposition engages in counter-propaganda. The equilibrium level of counter-propaganda increases with the opposition's benefit-cost ratio and with the precision of citizens' private signals, and decreases with the cost of attacking. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.04749 |
| By: | H\'ector Hermida-Rivera |
| Abstract: | This note shows that under the unrestricted domain, there exists a choice liberal and Nash implementable social choice rule if and only if there are at least three players and the outcome set is at least twice as large as the player set. A social choice rule is choice liberal if and only if for every player, there exists at least one pair of outcomes such that if this player strictly prefers one over the other, the one he prefers is socially desirable and the other one is not. A social choice rule is Nash implementable if and only if there exists a mechanism such that at every preference profile, the set of Nash equilibrium outcomes coincides with the set of socially desirable ones. The proof constructs an intuitive Nash implementing mechanism. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.16059 |
| By: | Cole Wittbrodt |
| Abstract: | In finite-horizon bargaining, deals are often made "on the courthouse steps", just before the deadline. Most classic finite-horizon bargaining models fail to generate deadline effects, or even delay, in equilibrium. Players foresee the future path of play, and come to a deal immediately to circumvent bargaining frictions. We propose a novel source of bargaining delay: absentmindedness. A bargainer who does not know the calendar time may rationally reject an "ultimatum offer" as the trade deadline looms. Rational confusion is a source of bargaining power for the absentminded player, as it induces the other party to make fair offers near the trade deadline to prevent negotiations from breaking down. The absentminded party may reject greedier offers in hope of receiving a fair offer closer to the deadline. If any offer is feasible, there are equilibria which feature delay if and only if players are patient. Such equilibria always involve history-dependent strategies. I provide a necessary and sufficient condition for there to exist a Markov perfect equilibrium with delay: the space of feasible offers must be sufficiently disconnected. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.05828 |
| By: | Dylan Laplace Mermoud |
| Abstract: | We adopt a continuous-time dynamical system approach to study the evolution of the state of a game driven by the willingness to reduce the total dissatisfaction of the coalitions about their payment. Inspired by the work of Grabisch and Sudh\"olter about core stability, we define a vector field on the set of preimputations from which is defined, for any preimputation, a cohesion curve describing the evolution of the state. We prove that for each preimputation, there exists a unique cohesion curve. Subsequently, we show that, for the cohesion flow of a balanced game, the core is the unique minimal attractor of the flow, the realm of which is the whole preimputation set. These results improve our understanding of the ubiquity of the core in the study of cooperative games with transferable utility. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.02918 |
| By: | Kota Murayama |
| Abstract: | This paper studies how payoff heterogeneity affects the value of information in beauty contest games. I show that public information is detrimental to welfare if and only if agents' Katz-Bonacich centralities exhibit specific forms of heterogeneity, stemming from the network of coordination motives. A key insight is that agents may value the commonality of information so differently that some are harmed by their neighbors knowing what others know. Leveraging this insight, I also show that when the commonality of information is endogenously determined through information sharing, the equilibrium degree of information sharing can be inefficiently low, even without sharing costs. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.17660 |
| By: | Georgy Lukyanov; David Li |
| Abstract: | This paper studies an infinite-horizon framework in which two large populations of players are randomly matched to play a Prisoner's Dilemma. Each player lives for two consecutive periods: as a young player from one group, and then as an old player in the other group. Each population has a known fraction of honest types - individuals who always cooperate unless paired with a player who has been observed to defect against a cooperating partner in the past. Because such defections (i.e., breakdowns of trust) are publicly observed, any defector risks carrying a stigma into future interactions. We show that when the benefits from defection are sufficiently large, there exists an equilibrium in which an increase in the fraction of honest types can reduce the likelihood of cooperation. Moreover, we demonstrate that introducing imperfect public memory - allowing past misdeeds to be probabilistically "cleared" - does not enhance cooperation. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.04748 |
| By: | Quentin Hoarau; Jean-Pierre Ponssard |
| Abstract: | This paper studies the adoption of clean technology in an oligopolistic setting, focusing on carbon capture and storage (CCS) in the cement sector. Firms can choose between two technologies: a carbon-intensive ("dirty") technology and a low-carbon ("clean") one. Initially, all firms operate with the dirty technology, whose variable cost increases over time with the social cost of carbon, following Hotelling’s rule. Clean technology has a constant marginal cost but requires a sunk investment cost. Firms engage in short-term Cournot competition, and the adoption decision is modeled as a dynamic game in continuous time. We show that imperfect competition leads to inefficiently delayed adoption due to preemption incentives, with firms eventually coordinating on a late joint adoption equilibrium. We propose two corrective public policies: a fixed-cost subsidy and a time-dependent subsidy on profit flows. Calibrating our model to the cement industry, assuming five competitors, we find that without policy intervention, CCS adoption would occur in 2042 rather than the socially optimal date of 2030. Obtaining optimal timing requires either a 70% fixed-cost subsidy or a time-dependent subsidy equivalent to 20% of that amount, although it requires more information for implementation. |
| Keywords: | imperfect competition, innovation, cement, carbon capture and storage |
| JEL: | L13 O31 Q5 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12127 |
| By: | Pau Balart (Universitat de les Illes Balears); Agustín Casas (Universidad CUNEF); Gerard Doménech-Gironell (University of Padova); Orestis Troumpounis (Ca Foscari University of Venice) |
| Abstract: | This paper develops a formal model of electoral competition in which parties first choose their platforms and then allocate campaign resources that serve both persuasive and mobilization purposes. Voters, in turn, endogenously sort into ideological and impressionable types. We characterize a unique subgame perfect equilibrium and derive comparative statics that illustrate how the returns to mobilization and persuasion shape equilibrium platforms, campaign spending, and turnout. Among other results, we show that while campaign spending and polarization do not necessarily move in the same direction, turnout consistently increases with polarization. |
| Keywords: | electoral competition, campaign spending, polarization, mobilization |
| JEL: | D72 |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:aoz:wpaper:371 |
| By: | Philippe Choné; Laurent Linnemer |
| Abstract: | Sellers face a critical choice: run competitive auctions or strike exclusive deals with preferred buyers. Contrary to conventional wisdom that sellers should rely on open competition, we show that a powerful seller optimally commits to a sequential `flexclusivity' arrangement - a strategic mix of exclusivity and competitive bidding. Under broad conditions, the seller chooses with positive probability to disregard alternative buyers entirely. We demonstrate, in a parsimonious model, that simple option contracts implement flexclusivity efficiently, increasing the expected joint profit of the contracting parties. When a preferred buyer declines the option, this credibly signals his weakness, allowing the seller to extract more rent from stronger buyers in subsequent auctions. The joint gain from such arrangements can represent as much as 75% of what vertical integration would achieve, without requiring commitment beyond the initial contracting stage. |
| Keywords: | selling mechanism, exclusivity, revenue-maximizing auction, option contract, vertical integration |
| JEL: | D44 D82 D86 L22 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12134 |
| By: | Nikhil Kumar |
| Abstract: | This paper presents a social learning model where the network structure is endogenously determined by signal precision and dimension choices. Agents not only choose the precision of their signals and what dimension of the state to learn about, but these decisions directly determine the underlying network structure on which social learning occurs. We show that under a fixed network structure, the optimal precision choice is sublinear in the agent's stationary influence in the network, and this individually optimal choice is worse than the socially optimal choice by a factor of $n^{1/3}$. Under a dynamic network structure, we specify the network by defining a kernel distance between agents, which then determines how much weight agents place on one another. Agents choose dimensions to learn about such that their choice minimizes the squared sum of influences of all agents: a network with equally distributed influence across agents is ideal. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.00249 |
| By: | Gurkirat Wadhwa; Akansh Verma; Veeraruna Kavitha; Priyank Sinha |
| Abstract: | In competitive supply chains (SCs), pricing decisions are crucial, as they directly impact market share and profitability. Traditional SC models often assume continuous pricing for mathematical convenience, overlooking the practical reality of discrete price increments driven by currency constraints. Additionally, customer behavior, influenced by loyalty and strategic considerations, plays a significant role in purchasing decisions. To address these gaps, this study examines a SC model involving one supplier and two manufacturers, incorporating realistic factors such as customer demand segmentation and discrete price setting. Our analysis shows that the Nash equilibria (NE) among manufacturers are not unique, we then discuss the focal equilibrium. Our analysis also reveals that low denomination factors can lead to instability as the corresponding game does not have NE. Numerical simulations demonstrate that even small changes in price increments significantly affect the competitive dynamics and market share distribution. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.17239 |
| By: | Toygar T. Kerman; Anastas P. Tenev; Konstantin Zabarnyi |
| Abstract: | We study a Bayesian persuasion setting in which a sender wants to persuade a critical mass of receivers by revealing partial information about the state to them. The homogeneous binary-action receivers are located on a communication network, and each observes the private messages sent to them and their immediate neighbors. We examine how the sender's expected utility varies with increased communication among receivers. We show that for general families of networks, extending the network can strictly benefit the sender. Thus, the sender's gain from persuasion is not monotonic in network density. Moreover, many network extensions can achieve the upper bound on the sender's expected utility among all networks, which corresponds to the payoff in an empty network. This is the case in networks reflecting a clear informational hierarchy (e.g., in global corporations), as well as in decentralized networks in which information originates from multiple sources (e.g., influencers in social media). Finally, we show that a slight modification to the structure of some of these networks precludes the possibility of such beneficial extensions. Overall, our results caution against presuming that more communication necessarily leads to better collective outcomes. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.09099 |
| By: | Peter Katuscak; Tomas Miklanek |
| Abstract: | Fischbacher, Gachter and Fehr (2001) let subjects condition their contributions in a linear public goods game on the average contribution of their groupmates using the strategy method. About half of their subjects exhibit “conditional cooperation†(CC) in that they contribute more the more the groupmates are assumed to contribute. This finding has been extensively replicated. However, recent studies have found large fractions of conditional cooperators (CCs) even in placebo settings in which we would not expect to see any CC, suggesting that the measure of CC is upwardly-biased. We investigate whether mitigating subject confusion and experimenter demand can eliminate or at least reduce the bias. We introduce several design features to mitigate confusion. To mitigate experimenter demand, we provide participants with “exit options†that allow them to avoid conditioning their contributions on those of their groupmates. We evaluate the extent of the bias by the proportion of subjects classified as CCs in a mirror placebo setting involving a meaningless conditioning variable. When we mitigate confusion but not experimenter demand, more than a quarter of subjects end up classified as CCs in the placebo mirror. When we also mitigate experimenter demand, this proportion drops to a level indistinguishable from random behavior. In a standard setting, mitigating experimenter demand reduces the proportion of CCs by almost 40 percent. We therefore conclude that CC should be measured in the presence of the exit options in order to mitigate experimenter demand. |
| Keywords: | conditional cooperation, experimental methodology |
| JEL: | H41 C91 D64 |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:cer:papers:wp798 |
| By: | Marczak, Martyn; Beissinger, Thomas |
| Abstract: | We develop a model that incorporates task-based production into a matching model with intrafirm wage bargaining. Unlike in existing task-based models, the representative firm derives the optimal task allocation as a function of capital and labor, rather than relative factor prices. Embedding this mechanism in a model with strategic employment choice, we show how the properties of task-level technology affect the extent of over |
| Keywords: | task approach, search and matching, Stole-Zwiebel bargaining, overhiring, wage bargaining, elasticity of complementarity |
| JEL: | J23 D24 E23 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:hohdps:325479 |
| By: | Matthew O. Jackson; Agathe Pernoud |
| Abstract: | We examine optimal regulation of financial networks with debt interdependencies between financial firms. We first characterize when it is firms have an incentive to choose excessively risky portfolios and overly correlate their portfolios with those of their counterparties. We then characterize how optimal regulation depends on a firm's financial centrality and its available investment opportunities. In standard core-periphery networks, optimal regulation depends non-monotonically on the correlation of banks' investments, with maximal restrictions for intermediate levels of correlation. Moreover, it can be uniquely optimal to treat banks asymmetrically: restricting the investments of one core bank while allowing an otherwise identical core bank (in all aspects, including network centrality) to invest freely. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.16648 |