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on Game Theory |
| By: | Yongyang Cai; Anastasios Xepapadeas; Aart de Zeeuw |
| Abstract: | Many resources are provided by an ecological system that is vulnerable to tipping when exceeding a certain level of pollution, with a sudden big loss of ecosystem services. An ecological system is usually also a common-pool resource and therefore vulnerable to suboptimal use resulting from non-cooperative behavior. An analysis requires methods to derive cooperative and non-cooperative solutions for managing a dynamical system with tipping points. Such a game is a differential game which has two well-defined non-cooperative solutions, the open-loop and feedback Nash equilibria. This paper provides new numerical methods for deriving open-loop and feedback Nash equilibria, for one-dimensional and two-dimensional dynamical systems. The methods are applied to the lake game, which is the classical example for these types of problems. Especially, two-dimensional feedback Nash equilibria are a novelty of this paper. This Nash equilibrium is close to the cooperative solution which has important policy implications. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.06646 |
| By: | Bixing Qiao; Jianfeng Zhang |
| Abstract: | This paper considers a continuous time Kyle-Back model which is a game problem between an insider and a market marker. The existing literature typically focuses on the existence of equilibrium by using the PDE approach, which requires certain Markovian structure and the equilibrium is in the bridge form. We shall provide a new approach which is used widely for stochastic controls and stochastic differential games. We characterize all equilibria through a coupled system of forward backward SDEs, where the forward one is the conditional law of the inside information and the backward one is the insider's optimal value. In particular, when the time duration is small, we show that the FBSDE is wellposed and thus the game has a unique equilibrium. This is the first uniqueness result in the literature, without restricting the equilibria to certain special structure. Moreover, this unique equilibrium may not be Markovian, indicating that the PDE approach cannot work in this case. We next study the set value of the game, which roughly speaking is the set of insider's values over all equilibria and thus is by nature unique. We show that, although the bridge type of equilibria in the literature does not satisfy the required integrability for our equilibria, its truncation serves as a desired approximate equilibrium and its value belongs to our set value. Finally, we characterize our set value through a level set of certain standard HJB equation. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.12281 |
| By: | Aurel Stenzel; Johannes Lohse; Till Requate; Israel Waichman |
| Abstract: | We characterize 'Games of Altruistic Cooperation' as a class of games in which cooperation leaves the individual and the group of decision-makers worse off than defection, but favors individuals outside the group. An example is climate change mitigation. In this context, we experimentally investigate whether decentralized institutions using costly punishment and/or communication support altruistic cooperation to sustain the welfare of future generations. Without punishment or communication, cooperation is low; communication alone even increases the incidence of zero contributions. However, combining peer punishment with communication strongly increases cooperation, showing that an effective decentralized solution to a Game of Altruistic Cooperation exists. |
| Keywords: | games of altruistic cooperation, social dilemma, intergenerational good game, punishment, communication |
| JEL: | C92 D74 H41 Q54 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11880 |
| By: | Piotr K\k{e}pczy\'nski; Oskar Skibski |
| Abstract: | We perform a comprehensive analysis of extensions of the Shapley value to groups. We propose a new, natural extension called the Union Shapley Value, which assesses a group's contribution by examining the impact of its removal from the game. This intuition is formalized through two axiomatic characterizations, closely related to existing axiomatizations of the Shapley value. Furthermore, we characterize the class of group semivalues and identify a dual approach that measures synergy instead of the value of a coalition. Our analysis reveals a novel connection between several group values previously proposed in the literature. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.21122 |
| By: | Philippe Bergault; Pierre Cardaliaguet; Wenbin Yan |
| Abstract: | This paper investigates the optimal hedging strategies of an informed broker interacting with multiple traders in a financial market. We develop a theoretical framework in which the broker, possessing exclusive information about the drift of the asset's price, engages with traders whose trading activities impact the market price. Using a mean-field game approach, we derive the equilibrium strategies for both the broker and the traders, illustrating the intricate dynamics of their interactions. The broker's optimal strategy involves a Stackelberg equilibrium, where the broker leads and the traders follow. Our analysis also addresses the mean field limit of finite-player models and shows the convergence to the mean-field solution as the number of traders becomes large. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.08992 |
| By: | Kiho Yoon |
| Abstract: | With a multilateral vertical contracting model of media markets, we examine upstream competition and contractual arrangements in content provision. We analyze the trade of content by the Nash bargaining solution and the downstream competition by the Hotelling location model. We characterize the equilibrium outcomes and the contractual arrangements for various vertical structures. We show that the possibility of exclusive contracts rises when the value of the premium content increases, the degree of horizontal differentiation in the downstream market decreases, the importance of advertising revenue decreases, and the relative bargaining power of upstream firm decreases. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.15063 |
| By: | Ignacio Esponda; Demian Pouzo |
| Abstract: | We introduce Berk--Nash rationalizability, a new solution concept for misspecified learning environments. It parallels rationalizability in games and captures all actions that are optimal given beliefs formed using the model that best fits the data in the agent's misspecified model class. Our main result shows that, with probability one, every \emph{limit action} -- any action played or approached infinitely often -- is Berk--Nash rationalizable. This holds regardless of whether behavior converges. We apply the concept to known examples and identify classes of environments where it is easily characterized. The framework provides a general tool for bounding long-run behavior without assuming convergence to a Berk--Nash equilibrium. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.20708 |
| By: | Maria Andraos; Mario Ghossoub; Michael B. Zhu |
| Abstract: | We consider a model of a reinsurance market consisting of multiple insurers on the demand side and multiple reinsurers on the supply side, thereby providing a unifying framework and extension of the recent literature on optimality and equilibria in reinsurance markets. Each insurer has preferences represented by a general Choquet risk measure and can purchase coverage from any or all reinsurers. Each reinsurer has preferences represented by a general Choquet risk measure and can provide coverage to any or all insurers. Pricing in this market is done via a nonlinear pricing rule given by a Choquet integral. We model the market as a sequential game in which the reinsurers have the first-move advantage. We characterize the Subgame Perfect Nash Equilibria in this market in some cases of interest, and we examine their Pareto efficiency. In addition, we consider two special cases of our model that correspond to existing models in the related literature, and we show how our findings extend these previous results. Finally, we illustrate our results in a numerical example. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.07291 |
| By: | David K Levine |
| Date: | 2025–06–18 |
| URL: | https://d.repec.org/n?u=RePEc:cla:levarc:735347000000000007 |
| By: | Shinnosuke Kawai; Kuninori Nakagawa |
| Abstract: | This paper explores price competition with exogenous product differentiation in a spatial model similar to that of Nakagawa (2023). Nakagawa examines product differentiation within the framework of Varian (1980). Nakagawa integrates Varian's concept of uninformed consumers, who lack complete price information, into a spatial model based on Hotelling (1929). While Nakagawa placed informed consumers at the center of the Hotelling line and used quadratic transportation costs, our study employs a uniform distribution of informed consumers and linear transportation costs. This approach enables a more direct comparison with established spatial competition literature, particularly Osborne and Pitchik (1987). We classify equilibrium candidates and characterize the parameter regions corresponding to each equilibrium. There is no pure equilibrium in the region where we construct mixed strategy equilibria. Furthermore, we compare the expected profit in the equilibrium of our model with the findings of Osborne and Pitchik (1987). Finally, we discuss the impact of captive buyers on the nature of spatial competition. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.06961 |
| By: | Nicolas Eschenbaum; Nicolas Greber |
| Abstract: | We analyze the vulnerability of decentralized autonomous organizations (DAOs) to speculative exploitation via their redemption mechanisms. Studying a game-theoretic model of repeated auctions for governance shares with speculators, we characterize the conditions under which -- in equilibrium -- an exploitative exit is guaranteed to occur, occurs in expectation, or never occurs. We evaluate four redemption mechanisms and extend our model to include atomic exits, time delays, and DAO spending strategies. Our results highlight an inherent tension in DAO design: mechanisms intended to protect members from majority attacks can inadvertently create opportunities for costly speculative exploitation. We highlight governance mechanisms that can be used to prevent speculation. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.21296 |
| By: | Benjamin Moll; Lenya Ryzhik |
| Abstract: | Mean Field Game (MFG) models implicitly assume "rational expectations", meaning that the heterogeneous agents being modeled correctly know all relevant transition probabilities for the complex system they inhabit. When there is common noise, this assumption results in the "Master equation" (a.k.a. "Monster equation"), a Hamilton-Jacobi-Bellman equation in which the infinite-dimensional density of agents is a state variable. The rational expectations assumption and the implication that agents solve Master equations is unrealistic in many applications. We show how to instead formulate MFGs with non-rational expectations. Departing from rational expectations is particularly relevant in "MFGs with a low-dimensional coupling", i.e. MFGs in which agents' running reward function depends on the density only through low-dimensional functionals of this density. This happens, for example, in most macroeconomics MFGs in which these low-dimensional functionals have the interpretation of "equilibrium prices." In MFGs with a low-dimensional coupling, departing from rational expectations allows for completely sidestepping the Master equation and for instead solving much simpler finite-dimensional HJB equations. We introduce an adaptive learning model as a particular example of non-rational expectations and discuss its properties. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.11838 |
| By: | Jos\'e Ignacio Rivero-Wildemauwe |
| Abstract: | Two agents trade an item in a simultaneous offer setting, where the exchange takes place if and only if the buyer's bid price weakly exceeds the seller's ask price. Each agent is randomly assigned the buyer or seller role. Both agents are characterized by a certain degree of Kantian morality, whereby they pick their bidding strategy behind a Veil of Ignorance, taking into account how the outcome would be affected if their trading partner adopted their strategy. I consider two variants with asymmetric information, respectively allowing buyers to have private information about their valuation or sellers to be privately informed about the item's quality. I show that when all trades are socially desirable, even the slightest degree of morality guarantees that the outcome is fully efficient. In turn, when quality is uncertain and some exchanges are socially undesirable, full efficiency is only achieved with sufficiently high moral standards. Moral concerns also ensure equal ex-ante treatment of the two agents in equilibrium. Finally, I show that if agents are altruistic rather than moral, inefficiencies persist even with a substantial degree of altruism. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.20551 |
| By: | Basak, Debasmita |
| Abstract: | It is commonly believed that common ownership deters entry by internalizing market competition which warrants pro-competitive entry regulations. Using a successive oligopoly model with common ownership, we challenge this conventional wisdom. We show that if the downstream sector alone operates under common ownership, entry is always socially excessive, i.e., more firms enter the market than is socially optimal. In contrast, when the upstream sector alone operates under common ownership, entry is socially excessive (insufficient) if the degree of common ownership in the upstream market is reasonably low (high). Finally, when both sectors are characterized by common ownership, entry is socially excessive if the degree of ownership in the downstream market is stronger than that in the upstream market. Therefore, our findings provide a rationale for anti-competitive, rather than pro-competitive entry regulations. |
| Keywords: | Common Ownership, Excessive Entry, Insufficient Entry, Successive Oligopoly |
| JEL: | D43 L11 L13 L22 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:esprep:319538 |
| By: | Dangxing Chen |
| Abstract: | In recent years, machine learning models have achieved great success at the expense of highly complex black-box structures. By using axiomatic attribution methods, we can fairly allocate the contributions of each feature, thus allowing us to interpret the model predictions. In high-risk sectors such as finance, risk is just as important as mean predictions. Throughout this work, we address the following risk attribution problem: how to fairly allocate the risk given a model with data? We demonstrate with analysis and empirical examples that risk can be well allocated by extending the Shapley value framework. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.06653 |
| By: | Cristian Chica; Yinglong Guo; Gilad Lerman |
| Abstract: | We introduce pricing formulas for competition and collusion models of two-sided markets with an outside option. For the competition model, we find conditions under which prices and consumer surplus may increase or decrease if the outside option utility increases. Therefore, neglecting the outside option can lead to either overestimation or underestimation of these equilibrium outputs. Comparing collusion to competition, we find that in cases of small cross-side externalities, collusion results in decreased normalized net deterministic utilities, reduced market participation and increased price, on both sides of the market. Additionally, we observe that as the number of platforms increases in the competition model, market participation rises. Profits, however, decrease when the net normalized deterministic utility is sufficiently low but increase when it is high. Furthermore, we identify specific conditions that quantify the change of price and consumer surplus when the competition increases. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.06109 |
| By: | Enrico Mattia Salonia (Toulouse School of Economics) |
| Abstract: | I study the behaviour of individuals who have preferences for universalisation. When considering a course of action, they evaluate the consequence that would occur if everyone else acted equivalently, according to some criterion of equivalence. That is, they universalise their behaviour. I develop and axiomatise a model for individuals who value their choices in light of the consequences they induce when their action is universalised. The key behavioural prediction is that the independence axiom is satisfied only among actions that are universalised equivalently. I impose conditions to single out the most prominent models of universalisation, compare them, highlight and arguably overcome their limitations. I propose a unifying model of universalisation inspired by the equal sacrifice principle. |
| Keywords: | Universalisation reasoning, Non-consequentialism, Kantian preferences, Equal sacrifice principle, Axiomatic model |
| JEL: | C70 C72 D01 D03 D90 |
| Date: | 2025–06–06 |
| URL: | https://d.repec.org/n?u=RePEc:rtv:ceisrp:603 |