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on Game Theory |
| By: | Halpern, Joe; Heller, Yuval; Winter, Eyal |
| Abstract: | We study the strategic advantages of coarsening one’s utility by clustering nearby payoffs together (i.e., classifying them the same way). Our solution concept, coarse-utility equilibrium (CUE) requires that (1) each player maximizes her coarse utility, given the opponent’s strategy, and (2) the classifications form best replies to one another. We characterize CUEs in various games. In particular, we show that there is a qualitative difference between CUEs in which only one of the players clusters payoffs, and those in which all players cluster their payoffs, and that the latter type induce players to treat co-players better than in Nash equilibria in the large class of games with monotone externalities. |
| Keywords: | Categorization, language, indirect evolutionary approach, monotone externalities, strategic complements, strategic substitutes. |
| JEL: | C73 D83 |
| Date: | 2022–01–25 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:111670&r= |
| By: | J. Sakovics; Françoise Forges (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS - Centre National de la Recherche Scientifique - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres, LEDa - Laboratoire d'Economie de Dauphine - IRD - Institut de Recherche pour le Développement - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | We formally assume that players in a game consider Nash Equilibrium (NE) thebehavioral norm. In önite games of perfect information this leads to a reönementof NE: Faithful Nash Equilibrium (FNE). FNE is outcome equivalent to NE of theìtrimmedî game, obtained by restricting the original tree to its NE paths. Thus,it always exists but it need not be unique. Iterating the norm ensures uniquenessof outcome. FNE may violate backward induction when subgame perfection requires play according to the SPE following a deviation from it. We thus provide analternative view of tenable threats in equilibrium analysis. |
| Keywords: | Nash Equilibrium,threat |
| Date: | 2022–01–20 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03537845&r= |
| By: | Argenton, Cedric (Tilburg University, Center For Economic Research); Ivanova-Stenzel, Radosveta; Müller, Wieland (Tilburg University, Center For Economic Research) |
| Keywords: | cournot; Bayesian game; Bayes-Nash equilibrium; repeated games; collusion; cooperation; experimental economics |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:bec182fc-5222-4ec2-9632-3369a281269f&r= |
| By: | Paolo Bertoletti |
| Abstract: | The quantity-setting (Cournot) oligopoly with perfect complements is dual to the price-setting (Bertrand) oligopoly with homogeneous goods. Under mild technical conditions, the former setting has a unique (pure strategy) Nash equilibrium with null quantities. |
| Keywords: | Cournot duopoly; Bertrand duopoly; perfect complements; homogeneous products. |
| JEL: | D11 D43 D61 |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:mib:wpaper:490&r= |
| By: | Bayer, Peter; Kozics, György; Szöke, Nora Gabriella |
| Abstract: | We study public goods games played on networks with possibly non-recip-rocal relationships between players. Examples for this type of interactions include one-sided relationships, mutual but unequal relationships, and par-asitism. It is well known that many simple learning processes converge to a Nash equilibrium if interactions are reciprocal, but this is not true in general for directed networks. However, by a simple tool of rescaling the strategy space, we generalize the convergence result for a class of directed networks and show that it is characterized by transitive weight matrices and quadratic best-response potentials. Additionally, we show convergence in a second class of networks; those rescalable into networks with weak exter-nalities. We characterize the latter class by the spectral properties of the absolute value of the network’s weight matrix and by another best-response potential structure. |
| Keywords: | Networks; externalities; local public goods; potential games; non-reciprocal relations |
| JEL: | C72 D62 D85 |
| Date: | 2022–01–21 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:126505&r= |
| By: | Bigoni, Maria (University of Bologna); Casari, Marco (University of Bologna); Salvanti, Andrea (Universitat Pompeu Fabra); Skrzypacz, Andrzej (Stanford GSB); Spagnolo, Giancarlo (Stockholm University) |
| Abstract: | In an experiment on the repeated prisoner’s dilemma where intended actions are implemented with noise, Fudenberg et al. (2012) observe that non-equilibrium strategies of the "tit-for-tat" family are largely adopted. Furthermore, they do not find support for risk dominance of TFT as a determinant of cooperation. This comment introduces the "Payback" strategy, which is similar to TFT but is sustainable in equilibrium. Using the data from the original article, we show that Payback captures most of the empirical support previously attributed to TFT, and that the risk dominance criterion based on Payback can explain the observed cooperation patterns. |
| Keywords: | asymmetric strategies, imperfect monitoring, indefinitely repeated games, risk dominance, strategic risk |
| JEL: | C72 C73 C91 D82 |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp15023&r= |
| By: | Bos, Iwan; Marini, Marco A.; Saulle, Riccardo D. |
| Abstract: | This paper examines capacity-constrained oligopoly pricing with sellers who seek myopic improvements. We employ the Myopic Stable Set solution concept and establish the existence of a unique pure-strategy price solution for any given level of capacity. This solution is shown to coincide with the set of pure-strategy Nash equilibria when capacities are large or small. For an intermediate range of capacities, it predicts a price interval that includes the mixed-strategy support. This stability concept thus encompasses all Nash equilibria and o ers a pure-strategy solution when there is none in Nash terms. It particularly provides a behavioral rationale for di erent pricing patterns, including Edgeworth price cycles and states of hypercompetition with supply shortages. We also analyze the impact of a change in firm size distribution. A merger among the biggest firms may lead to more price dispersion as it increases the maximum and decreases the minimum myopically stable price. |
| Keywords: | International Relations/Trade, Political Economy |
| Date: | 2021–12–21 |
| URL: | http://d.repec.org/n?u=RePEc:ags:feemwp:317126&r= |
| By: | Deepanshu Vasal; Randall Berry |
| Abstract: | In this paper, we consider a discrete-time Stackelberg mean field game with a leader and an infinite number of followers. The leader and the followers each observe types privately that evolve as conditionally independent controlled Markov processes. The leader commits to a dynamic policy and the followers best respond to that policy and each other. Knowing that the followers would play a mean field game based on her policy, the leader chooses a policy that maximizes her reward. We refer to the resulting outcome as a Stackelberg mean field equilibrium (SMFE). In this paper, we provide a master equation of this game that allows one to compute all SMFE. Based on our framework, we consider two numerical examples. First, we consider an epidemic model where the followers get infected based on the mean field population. The leader chooses subsidies for a vaccine to maximize social welfare and minimize vaccination costs. In the second example, we consider a technology adoption game where the followers decide to adopt a technology or a product and the leader decides the cost of one product that maximizes his returns, which are proportional to the people adopting that technology |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2201.05959&r= |
| By: | Soumendu Sarkar (Department of Economics, Delhi School of Economics); Dhritiman Gupta (O.P. Jindal Global University,Sonipat, India.) |
| Abstract: | An assembly problem refers to a situation where a buyer wants to purchase a fixed number of complementary items from sellers holding an item each. We model complementarity using graphs where nodes represent items, and edges between two nodes represent a complementary relationship between these items. The buyer wants to purchase a feasible path in the graph, i.e., a path of desired length, where the sum of valuations of the sellers owning the items do not exceed buyer’s own valuation. A seller is critical if he lies on every feasible path. We examine subgame perfect equilibria of an infinite horizon alternate-offer bargaining game between the buyer and the sellers. We show that there exist equilibria where the buyer can extract full surplus within two periods if and only if (a) there are no critical sellers and (b) there exist at least two feasible paths with minimum sum of seller valuations. We also characterize the upper bounds on buyer’s surplus when she cannot extract full surplus. Thus we characterize the trade-off between complementarity and competition in terms of buyer’s equilibrium surplus share in assembly problems. Key Words: Assembly, Bargaining, Competition, Complementarity, Contiguity, Holdout JEL Codes: C78 |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:cde:cdewps:319&r= |
| By: | Federico Echenique; Sumit Goel; SangMok Lee |
| Abstract: | We study discrete allocation problems, as in the textbook notion of an exchange economy, but with indivisible goods. The problem is well-known to be difficult. The model is rich enough to encode some of the most pathological bargaining configurations in game theory, like the roommate problem. Our contribution is to show the existence of stable allocations (outcomes in the weak core, or in the bargaining set) under different sets of assumptions. Specifically, we consider dichotomous preferences, categorical economies, and discrete TU markets. The paper uses varied techniques, from Scarf's balanced games to a generalization of the TTC algorithm by means of Tarski fixed points. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.04706&r= |
| By: | Ohnishi, Kazuhiro |
| Abstract: | This paper considers a two-stage game model with a nonlinear concave demand function where two socially concerned firms compete with each other. In the first stage, each firm decides simultaneously and independently whether to offer lifetime employment as a strategic commitment device. In the second stage, after observing the rival’s choice in the first stage, each firm chooses simultaneously and independently an actual output level. Each socially concerned firm maximizes its own profit plus a fraction of consumer surplus. The paper discusses the equilibrium outcomes of the model. |
| Keywords: | Concave demand function; Cournot duopoly model; Lifetime employment; Socially concerned firms |
| JEL: | C72 D21 L20 |
| Date: | 2022–01–22 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:111625&r= |
| By: | Chloe Tergiman; Marie Villeval (GATE - Groupe d'analyse et de théorie économique - UL2 - Université Lumière - Lyon 2 - ENS LSH - Ecole Normale Supérieure Lettres et Sciences Humaines - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | In a finitely repeated game with asymmetric information, we experimentally study how individuals adapt the nature of their lies when settings allow for reputation-building. While some lies can be detected ex post by the uninformed party, others remain deniable. We find that traditional market mechanisms such as reputation generate strong changes in the way people lie and lead to strategies in which individuals can maintain plausible deniability: people simply hide their lies better by substituting deniable lies for detectable lies. Our results highlight the limitations of reputation to root out fraud when a Deniable Lie strategy is available. |
| Keywords: | Lying,Deniability,Reputation,Financial Markets,Experiment |
| Date: | 2022–01–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-03512300&r= |
| By: | Nguyen, Cuong Viet; Vu, Linh Hoang |
| Abstract: | In this study, we tested the effect of time delays on sharing behavior. We conducted a dictator game to examine whether dictators change their sharing behaviors if they have more time between receiving and sharing money. When the response time was 2 hours, the sharing behavior of dictators was similar to sharing behavior in a standard game without time delay. However, if the dictators kept their received money for a week, they were remarkably less likely to share the money. This finding provides suggestive evidence of the ownership effect in sharing behavior. |
| Keywords: | Dictator games,endowment,experiment,time delay |
| JEL: | C70 D63 D64 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:glodps:1032&r= |
| By: | Xiaojuan Yu (Zhongnan University of Economics and Law); Vincent van den Berg (VU Amsterdam); Erik Verhoef (VU Amsterdam); ZhiChun Li (Huazhong University of Science and Technology) |
| Abstract: | Autonomous cars allow safe driving with a smaller headway than that required for normal human-driven cars, thereby potentially improving road capacity. To attain this capacity benefit, cooperation among autonomous cars is vital. However, the future market may have multiple car brands and the incentive for them to cooperate is unknown. This paper investigates competition and cooperation between multiple car brands, which may offer both autonomous and normal cars. In particular, we develop a two-stage game theoretic model to investigate brands' strategic interactions and evaluate, from both policy and organizational perspectives, the implications of their cooperation incentives and pricing competition. We compare four market structures: duopoly competition, perfect competition, a public welfare-maximizing monopoly, and a private profit-maximizing monopoly. Various parameters are evaluated, including factors such as price elasticity, capacity effects, and cooperation cost. This evaluation provides policy insights into actions that could be considered by regulators and organizations for the operation of autonomous cars. |
| Keywords: | Autonomous cars, Cooperation strategy, Duopoly competition, Game theory, Regulatory policy |
| JEL: | D21 R41 D43 |
| Date: | 2022–02–03 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20220003&r= |
| By: | Pablo Amorós (Departamento de Teoría e Historia Económica, Universidad de Málaga.) |
| Abstract: | We consider the problem of a group of experts who have to rank a set of candidates. Society's optimal choice relies on experts?honest judgments about the deserving ranking. However, experts' judgments are impossible to verify. Moreover, experts' judgments do not entirely determine their preferences. Then, experts might want to misreport their judgments if, by doing so, some ranking that they like best is selected. To solve this problem, we have to design a mechanism where the experts interact so that the socially optimal ranking is implemented. Whether this is possible depends on (1) how experts' judgments are aggregated to determine the socially optimal ranking and (2) how experts' preferences relate to their judgments. We state necessary and su¢ cient conditions on these two elements for the socially optimal ranking to be implementable in dominant strategies and Nash equilibrium. Then, we study the implementability of some widely used judgment aggregation rules, including extensions of scoring and Condorcet consistent voting rules. Finally, we propose a non-trivial judgment aggregation rule that is Nash implementable. |
| Keywords: | Evaluation; impartiality; manipulability; ranking of candidates; mechanism design; voting rules. |
| JEL: | C72 D71 D78 |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:mal:wpaper:2022-1&r= |
| By: | Henry Thille (Department of Economics and Finance, University of Guelph, Guelph ON Canada); Sebastien Mitraille (Toulouse Business School) |
| Abstract: | We examine the e?ects of ?rm heterogeneity when ?rms can compete in advance for future demand by either entering forward contracts or by selling to agents that store the good to meet future demand. Firms’ sales in the second period are reduced by aggregate advance sales, so high-cost ?rms may produce zero output in equilibrium if aggregate advance sales induce a price below their marginal cost. The endogenous number of active ?rms leads to the possibility of a deterrence equilibrium in which lower-cost ?rms act to deter the activity of higher-cost ?rms. In this case, the presence of inactive higher-cost ?rms in the market results in a lower price than would otherwise obtain. In addition, the advance sales equilibrium with heterogeneous ?rms has higher market shares for relatively e?cient ?rms compared to that in both the heterogeneous ?rm Cournot equilibrium and the homogeneous ?rm advance sales equilibrium. Consequently, the equilibrium outcome results in industry output produced at a lower average cost, which represents an additional welfare gain associated with the pro-competitive e?ects of strategic advance sales even though the reallocation of market shares leads to higher measured concentration. |
| Keywords: | Advance sales, oligopoly, quantity competition |
| JEL: | C72 D43 L13 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:gue:guelph:2022-01&r= |
| By: | Petrakis, Emmanuel; Skartados, Panagiotis |
| Abstract: | We consider a vertically related market where an upstream monopolist supplies two downstream Cournot competitors. We allow the vertical contract terms to be either interim observable or secret. We address a dichotomy in the literature by endogenizing the disclosure regime of contract terms. The latter could be set via a Non-Disclosure Agreement. Firms bargain over both the disclosure regime and the contract terms. Our results indicate that when firms trade over two-part tariffs, universal interim observability is the unique equilibrium no matter the bargaining power distribution or the product differentiation. Yet, when firms trade over linear tariffs there may be a multiplicity of equilibria. We also show that under competing vertical chains we get universal interim observability as a unique equilibrium no matter the upstream structure. Our results qualitatively hold under Bertrand competition too. Our welfare analysis indicates that universal interim observability and two-part tariffs yield the highest consumer surplus and total welfare. |
| Keywords: | Bilateral Contracting; Vertical Relations; Two-Part Tariffs; Bargaining; Nondisclosure Agreements; Secret Contracts |
| JEL: | D43 L13 L14 |
| Date: | 2022–02–16 |
| URL: | http://d.repec.org/n?u=RePEc:cte:werepe:34144&r= |
| By: | Buccella, Domenico; Meccheri, Nicola |
| Abstract: | This paper investigates the issue of strategic delegation by considering the role of management centrality in contracting with different stakeholders. Specifically, a sequential negotiation unionized duopoly model is analysed, in which the management relative bargaining power visà-vis shareholders and vis-à-vis unions can differ. In such a framework, differences in the relative bargaining power among involved stakeholders play a key role in determining the endogenous choice by firms' owners to delegate strategic decisions to the management, or, in other words, the choice of being an entrepreneurial or a managerial firm. Moreover, the distribution of stakeholders' relative bargaining power affects firms' profitability and overall welfare, also leading to novel results with regard to the received literature. In particular, to minimize potential conflict of interests between firms' owners and the overall society, regulation directed to soften the managers' bargaining strength vis-à-vis shareholders must be designed and implemented. |
| Keywords: | management centrality,strategic delegation,unions,bargaining power,social welfare,stakeholder conflict |
| JEL: | D21 L13 L14 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:glodps:1025&r= |
| By: | Dughera, Stefano; Marciano, Alain (University of Turin) |
| Abstract: | The Samaritan’s Dilemma has largely been investigated, frequently by assuming that Samaritans help recipients out of altruism. Yet, Buchanan did not make any behavioral assumption regarding the Samaritan’s motives. In this paper, we explicitly introduce this assumption in Buchanan’s original model and analyze how this changes the nature of the game. We show that altruism alone does not explain the dilemma. A parameter that captures the disutility the Samaritan feels when helping someone who does not reciprocate her benevolence must be introduced to make sense of the different version of Buchanan’s Samaritan’s Dilemma. We also show that the Samaritan’s dilemma is an evolutionary stable outcome, which confirms Buchanan’s intuitions. Finally, a third important point put forward in the paper is that the more altruistic are the Samaritans, the less likely it is that they will show the kind of strategic courage envisaged by Buchanan, which is one of the most important traits Samaritans should display to avoid being trapped in a dilemma. |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:uto:dipeco:202201&r= |
| By: | Albers, H. J.; Preonas, L.; Capitán, T.; Robinson, Elizabeth; Madrigal-Ballestero, R. |
| Abstract: | The design of protected areas, whether marine or terrestrial, rarely considers how people respond to the imposition of no-take sites with complete or incomplete enforcement. Consequently, these protected areas may fail to achieve their intended goal. We present and solve a spatial bio-economic model in which a manager chooses the optimal location, size, and enforcement level of a marine protected area (MPA). This manager acts as a Stackelberg leader, and her choices consider villagers’ best response to the MPA in a spatial Nash equilibrium of fishing site and effort decisions. Relevant to lower income country settings but general to other settings, we incorporate limited enforcement budgets, distance costs of traveling to fishing sites, and labor allocation to onshore wage opportunities. The optimal MPA varies markedly across alternative manager goals and budget sizes, but always induce changes in villagers’ decisions as a function of distance, dispersal, and wage. We consider MPA managers with ecological conservation goals and with economic goals, and identify the shortcomings of several common manager decision rules, including those focused on: (1) fishery outcomes rather than broader economic goals, (2) fish stocks at MPA sites rather than across the full marinescape, (3) absolute levels rather than additional values, and (4) costless enforcement. Our results demonstrate that such naïve or overly narrow decision rules can lead to inefficient MPA designs that miss economic and conservation opportunities. |
| Keywords: | additionality; bio-economic model; enforcement; leakage; marine spatial planning; Nash equilibrium; no-take reserves; park effectiveness; reserve site selection; spatial prioritization; systematic conservation planning |
| JEL: | R14 J01 |
| Date: | 2020–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:113552&r= |
| By: | Jean Barthélemy; Eric Mengus; Guillaume Plantin |
| Abstract: | This paper studies a model in which the price level is the outcome of dynamic strategic interactions between a fiscal authority, a monetary authority, and investors in government bonds and reserves. The ''unpleasant monetarist arithmetic'' whereby aggressive fiscal expansion forces the monetary authority to chicken out and inflate away public liabilities may be contained by market forces: Monetary dominance prevails if such fiscal expansion is met with a higher real interest rate on public liabilities, due for example to the crowding out of private investment opportunities. The model delivers empirical implications regarding the joint dynamics of public liabilities and price level, and policy implications regarding the management of central banks' balance sheets. |
| Keywords: | Fiscal-Monetary Interactions, Game of Chicken |
| JEL: | E63 E50 E42 E31 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:bfr:banfra:855&r= |
| By: | Ma, Siyu; Sen, Debapriya; Tauman, Yair |
| Abstract: | We consider the licensing of a cost-reducing innovation in a Cournot oligopoly where an outside innovator uses three part tariffs that are combinations of upfront fees, per unit royalties and ad valorem royalties. The key insight of our analysis is per unit royalties have a location effect and ad valorem royalties have a scale effect on marginal costs. Using these two effects, we show that the same market outcome (price, quantities, operating profits) can be sustained by multiple combinations of per unit and ad valorem royalties. In the monopoly case, under three part tariffs it is optimal to set a pure upfront fee while the unique optimal two part royalty is a pure ad valorem royalty. In the case of a general oligopoly with linear demand, for relatively insignificant innovations, it is optimal to set a pure upfront fee; otherwise there is a continuum of optimal policies and there always exists an optimal policy consisting of a positive per unit royalty and upfront fee but no ad valorem royalty. For intermediate innovations, provided the demand intercept is relatively large, there exists an optimal policy that has both kinds of royalties but no fees. Finally in a Cournot duopoly it is illustrated that when the innovator is one of the incumbent firms rather than an outsider, market outcomes separately depend on two kinds of royalties and a pure ad valorem royalty is optimal among all three part tariffs. |
| Keywords: | patent licensing; per unit royalties; ad valorem royalties; three part tariffs; acceptability and feasibility constraints |
| JEL: | D43 D45 L13 L14 |
| Date: | 2022–01–21 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:111624&r= |
| By: | Sen, Neelanjan; Minocha, Priyansh; Dutta, Arghya |
| Abstract: | This paper considers the possibility of technology licensing and tacit collusion between firms that produce homogeneous goods under asymmetric cost structures and compete in quantities. We discuss the possibility of collusion under Grim-Trigger strategies when technology may be licensed via fixed fee or royalty or two-part tariff. Irrespective of the type of licensing contract, the possibility that a stable cartel is formed is the same. In the no-licensing stage, the cartel formation is more likely if the cost difference between the firms is higher. In contrast to Lin (1996), all forms of licensing facilitate (obstruct) collusion, if the initial cost difference between the firms is less (more). Technology will always be licensed in the first stage and the optimal form of licensing is either fixed-fee or royalty or two-part tariff. The cartel will be formed if the firms are relatively patient and welfare either increases or decreases in the post-licensing stage. |
| Keywords: | Technology licensing; Oligopoly; Cartel; Grim-Trigger Strategy; Cournot Competition |
| JEL: | D24 L13 L24 |
| Date: | 2022–02–23 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:111639&r= |
| By: | Masaaki Fujii (Quantitative Finance Course, Graduate School of Economics, The University of Tokyo); Akihiko Takahashi (Quantitative Finance Course, Graduate School of Economics, The University of Tokyo) |
| Abstract: | In this article, we consider the problem of equilibrium price formation in an incomplete securities market consisting of one major financial firm and a large number of minor firms. They carry out continuous trading via the securities exchange to minimize their cost while facing idiosyncratic and common noises as well as stochastic order flows from their individual clients. The equilibrium price process that balances demand and supply of the securities, including the functional form of the price impact for the major firm, is derived endogenously both in the market of finite population size and in the corresponding mean field limit. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:cfi:fseres:cf533&r= |