nep-gth New Economics Papers
on Game Theory
Issue of 2018‒06‒25
twenty-six papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Revenue Guarantee Equivalence By Bergemann, Dirk; Brooks, Benjamin A; Morris, Stephen
  2. Axiomatic Foundations of a Unifying Concept of the Core of Games in Effectiveness Form By Stéphane Gonzalez; Aymeric Lardon
  3. Monotone Global Games By Hoffmann, Eric; Sabarwal, Tarun
  4. Open Rule Legislative Bargaining By Gersbach, Hans; Volker, Britz
  5. Aggregating experts' ?opinions to select the winner of a competition By Pablo Amorós
  6. Bandwagon investment equilibrium of a preemption game By Kim, KiHyung; Deshmukh, Abhijit
  7. Peers or Police? Detection and Sanctions in the Provision of Public Goods By DeAngelo, Gregory; Gee, Laura Katherine
  8. Status maximization as a source of fairness in a networked dictator game By Jan E. Snellman; Gerardo I\~niguez; J\'anos Kert\'esz; R. A. Barrio; Kimmo K. Kaski
  9. Tax Evasion on a Social Network By Gamannossi degl’Innocenti, Duccio; Rablen, Matthew D.
  10. All-Pay Oligopolies: Price Competition with Unobservable Inventory Choices By Montez, João; Schutz, Nicolas
  11. Cream Skimming and Information Design in Marching Markets By Romanyuk, Gleb; Smolin, Alexey
  12. An Aggregative Games Approach to Merger Analysis in Multiproduct-Firm Oligopoly By Volker Nocke; Nicolas Schutz
  13. A Note on Local Public Good Induced Spillovers between a Leading and a Lagging Region By Batabyal, Amitrajeet
  14. Tax consultants' incentives: A game-theoretic investigation into the behavior of tax consultants, taxpayers, and the tax authority in a setting of tax complexity By Grottke, Markus; Lorenz, Johannes
  15. The Scope of Sequential Screening with Ex-Post Participation Constraints By Dirk Bergemann; Francisco Castro; Gabriel Weintraub
  16. How much income inequality is fair? Nash bargaining solution and its connection to entropy By Venkat Venkatasubramanian; Yu Luo
  17. Stable Sets for Exchange Economies with Interdependent Preferences By Maria Gabriella Graziano; Claudia Meo; Nicholas C. Yannelis
  18. Noisy Agents By Francisco Espinosa; Debraj Ray
  19. An environmentally sustainable global economy. A coopetitive model By Carfì, David; Donato, Alessia; Schilirò, Daniele
  20. Do tax information exchange agreements curb transfer pricing-induced tax avoidance? By Diller, Markus; Lorenz, Johannes
  21. Dynamic Mechanism Design: An Introduction By Dirk Bergemann; Juuso Valimaki
  22. Dark Markets with Multiple Assets: Segmentation, Asymptotic Stability, and Equilibrium Prices By Alain B\'elanger; Ndoun\'e Ndoun\'e; Roland Pongou
  23. Optimal Capital Structure and Bankruptcy Choice: Dynamic Bargaining vs Liquidation By Antill, Samuel; Grenadier, Steven
  24. Multiple Long-Run Equilibria in a Free-Entry Mixed Oligopoly By Haraguchi, Junichi; Matsumura, Toshihiro
  25. The Carbon Abatement Game By Christoph Hambel; Holger Kraft; Eduardo S. Schwartz
  26. A Macroscopic Portfolio Model: From Rational Agents to Bounded Rationality By Torsten Trimborn

  1. By: Bergemann, Dirk; Brooks, Benjamin A; Morris, Stephen
    Abstract: We revisit the revenue comparison of standard auction formats, including first-price, second-price, and English auctions. We rank auctions according to their revenue guarantees, i.e., the greatest lower bound of revenue across all informational environments, where we hold fixed the distribution of bidders' values. We conclude that if we restrict attention to the symmetric affiliated models of Milgrom and Weber (1982) and monotonic pure-strategy equilibria, first-price, second-price, and English auctions all have the same revenue guarantee, which is equal to that of the first-price auction as characterized by Bergemann, Brooks and Morris (2017). If we consider all equilibria or if we allow more general models of information, then first-price auctions have a greater revenue guarantee than all other auctions considered.
    Keywords: affiliated values; common values; English auction; First-price auction; revenue equivalence; Revenue guarantee; revenue ranking; second-price auction
    JEL: C72 D44 D82 D83
    Date: 2018–05
  2. By: Stéphane Gonzalez (Univ Lyon, UJM Saint-Etienne, France; GATE L-SE CNRS UMR 5824); Aymeric Lardon (Université Côte d'Azur, France; GREDEG CNRS)
    Abstract: We provide an axiomatic characterization of the core of games in effectiveness form. We point out that the core, whenever it applies to appropriate classes of these games, coincides with a wide variety of prominent stability concepts in social choice and game theory, such as the Condorcet winner, the Nash equilibrium, the pairwise stability, and the stable matchings, among others. Our characterization of the core invokes the axioms of non-emptiness, coalitional unanimity, and Maskin monotonicity together with a principle of independence of irrelevant states, and uses in its proof a holdover property echoing the conventional ancestor property. Taking special cases of this general characterization of the core, we derive new characterizations of the previously mentioned stability concepts.
    Keywords: Effectiveness function, core, axiomatization, holdover property, consistency principle
    JEL: C70 C71
    Date: 2018–06
  3. By: Hoffmann, Eric; Sabarwal, Tarun
    Abstract: We extend the global games method to finite player, finite action, monotone games. These games include games with strategic complements, games with strategic substitutes, and arbitrary combinations of the two. Our result is based on common order properties present in both strategic complements and substitutes, the notion of p-dominance, and the use of dominance solvability as the solution concept. In addition to being closer to the original arguments in Carlsson and van Damme (1993), our approach requires fewer additional assumptions. In particular, we require only one dominance region, and no assumptions on state monotonicity, or aggregative structure, or overlapping dominance regions. As expected, the p-dominance condition becomes more restrictive as the number of players increases. In cases where the probabilistic burden in belief formation may be reduced, the p-dominance condition may be relaxed as well. We present some examples that are not covered by existing results.
    Keywords: Global games, strategic complements, strategic substitutes, monotone games, equilibrium selection
    JEL: C70 C72
    Date: 2018–05–15
  4. By: Gersbach, Hans; Volker, Britz
    Abstract: We consider non-cooperative bargaining on the division of a surplus under a simple majority rule. Bargaining takes place according to an "open rule" as originally suggested by Baron and Ferejohn (1989): Under an open rule, proposals can be amended before they are voted on. We point out some gaps in Baron and Ferejohn's earlier work, and provide a fresh analysis of open rule bargaining. We devise a method to construct equilibrium candidates and to test whether these candidates are indeed equilibria. When players are sufficiently patient, we explicitly compute equilibrium outcomes. Compared to the canonical closed rule bargaining game, the equilibrium outcomes of open rule bargaining involve delays, but lead to more egalitarian surplus allocations. However, our results suggest that equilibrium delays tend to be longer, and surplus allocations tend to be less egalitarian than predicted by Baron and Ferejohn.
    Keywords: Bargaining; Baron and Ferejohn; Legislatures; Open Rules; Stationary Equilibrium
    JEL: C72 C78 D72
    Date: 2018–05
  5. By: Pablo Amorós (Department of Economics, University of Málaga)
    Abstract: The honest opinions of a group of experts must be aggregated to determine the deserving winner of a competition. The aggregation procedure is majoritarian if, whenever a majority of experts honestly believe that a contestant is the best one, then that contestant is considered the deserving winner. The fact that an expert believes that a contestant is the best one does not necessarily imply that she wants this contestant to win as, for example, she might be biased in favor of some other contestant. Then, we have to design a mechanism that implements the deserving winner. We show that, if the aggregation procedure is majoritarian, such a mechanism exists only if the experts are totally impartial. This impossibility result is very strong as it does not depend on the equilibrium concept considered.
    Keywords: mechanism design; social choice; aggregation of experts'? opinions; jury
    JEL: C72 D71 D78
    Date: 2018–06
  6. By: Kim, KiHyung; Deshmukh, Abhijit
    Abstract: In stochastic and competitive environments, investors face an investment dilemma because the environments provide conflicting incentives. Empirical research reports various behaviors exhibited by investors, including voluntary concurrent investments, which are called bandwagon investments. However, the current theoretical understanding is still limited in explaining under which condition the investment bandwagon effect occurs. The authors investigated the closed-loop subgame perfect equilibrium of an investment timing game that describes voluntary simultaneous investments. They showed that investors are on the investment bandwagon when the second mover's additional profit rate exceeds a threshold value. Otherwise, investors sequentially invest. It explains the frequently observed investment herd effect. Moreover, it shows that the investment bandwagon effect does not exist for entering firms.
    Keywords: option exercise games,preemption games,bandwagon investment,closed-loop equilibrium
    JEL: C73 D43 D92 L13
    Date: 2018
  7. By: DeAngelo, Gregory (West Virginia University); Gee, Laura Katherine (Tufts University)
    Abstract: Sanctions are a common method to discourage free-riding in the provision of public goods. However, we can usually only sanction those who are detected performing the bad act of free-riding. There has been considerable research on the type of sanctions imposed, but this research almost always automatically detects everyone's actions and broadcasts them to the group. This is akin to assuming that a group always has a police force or motivated peer reporting to detect and announce the actions of bad actors. However, in many situations bad acts go undetected and unknown to others. We use a lab experiment to compare public good contribution decisions in an environment where we relax the assumption that detection is automated. The common result that sanctions and the likelihood of detection share an inverse relationship continues to be found in our results. However, free-riders are unwilling to pay for detection when sanctioning is conducted at the group level, because a criminal does not want to fund the police who will catch his bad acts. But, when detection is conducted among peers, free-riders are willing to pay to detect other individuals that free-ride.
    Keywords: public goods, punishment, detection, deterrence
    JEL: C72 C91 C92 D7 H41
    Date: 2018–05
  8. By: Jan E. Snellman; Gerardo I\~niguez; J\'anos Kert\'esz; R. A. Barrio; Kimmo K. Kaski
    Abstract: Human behavioural patterns exhibit selfish or competitive, as well as selfless or altruistic tendencies, both of which have demonstrable effects on human social and economic activity. In behavioural economics, such effects have traditionally been illustrated experimentally via simple games like the dictator and ultimatum games. Experiments with these games suggest that, beyond rational economic thinking, human decision-making processes are influenced by social preferences, such as an inclination to fairness. In this study we suggest that the apparent gap between competitive and altruistic human tendencies can be bridged by assuming that people are primarily maximising their status, i.e., a utility function different from simple profit maximisation. To this end we analyse a simple agent-based model, where individuals play the repeated dictator game in a social network they can modify. As model parameters we consider the living costs and the rate at which agents forget infractions by others. We find that individual strategies used in the game vary greatly, from selfish to selfless, and that both of the above parameters determine when individuals form complex and cohesive social networks.
    Date: 2018–06
  9. By: Gamannossi degl’Innocenti, Duccio (University of Exeter); Rablen, Matthew D. (University of Sheffield)
    Abstract: We relate tax evasion behavior to a substantial literature on self and social comparison in judgements. Taxpayers engage in tax evasion as a means to boost their expected consumption relative to others in their "local" social network, and relative to past consumption. The unique Nash equilibrium of the model relates optimal evasion to a (Bonacich) measure of network centrality: more central taxpayers evade more. The indirect revenue effects from auditing are shown to be ordinally equivalent to a related Bonacich centrality. We generate networks corresponding closely to the observed structure of social networks observed empirically. In particular, our networks contain celebrity taxpayers, whose consumption is widely observed, and who are systematically of higher wealth. In this context we show that, if the tax authority can observe the social network, it is able to raise its audit revenue by around six percent.
    Keywords: tax evasion, social networks, network centrality, optimal auditing, social comparison, self comparison, habit, indirect effects, relative consumption
    JEL: H26 D85 K42
    Date: 2018–05
  10. By: Montez, João; Schutz, Nicolas
    Abstract: We study a class of games where stores source unobservable inventories in advance, and then simultaneously set prices. Our framework allows for firm asymmetries, heterogeneity in consumer tastes, endogenous consumer information through advertising, and salvage values for unsold units. The payoff structure relates to a complete-information all-pay contest with outside options, non-monotonic winning and losing functions, and conditional investments. In the generically unique equilibrium, stores randomize their price choice and, conditional on that choice, serve all their targeted demand---thus, some inventories may remain unsold. As inventory costs become fully recoverable, the equilibrium price distribution converges to an equilibrium of the associated Bertrand game (where firms first choose prices and then produce to order). This suggests that with production in advance, the choice between a Cournot analysis and a Bertrand-type analysis, as properly generalized in this paper, should depend on whether or not stores observe rivals' inventories before setting prices.
    Keywords: all-pay contests; Bertrand convergence.; inventories; oligopoly; production in advance
    JEL: L13
    Date: 2018–05
  11. By: Romanyuk, Gleb; Smolin, Alexey
    Abstract: Short-lived buyers arrive to a platform over time and randomly match with sellers. The sellers stay at the platform and sequentially decide whether to accept incoming requests. The platform designs what buyer information the sellers observe before deciding to form a match. We show full information disclosure leads to a market failure because of excessive rejections by the sellers. If sellers are homogeneous, then coarse information policies are able to restore efficiency. If sellers are heterogeneous, then simple censorship policies are often constrained efficient as shown by a novel method of calculus of variations.
    Keywords: cream skimming, matching markets, market failure, information design, calculus of variations
    JEL: C73 C78 D82 D83
    Date: 2018–05–14
  12. By: Volker Nocke; Nicolas Schutz
    Abstract: Using an aggregative games approach, we analyze horizontal mergers in a model of multiproduct-firm price competition with nested CES or nested logit demands. We show that the Herfindahl index provides an adequate measure of the welfare distortions introduced by market power, and that the induced change in the naively-computed Herfindahl index is a good approximation for the market power effect of a merger. We also provide conditions under which a merger raises consumer surplus, and conditions under which a myopic, consumer-surplus-based merger approval policy is dynamically optimal. Finally, we study the aggregate surplus and external effects of a merger.
    Date: 2018–06
  13. By: Batabyal, Amitrajeet
    Abstract: We analyze spatial spillovers in an aggregate economy consisting of a leading and a lagging region where the spillovers stem from the provision of a local public good. Specifically, if the leading region provides the public good then the lagging region obtains some spillover benefits and vice versa. We first solve for the Nash equilibrium levels of the local public goods in the two regions when public investment decisions are simultaneous; next, we determine the equilibrium welfare levels in each region. Second, on the assumption that the public investment decisions are centralized, we compute the levels of the local public goods that maximize aggregate welfare. Finally, we describe an interregional transfer scheme that leads each region to choose non-cooperatively in a Nash equilibrium the same public investment levels as those that arise when aggregate welfare is maximized.
    Keywords: Lagging Region, Leading Region, Local Public Good, Spatial Spillover
    JEL: O18 R11
    Date: 2018–05–31
  14. By: Grottke, Markus; Lorenz, Johannes
    Abstract: We propose a game-theoretic investigation to capture the interplay between the behavior of tax consultants, taxpayers, and the tax authority in a setting of tax complexity. Our purpose is to provide answers to two research questions: Which aspects of the strategic interaction between the players induce tax consultants to provide inaccurate consulting services? How can we change the incentive structure in order to improve tax consulting quality? We find that tax consultants can be best motivated to work accurately by exogenously increasing the probability of tax underpayment and by ensuring that the tax authority corrects both tax underpayment and tax overpayment.
    Keywords: tax consultant,tax law,game theory
    JEL: H2 M48 P48 K34
    Date: 2017
  15. By: Dirk Bergemann (Cowles Foundation, Yale University); Francisco Castro (Graduate School of Business, Columbia University); Gabriel Weintraub (Graduate School of Business, Stanford University)
    Abstract: We study the classic sequential screening problem in the presence of buyers’ ex-post participation constraints. A leading example is the online display advertising market, in which publishers frequently do not use up-front fees and instead use transaction-contingent fees. We establish conditions under which the optimal selling mechanism is static and buyers are not screened with respect to their interim type, or sequential and the buyers are screened with respect to their interim type. In particular, we provide an intuitive necessary and su?icient condition under which the static contract is optimal for general distributions of ex-post values. Further, we completely characterize the optimal sequential contract with binary interim types and continuum of ex-post values when this condition fails. Importantly, the latter contract randomizes the allocation of the low type buyer while giving a deterministic allocation to the high type. We also provide partial results for the case of multiple interim types.
    Keywords: Sequential screening, Ex-post participation constraints, Static contract, Sequential contract
    JEL: C72 D82 D83
    Date: 2017–02
  16. By: Venkat Venkatasubramanian; Yu Luo
    Abstract: The question about fair income inequality has been an important open question in economics and in political philosophy for over two centuries with only qualitative answers such as the ones suggested by Rawls, Nozick, and Dworkin. We provided a quantitative answer recently, for an ideal free-market society, by developing a game-theoretic framework that proved that the ideal inequality is a lognormal distribution of income at equilibrium. In this paper, we develop another approach, using the Nash Bargaining Solution (NBS) framework, which also leads to the same conclusion. Even though the conclusion is the same, the new approach, however, reveals the true nature of NBS, which has been of considerable interest for several decades. Economists have wondered about the economic meaning or purpose of the NBS. While some have alluded to its fairness property, we show more conclusively that it is all about fairness. Since the essence of entropy is also fairness, we see an interesting connection between the Nash product and entropy for a large population of rational economic agents.
    Date: 2018–06
  17. By: Maria Gabriella Graziano (Università di Napoli Federico II and CSEF); Claudia Meo (Università di Napoli Federico II); Nicholas C. Yannelis (University of Iowa)
    Abstract: We analyze housing market models à la Shapley and Scarf with externalities in consumption; that is, agents care about others and their preferences are defined over allocations rather than over single indivisible goods. After collecting some negative results about the existence of several cooperative solutions, we focus on stable allocations and search for special domains of preferences that can guarantee that they both exist and form a stable set à la von Neumann and Morgenstern.
    Keywords: Indivisible goods; other-regarding preferences; core; stable allocations; stable sets.
    JEL: C70 C78 D51 D62 D64
    Date: 2018–06–09
  18. By: Francisco Espinosa; Debraj Ray
    Abstract: Agents signal their type in a principal-agent model; the principal seeks to retain good agents. Types are signaled with some ambient noise. Agents can choose to add or remove additional noise at a cost. It is shown that monotone retention strategies, in which the principal keeps the agent if the signal crosses some threshold, are generically never equilibria. The main result identifies an equilibrium with a bounded retention zone, in which the principal is wary of both excessively good and excessively bad signals: she retains the agent if the signal is “moderate” and replaces him otherwise. The equilibria we uncover are robust to various extensions: non-normal signal structures, non-binary types, interacting agents, costly mean-shifting, or dynamics with term limits. We discuss applications to risky portfolio management, fake news and noisy government statistics.
    JEL: D72 D82 D86
    Date: 2018–05
  19. By: Carfì, David; Donato, Alessia; Schilirò, Daniele
    Abstract: This paper proposes a model representing a global economy which aims to become environmentally sustainable. The model looks both at the production side and the consumption side of the economy. Regarding the production side, the suggested model considers investment and innovation in climate technologies, whereas on the side of the consumption it takes into account economic and policy instruments to change the patterns of consumption of the households. The model follows a game theory approach and applies a theoretical framework à la Cournot. The results of the paper are the following: the model provides win-win solutions, namely strategic situations in which each country takes advantages by cooperating and competing at the same time within the global economy, and where each country gets a positive return. In fact, the model shows the convenience for each country to cooperate and suggests the implementation of policies in order to satisfy the basic requirements of 2030 Agenda for Sustainable Development, in terms of production, consumption and climate change.
    Keywords: Climate Change; Environmental Sustainability; Model à la Cournot; Coopetitive Games; Green Economy
    JEL: C71 C72 C78 Q40 Q48 Q50
    Date: 2018–06
  20. By: Diller, Markus; Lorenz, Johannes
    Abstract: We propose a game theoretical model where a multinational company with divisions in two countries and the respective tax authorities interact with each other. Prior to an audit the functional profile of the divisions is unknown to the tax authorities. In equilibrium, tax avoidance emerges in both countries. It turns out that the audit pressure is highest for firms with a hybrid functional profile, dampening their production and reducing their after-tax profit. We find that introducing a bilateral Tax Information Exchange Agreement reduces tax avoidance by aggressive transfer pricing in the high-tax ("domestic") country and precludes tax avoidance in the lowtax ("foreign") country. The volume of production increases. The foreign tax authority discontinues its audit activities, while the domestic tax authority audits less often at least if the foreign division is a toll manufacturer ("routine function"). While the expected net tax revenues increase in the foreign country, they may decrease in the domestic country.
    Keywords: transfer pricing,tax evasion,cooperation
    JEL: H26 F23 K34
    Date: 2017
  21. By: Dirk Bergemann (Cowles Foundation, Yale University); Juuso Valimaki (Aalto School of Economics)
    Abstract: We provide an introduction to the recent developments in dynamic mechanism design, with a primary focus on the quasilinear case. First, we describe socially optimal (or e?icient) dynamic mechanisms. These mechanisms extend the well-known Vickrey-Clark-Groves and D’Aspremont-Gérard-Varet mechanisms to a dynamic environment. Second, we discuss revenue optimal mechanisms. We cover models of sequential screening and revenue maximizing auctions with dynamically changing bidder types. We also discuss models of information management where the mechanism designer can control (at least partially) the stochastic process governing the agents’ types. Third, we consider models with changing populations of agents over time. After discussing related models with risk-averse agents and limited liability, we conclude with a number of open questions and challenges that remain for the theory of dynamic mechanism design.
    Keywords: Dynamic Mechanism Design, Sequential Screening, Dynamic Pivot Mechanism, Bandit Auctions, Information Management, Dynamic Pricing
    JEL: D44 D82 D83
    Date: 2017–08
  22. By: Alain B\'elanger; Ndoun\'e Ndoun\'e; Roland Pongou
    Abstract: We study a generalization of the model of a dark market due to Duffie-G\^arleanu- Pedersen [6]. Our market is segmented and involves multiple assets. We show that this market has a unique asymptotically stable equilibrium. In order to establish this result, we use a novel approach inspired by a theory due to McKenzie and Hawkins-Simon. Moreover, we obtain a closed form solution for the price of each asset at which investors trade at equilibrium. We conduct a comparative statics analysis which shows, among other sensitivities, how equilibrium prices respond to the level of interactions between investors.
    Date: 2018–06
  23. By: Antill, Samuel (Stanford University); Grenadier, Steven (Stanford University)
    Abstract: We model a firm's optimal capital structure decision in a framework in which it may later choose to enter either Chapter 11 reorganization or Chapter 7 liquidation. Creditors anticipate equityholders' ex-post reorganization incentives and price them into the ex-ante credit spreads. Using a realistic dynamic bargaining model of reorganization, the implied capital structure results in both higher credit spreads and dramatically lower leverage than existing models. If reorganization is less efficient than liquidation, the added option of reorganization can actually make equityholders worse off ex-ante, even when they liquidate on the equilibrium path.
    Date: 2017–09
  24. By: Haraguchi, Junichi; Matsumura, Toshihiro
    Abstract: We investigate a free-entry mixed oligopoly with constant marginal costs. A privatization policy is implemented after private firms enter the market. We find that both full privatization and full nationalization are equilibrium policies, and the former is the worst privatization policy for welfare.
    Keywords: entry-then-privatization, constant marginal costs, profit-enhancing entry, two polar equilibrium privatization policies
    JEL: D43 H44 L33
    Date: 2018–05–14
  25. By: Christoph Hambel; Holger Kraft; Eduardo S. Schwartz
    Abstract: Climate change is considered as one of the major global challenges. Although countries past and future contributions to the accumulation of greenhouse gases in the atmosphere are different, all countries are affected, but not necessarily in the same way (e.g. rising sea levels). This is the reason why it is so hard to reach global agreements on this matter. We study this issue in a dynamic game-theoretical model (stochastic differential game) with multiple countries that are open economies, i.e. we allow for international trade between the countries. Our framework involves stochastic dynamics for CO2-emissions and economic output of the countries. Each country is represented by a recursive-preference functional. Despite its complexity, the model is tractable and we can quantify each country's decision on consumption, investment, carbon abatement and the social cost of carbon, explicitly. One key finding is that both the country-specific and global social cost of carbon are increasing in the trade volume. This result is robust to adding capital transfers between countries. Our numerical examples suggest that disregarding trade might lead to a significant underestimation of the SCC.
    JEL: D81 Q5 Q54
    Date: 2018–05
  26. By: Torsten Trimborn
    Abstract: We present a macroscopic portfolio model which considers the time evolution of the stock price and the investments in bonds and stocks. The asset allocation between bonds and stocks is determined by an combination of a fundamentalist or chartist strategy. The stock price is determined by the inflow or outflow of stock investments. The model is able to replicate the most prominent features of financial markets, namely booms and crashes. In the case of random fundamental prices the model is even able to reproduce fat tails in logarithmic stock price return data. We want to point out that we derive the model from microscopic agent dynamics. On the microscopic level each financial agent is faced with an optimization problem, where each agent seeks to find a Nash equilibrium solution. We use model predictive control to approximate the control problem. This allows us to give a precise mathematical definition of rational and bounded rational financial agents. Moreover the approximation scheme of the microscopic optimal control problem gives a natural connections between rational and bounded rational agents. In fact the model can be regarded as the result of the simplest approximation of the optimal control problem and thus considers financial agents of maximum boundedness. Mathematically, the model can be regarded as the moment model of the recently introduced mesoscopic kinetic portfolio model(Trimborn, Pareschi, Frank: Portfolio Optimization and Model Predictive Control: A Kinetic Approach, arXiv:1711.03291).
    Date: 2018–05

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