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on Game Theory |
| By: | Alessandro Micheli; Johannes Muhle-Karbe; Eyal Neuman |
| Abstract: | We study a multi-player stochastic differential game, where agents interact through their joint price impact on an asset that they trade to exploit a common trading signal. In this context, we prove that a closed-loop Nash equilibrium exists if the price impact parameter is small enough. Compared to the corresponding open-loop Nash equilibrium, both the agents' optimal trading rates and their performance move towards the central-planner solution, in that excessive trading due to lack of coordination is reduced. However, the size of this effect is modest for plausible parameter values. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.02961&r= |
| By: | Ren\'e A\"id; Lamia Ben Ajmia; M'hamed Ga\"igi; Mohamed Mnif |
| Abstract: | We study a nonzero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The objective of each player is to maximize her total expected discounted profits. The resolution methodology relies on the connection between Nash equilibrium and the corresponding system of quasi-variational inequalities (QVIs in short). We prove, by means of the weak dynamic programming principle for the stochastic differential game, that the value function of each player is a constrained viscosity solution to the associated QVIs system in the class of linear growth functions. We also introduce a family of value functions converging to our value function of each player, and which is characterized as the unique constrained viscosity solutions of an approximation of our QVIs system. This convergence result is useful for numerical purpose. We apply a probabilistic numerical scheme which approximates the solution of the QVIs system to the case of the competition between two electricity retailers. We show how our model reproduces the qualitative behaviour of electricity retail competition. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.10213&r= |
| By: | Arvind Shrivats; Dena Firoozi; Sebastian Jaimungal |
| Abstract: | Principal agent games are a growing area of research which focuses on the optimal behaviour of a principal and an agent, with the former contracting work from the latter, in return for providing a monetary award. While this field canonically considers a single agent, the situation where multiple agents, or even an infinite amount of agents are contracted by a principal are growing in prominence and pose interesting and realistic problems. Here, agents form a Nash equilibrium among themselves, and a Stackelberg equilibrium between themselves as a collective and the principal. We apply this framework to the problem of implementing emissions markets. We do so while incorporating market clearing as well as agent heterogeneity, and distinguish ourselves from extant literature by incorporating the probabilistic approach to MFGs as opposed to the analytic approach, with the former lending itself more naturally for our problem. For a given market design, we find the Nash equilibrium among agents using techniques from mean field games. We then provide preliminary results for the optimal market design from the perspective of the regulator, who aims to maximize revenue and overall environmental benefit. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.11963&r= |
| By: | Martin Peitz; Lily Samkharadze |
| Abstract: | Platform competition can be intense when offering non-differentiated services. However, competition is somewhat relaxed if platforms cannot set negative prices. If platforms collude they may be able to implement the outcome that maximizes industry profits. In an infinitely repeated game with perfect monitoring, this is feasible if the discount factor is sufficiently large. When this is not possible, under some condition, a collusive outcome with one-sided rent extraction along the equilibrium path can be sustained that leads to higher profits than the non-cooperative outcome. |
| Keywords: | Two-sided markets, tacit collusion, cartelization, price structure, platform competition |
| JEL: | L41 L13 D43 |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2022_331&r= |
| By: | Raouf Boucekkine; Giorgio Fabbri; Salvatore Federico; Fausto Gozzi |
| Abstract: | We characterize the shape of spatial externalities in a continuous time and space differential game with transboundary pollution. We posit a realistic spatiotemporal law of motion for pollution (diffusion and advection), and tackle spatiotemporal non-cooperative (and cooperative) differential games. Precisely, we consider a circle partitioned into several states where a local authority decides autonomously about its investment, production and depollution strategies over time knowing that investment/production generates pollution, and pollution is transboundary. The time horizon is infinite. We allow for a rich set of geographic heterogeneities across states. We solve analytically the induced non-cooperative differential game and characterize its long-term spatial distributions. In particular, we prove that there exist a Perfect Markov Equilibrium, unique among the class of the affine feedbacks. We further provide with a full exploration of the free riding problem and the associated border effect. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.10584&r= |
| By: | Kene Boun My (BETA - Bureau d'Économie Théorique et Appliquée - UNISTRA - Université de Strasbourg - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Camille Cornand (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - CNRS - Centre National de la Recherche Scientifique - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UL2 - Université Lumière - Lyon 2 - ENS Lyon - École normale supérieure - Lyon); Rodolphe dos Santos Ferreira (BETA - Bureau d'Économie Théorique et Appliquée - UNISTRA - Université de Strasbourg - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, Universidade Católica Portuguesa [Porto]) |
| Abstract: | In the standard beauty contest game of Morris and Shin (2002), agents have to choose actions in accordance with an expected fundamental value and with the conventional value expected to be set by the market. In doing so, agents respond to fundamental and coordination motives, respectively, the prevalence of either motive being set exogenously. Our contribution is to consider whether agents favor the fundamental or the coordination motive as the result of a strategic choice. First, we extend the generic beauty contest game by endogenizing the weight put on the coordination motive and show that the mere presence of public information theoretically leads agents to fully favor the coordination motive. The prevalence of the coordination motive over the fundamental one yields a disconnection of average actions from the fundamental. Second, we test this game through a laboratory experiment. Subjects tend to conform to theoretical predictions, except when private information is very precise in comparison to public information, qualifying the focal role of public information. |
| Keywords: | Experiment,Coordination,Beauty contest,Public information,Dispersed information |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03468870&r= |
| By: | Agustín Casas (CUNEF); Martín Gonzalez-Eiras (University of Copenhagen) |
| Abstract: | We study a legislative-bargaining divide-the-pie game in which some legislators have the ability to a ect the amount of resources to be distributed (positively or negatively). If included in the winning coalition, these legislators cooperate and increase the size of the pie. If excluded, they retaliate and decrease it. Cooperation and retaliation produce significant changes in the equilibrium allocation relative to Baron and Ferejohn (1989): The bargaining position of cooperating and retaliating legislators improves, and thus they are more likely to be included in the winning coalition (which may be larger-than-minimum). Some of these legislators may be excluded from the winning coalition, creating inefficient output losses. Moreover, output losses increase with legislators' patience. |
| Keywords: | Legislative bargaining, non-minimum winning coalitions, spillovers,allocative efficiency. |
| JEL: | D72 D74 D61 |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:aoz:wpaper:95&r= |
| By: | Romain Baeriswyl (Swiss National Bank); Kene Boun My (BETA - Bureau d'Économie Théorique et Appliquée - UNISTRA - Université de Strasbourg - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Camille Cornand (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - CNRS - Centre National de la Recherche Scientifique - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UL2 - Université Lumière - Lyon 2 - ENS Lyon - École normale supérieure - Lyon) |
| Abstract: | Central banks' disclosures, such as forward guidance, have a weaker effect on the economy in reality than in theoretical models. The present paper contributes to understanding how people pay attention and react to various sources of information. In a beauty-contest with information acquisition, we show that strategic complementarities give rise to a double overreaction to public disclosures by increasing agents equilibrium attention, which, in turn, increases the weight assigned to them in equilibrium action. A laboratory experiment provides evidence that the effect of strategic complementarities on the realised attention and the realised action is qualitatively consistent with theoretical predictions, though quantitatively weaker. Both the lack of attention to public disclosures and a limited level of reasoning by economic agents account for the weaker realised reaction. This suggests that it is just as important for a central bank to control reaction to public disclosures by swaying information acquisition by recipients as it is by shaping information disclosures themselves. |
| Keywords: | Overreaction,Information acquisition,Beauty-contest,Central bank communication |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03468857&r= |
| By: | Wanying Huang; Philipp Strack; Omer Tamuz |
| Abstract: | We study how long-lived, rational, exponentially discounting agents learn in a social network. In every period, each agent observes the past actions of his neighbors, receives a private signal, and chooses an action with the objective of matching the state. Since agents behave strategically, and since their actions depend on higher order beliefs, it is difficult to characterize equilibrium behavior. Nevertheless, we show that regardless of the size and shape of the network, and the patience of the agents, the equilibrium speed of learning is bounded by a constant that only depends on the private signal distribution. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.14265&r= |
| By: | Tergiman, Chloe (Pennsylvania State University); Villeval, Marie Claire (CNRS, GATE) |
| 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 |
| JEL: | C91 D01 G41 M21 |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp14931&r= |
| By: | Khan, Abhimanyu |
| Abstract: | I develop the notion of evolutionary stability of behavioural rules in a game-theoretic setting. Each individual chooses a strategy, possibly taking into account the game's history, and the manner in which he chooses his strategy is encapsulated by a behavioural rule. The payoffs obtained by individuals following a particular behavioural rule determine that rule's fitness. A population is stable if whenever some individuals from an incumbent behavioural rule mutate and follow another behavioural rule, the fitness of each incumbent behavioural rule exceeds that of the mutant behavioural rule. I show that any population comprised of more than one behavioural rule is not stable, and present necessary and sufficient conditions for stability of a population comprised of a single behavioural rule. |
| Keywords: | behavioural rules, evolutionary stability |
| JEL: | C73 |
| Date: | 2021–12–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:111309&r= |
| By: | Qi Shi; Dong Hao |
| Abstract: | In a crowdsourcing contest, a requester holding a task posts it to a crowd. People in the crowd then compete with each other to win the rewards. Although in real life, a crowd is usually networked and people influence each other via social ties, existing crowdsourcing contest theories do not aim to answer how interpersonal relationships influence peoples' incentives and behaviors, and thereby affect the crowdsourcing performance. In this work, we novelly take peoples' social ties as a key factor in the modeling and designing of agents' incentives for crowdsourcing contests. We then establish a new contest mechanism by which the requester can impel agents to invite their neighbours to contribute to the task. The mechanism has a simple rule and is very easy for agents to play. According to our equilibrium analysis, in the Bayesian Nash equilibrium agents' behaviors show a vast diversity, capturing that besides the intrinsic ability, the social ties among agents also play a central role for decision-making. After that, we design an effective algorithm to automatically compute the Bayesian Nash equilibrium of the invitation crowdsourcing contest and further adapt it to large graphs. Both theoretical and empirical results show that, the invitation crowdsourcing contest can substantially enlarge the number of contributors, whereby the requester can obtain significantly better solutions without a large advertisement expenditure. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.02884&r= |
| By: | Piazolo, David; Vanberg, Christoph |
| Abstract: | We present a three-person, two-period bargaining game with private information. A single proposer is seeking to secure agreement to a proposal under either majority or unanimity rule. Two responders have privately known "breakdown values" which determine their payoff in case of "breakdown". Breakdown occurs with some probability if the first proposal fails and with certainty if the second proposal fails. We characterize Bayesian Equilibria in Sequentially Weakly Undominated Strategies. Our central result is that responders have a signaling incentive to vote "no" on the first proposal under unanimity rule, whereas no such incentive exists under majority rule. The reason is that being perceived as a "high breakdown value type" is advantageous under unanimity rule, but disadvantageous under majority rule. As a consequence, responders are "more expensive" under unanimity rule and disagreement is more likely. These results confirm intuitions that have been stated informally before and in addition yield deeper insights into the underlying incentives and what they imply for optimal behavior in bargaining with private information. |
| Date: | 2022–01–13 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0709&r= |
| By: | Michael Curry; Alexander Trott; Soham Phade; Yu Bai; Stephan Zheng |
| Abstract: | Real economies can be seen as a sequential imperfect-information game with many heterogeneous, interacting strategic agents of various agent types, such as consumers, firms, and governments. Dynamic general equilibrium models are common economic tools to model the economic activity, interactions, and outcomes in such systems. However, existing analytical and computational methods struggle to find explicit equilibria when all agents are strategic and interact, while joint learning is unstable and challenging. Amongst others, a key reason is that the actions of one economic agent may change the reward function of another agent, e.g., a consumer's expendable income changes when firms change prices or governments change taxes. We show that multi-agent deep reinforcement learning (RL) can discover stable solutions that are epsilon-Nash equilibria for a meta-game over agent types, in economic simulations with many agents, through the use of structured learning curricula and efficient GPU-only simulation and training. Conceptually, our approach is more flexible and does not need unrealistic assumptions, e.g., market clearing, that are commonly used for analytical tractability. Our GPU implementation enables training and analyzing economies with a large number of agents within reasonable time frames, e.g., training completes within a day. We demonstrate our approach in real-business-cycle models, a representative family of DGE models, with 100 worker-consumers, 10 firms, and a government who taxes and redistributes. We validate the learned meta-game epsilon-Nash equilibria through approximate best-response analyses, show that RL policies align with economic intuitions, and that our approach is constructive, e.g., by explicitly learning a spectrum of meta-game epsilon-Nash equilibria in open RBC models. |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2201.01163&r= |
| By: | Xiaoliang Li |
| Abstract: | In this discussion draft, we explore heterogeneous oligopoly games of increasing players with quadratic costs, where the market is supposed to have the isoelastic demand. For each of the models considered in this draft, we analytically investigate the necessary and sufficient condition of the local stability of its positive equilibrium. Furthermore, we rigorously prove that the stability regions are enlarged as the number of involved firms is increasing. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.13844&r= |
| By: | Qian Lei; Chi Seng Pun |
| Abstract: | This paper proves the existence and uniqueness results (in the sense of maximally defined regularity) as well as the stability analysis for the solutions to a class of nonlocal fully-nonlinear parabolic systems, where the nonlocality stems from the flow feature (controlled by an external temporal parameter) of the systems. The derived mathematical results generalize the theory of stochastic differential games to incorporate with behavioral factors such as time-inconsistent preferences, which facilitate developments of many studies in financial economics including robust stochastic controls and games under relative performance concerns. Moreover, with the well-posedness results, we establish a general multidimensional Feynman--Kac formula in the presence of nonlocality (time inconsistency). |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.14409&r= |
| By: | Braut, Beatrice (University of Turin) |
| Abstract: | This work investigates the stability of the gender gap in competitiveness and tests a possible mechanism that influences it. Subjects play bargaining games where the two roles differ by decision contest - one has an advantageous position - and by the extreme values of their possible payment - the more advantaged can earn more. For all the experiment subjects are randomly assigned to be in the advantaged role or not. Competition takes place between subjects who are in the same role and it is based on their payoff in the bargaining. By comparing competitive behaviour of subjects assigned to the advantaged role or not, the experiment identifies the effect of having advantages, given the remaining factors. The main result is that when in the advantaged position, behaviour is more rational and does not differ by gender, while when not the gender gap in competitiveness exists and it causes inefficiencies. Giving an advantageous role makes men with low performances in the game competing less and women with high performances doing it more, closing down the total gender gap. This finding helps to explain the competitiveness gap and provides insights on which are the characteristics of the context that make competition detrimental for gender parity and also for efficiency. |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:uto:dipeco:202121&r= |
| By: | Pierre Courtois (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UMR 5211 - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Tarik Tazdaït (CIRED - Centre International de Recherche sur l'Environnement et le Développement - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - EHESS - École des hautes études en sciences sociales - AgroParisTech - ENPC - École des Ponts ParisTech - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | Lacan's contribution in applying and promoting game theory in the early 1950s is mostly ignored in the history of game theory. Yet his early analyses of logical reasoning made him one of the first social scientists to consider the importance of the hypothesis of common knowledge. By retracing Lacan's path in his discovery of game theory, we show how much he has been a precursor in applying it. While accommodating a narrative approach, he demonstrated rigour and originality. Soliciting mathematicians open to interdisciplinarity, he introduced as early as 1945 modes of reasoning which corresponds to reasoning based on common knowledge. |
| Keywords: | la Lettre Volée,enigma of the three prisoners,common knowledge,Lacan |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03179414&r= |
| By: | Xiaoliang Li |
| Abstract: | In this paper, we investigate two heterogeneous triopoly games where the demand function of the market is isoelastic. The local stability and the bifurcation of these games are systematically analyzed using the symbolic approach proposed by the author. The novelty of the present work is twofold. On one hand, the results of this paper are analytical, which are different from the existing results in the literature based on observations through numerical simulations. In particular, we rigorously prove the existence of double routes to chaos through the period-doubling bifurcation and through the Neimark-Sacker bifurcation. On the other hand, for the special case of the involved firms having identical marginal costs, we acquire the necessary and sufficient conditions of the local stability for both models. By further analyzing these conditions, it seems that that the presence of the local monopolistic approximation (LMA) mechanism might have a stabilizing effect for heterogeneous triopoly games with the isoelastic demand. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.05950&r= |
| By: | Kevin He; Fedor Sandomirskiy; Omer Tamuz |
| Abstract: | In a private private information structure, agents' signals contain no information about the signals of their peers. We study how informative such structures can be, and characterize those that are on the Pareto frontier, in the sense that it is impossible to give more information to any agent without violating privacy. In our main application, we show how to optimally disclose information about an unknown state under the constraint of not revealing anything about a correlated variable that contains sensitive information. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.14356&r= |
| By: | Hernán Bejarano (CIDE / ESI Chapman University); Joris Gillet (Middlesex University London); Ismael Rodriguez-Lara (Universidad de Granada) |
| Abstract: | We study behavior in a trust game where first-movers initially have a higher endowment than second-movers but the occurrence of a positive random shock can eliminate this inequality by increasing the endowment of the second-mover before the decision of the first-mover. We find that second-movers return less (i.e., they are less trustworthy) when they have a lower endowment than first-movers, compared with the case in which first and second-movers have the same endowment. Second-movers who have experienced the positive shock return more than those who did not; in fact, second-movers who have experienced the positive shock return more than secondmovers who had the same endowment as the first-mover from the outset. First-movers do not seem to anticipate this behavior from second-movers. They send less to secondmovers who benefited from a shock. These findings suggest that in addition to the distribution of the endowments the source of this distribution plays an important role in determining the levels of trust and trustworthiness. This, in turn, implies that current models of inequality aversion should be extended to accommodate for reference points if random positive shocks are possible in the trust game. |
| Keywords: | Trust game, endowment heterogeneity, random shocks, luck, inequality, aversion, reference-dependent utility, reference points. |
| JEL: | C91 D02 D03 D69 |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:aoz:wpaper:96&r= |
| By: | Garrett, Daniel F.; Gomes, Renato; Maestri, Lucas |
| Abstract: | We study competition by firms that simultaneously post (potentially nonlinear) tariffs to consumers who are privately informed about their tastes. Market power stems from informational frictions, in that consumers are heterogeneously informed about firms’ offers. In the absence of regulation, all firms offer quantity discounts. As a result, relative to Bertrand pricing, imperfect competition benefits disproportionately more consumers whose willingness to pay is high, rather than low. Regulation imposing linear pricing hurts the former but benefits the latter consumers. While consumer surplus increases, firms’ profits decrease, enough to drive down utilitarian welfare. By contrast, improvements in market transparency increase utilitarian welfare, and achieve similar gains on consumer surplus as imposing linear pricing, although with limited distributive impact. On normative grounds, our analysis suggests that banning price discrimination is warranted only if its distributive benefits have a weight on the societal objective. |
| Keywords: | oligopoly,; nonlinear pricing,; linear pricing; informational frictions; asymmetric information |
| JEL: | D82 |
| Date: | 2022–01–10 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:126354&r= |