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on Game Theory |
| By: | Hanchao Liu; Dena Firoozi; Mich\`ele Breton |
| Abstract: | Risk sensitivity plays an important role in the study of finance and economics as risk-neutral models cannot capture and justify all economic behaviors observed in reality. Risk-sensitive mean field game theory was developed recently for systems where there exists a large number of indistinguishable, asymptotically negligible and heterogeneous risk-sensitive players, who are coupled via the empirical distribution of state across population. In this work, we extend the theory of Linear Quadratic Gaussian risk-sensitive mean-field games to the setup where there exists one major agent as well as a large number of minor agents. The major agent has a significant impact on each minor agent and its impact does not collapse with the increase in the number of minor agents. Each agent is subject to linear dynamics with an exponential-of-integral quadratic cost functional. Moreover, all agents interact via the average state of minor agents (so-called empirical mean field) and the major agent's state. We develop a variational analysis approach to derive the best response strategies of agents in the limiting case where the number of agents goes to infinity. We establish that the set of obtained best-response strategies yields a Nash equilibrium in the limiting case and an $\varepsilon$-Nash equilibrium in the finite player case. We conclude the paper with an illustrative example. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.15364&r=gth |
| By: | Louis Abraham |
| Abstract: | In this study, we present models where participants strategically select their risk levels and earn corresponding rewards, mirroring real-world competition across various sectors. Our analysis starts with a normal form game involving two players in a continuous action space, confirming the existence and uniqueness of a Nash equilibrium and providing an analytical solution. We then extend this analysis to multi-player scenarios, introducing a new numerical algorithm for its calculation. A key novelty of our work lies in using regret minimization algorithms to solve continuous games through discretization. This groundbreaking approach enables us to incorporate additional real-world factors like market frictions and risk correlations among firms. We also experimentally validate that the Nash equilibrium in our model also serves as a correlated equilibrium. Our findings illuminate how market frictions and risk correlations affect strategic risk-taking. We also explore how policy measures can impact risk-taking and its associated rewards, with our model providing broader applicability than the Diamond-Dybvig framework. We make our methodology and open-source code available at https://github.com/louisabraham/cfrgame Finally, we contribute methodologically by advocating the use of algorithms in economics, shifting focus from finite games to games with continuous action sets. Our study provides a solid framework for analyzing strategic interactions in continuous action games, emphasizing the importance of market frictions, risk correlations, and policy measures in strategic risk-taking dynamics. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.18941&r=gth |
| By: | Heller, Yuval; Tubul, Itay |
| Abstract: | This study uses k-means clustering to analyze the strategic choices made by participants playing the infinitely repeated prisoner’s dilemma in laboratory experiments. We identify five distinct strategies that closely resemble well-known pure strategies: always defecting, suspicious tit-for-tat, grim, tit-for-tat, and always cooperating. Our analysis reveals moderate systematic deviations of the clustered strategies from their pure counterparts, and these deviations are important for capturing the experimental behavior. Additionally, we demonstrate that our approach significantly enhances the predictive power of previous analyses. Finally, we examine how the frequencies and payoffs of these clustered strategies vary based on the underlying game parameters. |
| Keywords: | k-means clustering, machine-learning, memory, laboratory experiment, repeated games. |
| JEL: | C7 C91 |
| Date: | 2023–05–25 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:117444&r=gth |
| By: | Irene Maria Buso (Department of Economics, University Of Venice Cà Foscari); Lorenzo Ferrari (Italian Competition Authority); Werner Güth (Max Planck Institute for Research on Collective Goods,); Luisa Lorè (Department of Economics, Universität Innsbruck); Lorenzo Spadoni (Department of Economics and Law, University of Cassino and Southern Lazio) |
| Abstract: | In this study, we test whether purely behavioral aspects affect voluntary cooperativeness in Prisoner’s Dilemma and Public Good Games, thereby questioning their isomorphic invariance. The experiment compares games whose identical payoffs are described as of the Prisoners’ Dilemma or as of linear Public Good. Social dilemma frames are compared between subjects whereas 2- or 3-person games are compared within subjects. We either confront participants with the 2-person before the 3-person game or in reverse order, always without feedback information between rounds. The analysis rejects isomorphic invariance and shows less average cooperativeness, especially more likely free riding, in the case of the Public Good type. |
| Keywords: | Social dilemma experiments, Isomorphic invariance, Public goods game, Prisoners’ dilemma game, Voluntary cooperation. |
| JEL: | C71 C92 D70 D90 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2023:09&r=gth |
| By: | Boyu Zhang; Yali Dong; Cheng-Zhong Qin; Sergey Gavrilets |
| Abstract: | Kin selection and direct reciprocity are two most basic mechanisms for promoting cooperation in human society. Generalizing the standard models of the multi-player Prisoner's Dilemma and the Public Goods games for heterogeneous populations, we study the effects of genetic relatedness on cooperation in the context of repeated interactions. Two sets of interrelated results are established: a set of analytical results focusing on the subgame perfect equilibrium and a set of agent-based simulation results based on an evolutionary game model. We show that in both cases increasing genetic relatedness does not always facilitate cooperation. Specifically, kinship can hinder the effectiveness of reciprocity in two ways. First, the condition for sustaining cooperation through direct reciprocity is harder to satisfy when relatedness increases in an intermediate range. Second, full cooperation is impossible to sustain for a medium-high range of relatedness values. Moreover, individuals with low cost-benefit ratios can end up with lower payoffs than their groupmates with high cost-benefit ratios. Our results point to the importance of explicitly accounting for within-population heterogeneity when studying the evolution of cooperation. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.19026&r=gth |
| By: | Marina Agranov; Jeongbin Kim; Leeat Yariv |
| Abstract: | The experimental literature on repeated games has largely focused on settings where players discount the future identically. In applications, however, interactions often occur between players whose time preferences differ. We study experimentally the effects of discounting differentials in infinitely repeated coordination games. In our data, differential discount factors play two roles. First, they provide a coordination anchor: more impatient players get higher payoffs first. Introducing even small discounting differentials reduces coordination failures significantly. Second, with pronounced discounting differentials, intertemporal trades are prevalent: impatient players get higher payoffs for an initial phase and patient players get higher payoffs in perpetuity afterward. |
| JEL: | C73 C92 D15 D25 |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:31288&r=gth |
| By: | Franke, Jörg; Metzger, Lars P. |
| Abstract: | We consider a simple contest game with draws where with some probability none of the contestants is selected as winner. If such an outcome occurs, then the contest is repeated in the next period unless either one of the contestants wins the prize or until a final last period is reached. Allowing for finite as well as infinite time horizons and different variations in the timing of effort decisions, the theoretical analysis of this model reveals that the dynamic contest structure has profound implications for intertemporal effort substitution and contest revenue. |
| Keywords: | Contest theory, repeated contest, dynamic contest, contest with draws |
| JEL: | C72 C73 D72 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:rwirep:1016&r=gth |
| By: | Emiliano Catonini; Nicodemo De Vito |
| Abstract: | We define notions of cautiousness and cautious belief to provide epistemic conditions for iterated admissibility in finite games. We show that iterated admissibility characterizes the behavioral implications of "cautious rationality and common cautious belief in cautious rationality" in a terminal lexicographic type structure. For arbitrary type structures, the behavioral implications of these epistemic assumptions are characterized by the solution concept of self-admissible set (Brandenburger, Friedenberg and Keisler 2008). We also show that analogous conclusions hold under alternative epistemic assumptions, in particular if cautiousness is "transparent" to the players. KEYWORDS: Epistemic game theory, iterated admissibility, weak dominance, lexicographic probability systems. JEL: C72. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.15330&r=gth |
| By: | Anabel Doñate-Buendía (Universitat Jaume I); Hernán Bejarano (Centro de Investigación y Docencias Económicas); Aurora García-Gallego (Universitat Jaume I) |
| Abstract: | In the impunity game, a proposer offers a division of money and a responder decides whether to accept or reject the offer. If the offer is accepted, the proposer and the responder receive the amount specified in the proposal. If the offer is rejected, the responder earns nothing and the proposer keeps the money he designated for himself. Thus, the theoretical prediction of this game states that the responder should accept any offer. An experiment is designed aiming at analysing both players’ behaviour in the impunity game when subjects are aware of the gender of their partner. Additionally, we examine the effect of different stake sizes. An online experiment with eight different treatments is implemented, with a total number of 1, 210 observations. The main findings are that proposers give to responders an important (around 35%) share on average, and that both the stake size and gender identification influence their decisions. Moreover, responders’ rejection patterns follow the game theoretical prediction, although the hypothesis that knowing your counterpart sex/gender affects responders’ behaviour cannot be rejected. Finally, subjects’ behaviour in this game is found to be determined by their personality and psychopathy traits, as well as by their emotional intelligence level. Other sociodemographic characteristics like place of birth or their employment status are found to also influence their decisions. |
| Keywords: | impunity game; experiment; gender identification; stake size |
| JEL: | C90 C88 D63 D64 D91 |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:aoz:wpaper:249&r=gth |
| By: | José Ignacio Rivero Wildemauwe (Université de Cergy-Pontoise, THEMA) |
| Abstract: | I study a bilateral trade setting with asymmetric information, where one side has all the bargaining power and makes a take-it-or-leave-it price offer. Both agents hold a certain degree of Kantian morality and thus care about what would have happened had their actions been adopted by their counterpart. In order to capture this, I implement a Veil-of-Ignorance approach, whereby players are uncertain about their role and are thus forced to submit strategies for both the case where they are the Buyer and the Seller. More precisely, in the first stage, both agents propose the price at which they would be willing to buy, while in a second stage they decide whether they would accept to sell at the offered price. Buyer and Seller roles are randomly assigned in the last stage. I consider adverse selection by assuming that the Seller is fully informed about the product’s quality, while the Buyer can only form an expectation about it. I show that when the degree of morality is low, the expected quality necessary to produce efficient equilibria is lower than that required by purely selfish agents and, moreover, it is decreasing in the intensity of the moral concern. I also find a threshold degree of morality above which only efficient equilibria are possible for any expectation about quality. Moral preferences thus mitigate the adverse selection problem and completely eliminate it when sufficiently strong. |
| Keywords: | bilateral trade; sequential; asymmetric information; homo moralis; Veil of Ignorance. |
| JEL: | D03 D82 D91 C78 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ema:worpap:2023-11&r=gth |
| By: | Dongwei Zhao; Audun Botterud; Marija Ilic |
| Abstract: | This paper evaluates market equilibrium under different pricing mechanisms in a two-settlement 100%-renewables electricity market. Given general probability distributions of renewable energy, we establish game-theoretical models to analyze equilibrium bidding strategies, market prices, and profits under uniform pricing (UP) and pay-as-bid pricing (PAB). We prove that UP can incentivize suppliers to withhold bidding quantities and lead to price spikes. PAB can reduce the market price, but it may lead to a mixed-strategy price equilibrium. Then, we present a regulated uniform pricing scheme (RUP) based on suppliers' marginal costs that include penalty costs for real-time deviations. We show that RUP can achieve lower yet positive prices and profits compared with PAB in a duopoly market, which approximates the least-cost system outcome. Simulations with synthetic and real data find that under PAB and RUP, higher uncertainty of renewables and real-time shortage penalty prices can increase the market price by encouraging lower bidding quantities, thereby increasing suppliers' profits. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.12309&r=gth |
| By: | Yuanyuan Chang; Dena Firoozi; David Benatia |
| Abstract: | This paper aims to investigate the impact of large banks on the financial system stability. To achieve this, we employ a linear-quadratic-Gaussian (LQG) mean-field game (MFG) model of an interbank market, which involves one large bank and multiple small banks. Our approach involves utilizing the MFG methodology to derive the optimal trading strategies for each bank, resulting in an equilibrium for the market. Subsequently, we conduct Monte Carlo simulations to explore the role played by the large bank in systemic risk under various scenarios. Our findings indicate that while the major bank, if its size is not too large, can contribute positively to stability, it also has the potential to generate negative spillover effects in the event of default, leading to increased systemic risk. We also discover that as banks become more reliant on the interbank market, the overall system becomes more stable but the probability of a rare systemic failure increases. This risk is further amplified by the presence of a large bank, its size, and the speed of interbank trading. Overall, the results of this study provide important insights into the management of systemic risk. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.17830&r=gth |
| By: | Minhyeok Lee |
| Abstract: | In this paper, we navigate the intricate domain of reviewer rewards in open-access academic publishing, leveraging the precision of mathematics and the strategic acumen of game theory. We conceptualize the prevailing voucher-based reviewer reward system as a two-player game, subsequently identifying potential shortcomings that may incline reviewers towards binary decisions. To address this issue, we propose and mathematically formalize an alternative reward system with the objective of mitigating this bias and promoting more comprehensive reviews. We engage in a detailed investigation of the properties and outcomes of both systems, employing rigorous game-theoretical analysis and deep reinforcement learning simulations. Our results underscore a noteworthy divergence between the two systems, with our proposed system demonstrating a more balanced decision distribution and enhanced stability. This research not only augments the mathematical understanding of reviewer reward systems, but it also provides valuable insights for the formulation of policies within journal review system. Our contribution to the mathematical community lies in providing a game-theoretical perspective to a real-world problem and in the application of deep reinforcement learning to simulate and understand this complex system. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.12088&r=gth |
| By: | Antelo, Manel; Bru, Lluís |
| Abstract: | We study the licensing of a product innovation from an external innovator in a duopoly of firms that compete sequentially with each other through quantities or prices. We find that the innovation is only licensed to a single firm, regardless of market competition. However, both the licensee and contractual terms under quantity competition differ from those under price competition. In the first case, the innovation is licensed to the market-leading firm through a non-distorting contract, and in the second case, to the market-following firm by means of a two-part tariff (distorting) contract involving a per-unit royalty. |
| Keywords: | Product innovation, licensing, Stackelberg duopoly, quantity competition, price competition |
| JEL: | D43 D45 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:117542&r=gth |
| By: | Marco Magnani (University of Padova and ARERA); Federico Navarra (University of Padova) |
| Abstract: | We study the incentives of a monopolistic hybrid platform in sharing its superior market information with the third-party seller hosted on its marketplace. After observing platform information-sharing policy, the seller competes in prices with the platform over a horizontally differentiated good. Despite platform duality, an equilibrium in which the platform shares information with the seller occurs. We highlight how the platform has incentives to share information either for relaxing price-competition or for increasing the volume of transactions. Platform incentives to share information are strongest for intermediate degrees of product differentiation. Information provision results in consumer surplus extraction such that the total welfare is reduced. Although entering as a seller and providing market information is profitable, when analysing platform entry as the acquisition of one of the sellers we may observe equilibria in which the platform either sticks to agency or does not provide information since this would increase the entry cost. |
| Keywords: | hybrid platforms, information provision, data sharing, vertical integration. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:pad:wpaper:0301&r=gth |
| By: | Qianjun Lyu; Wing Suen; Yimeng Zhang |
| Abstract: | We study an information design problem with continuous state and discrete signal space. We find that the designer's interim value function affects the solution only through its curvature. There is a dual relation between the prior distribution and the marginal value function. Under convex value functions, the optimal information structure is interval-partitional. Moreover, in logconcave environments, a center of scrutiny emerges and information becomes coarser for states farther from it. We locate the scrutiny center and provide comparative statics on information structure with respect to prior distributions and value functions. The analysis can be extended to S-shaped value functions. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.18020&r=gth |
| By: | Akaki Mamageishvili; Mahimna Kelkar; Jan Christoph Schlegel; Edward W. Felten |
| Abstract: | We design a practical algorithm for transaction ordering that takes into account both transaction timestamps and bids. The algorithm guarantees that users get their transactions published with bounded delay against a bid, while it extracts a fair value from sophisticated users that have an edge in latency, by moving expenditure from investment in latency improvement technology to bidding. The algorithm creates a score from timestamps and bids, and orders transactions based on the score. We first show that a scoring rule is the only type of rule that satisfies the independence of latency races. We provide an economic analysis of the protocol in an environment of private information, where investment in latency is made ex-ante or interim stages, while bidding happens at the interim stage where private signals have been observed. The algorithm is useful for transaction sequencing in rollups or in other environments where the sequencer has privileged access to order flows. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.02179&r=gth |