|
on Game Theory |
| By: | Olivier GOSSNER (CNRS – CREST, Institut Polytechnique de Paris and Department of Mathematics, London School of Economics.) |
| Abstract: | We study the robustness of equilibria with regards to small payoff perturbations of the dynamic game. We show that complete penal codes, that specify players’ strategies after every history, have only limited robustness. We define incomplete penal codes as partial descriptions of equilibrium strategies and introduce a notion of robustness for incomplete penal codes. We prove a Folk Theorem in robust incomplete codes that generates a Folk Theorem in a class of stochastic games. |
| Keywords: | Repeated games, stochastic games, Folk Theorem, robust equilibrium. |
| Date: | 2020–12–09 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpaper:2020-29&r=all |
| By: | Vincent Boucher (CRREP - Centre de recherche sur les risques, les enjeux économiques, et les politiques publiques - ULaval - Université Laval [Québec], CREATE, Centre de Recherche en économie de l'Environnement, de l'Agroalimentaire, des Transports et de l'Énergie - ULaval - Université Laval [Québec]); Yann Bramoullé (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université) |
| Abstract: | Heckman and MaCurdy (1985) first showed that binary outcomes are compatible with linear econometric models of interactions. This key insight was unduly discarded by the literature on the econometrics of games. We consider general models of linear interactions in binary outcomes that nest linear models of peer effects in networks and linear models of entry games. We characterize when these models are well defined. Errors must have a specific discrete structure. We then analyze the models' game-theoretic microfoundations. Under complete information and linear utilities, we characterize the preference shocks under which the linear model of interactions forms a Nash equilibrium of the game. Under incomplete information and independence, we show that the linear model of interactions forms a Bayes-Nash equilibrium if and only if preference shocks are iid and uniformly distributed. We also obtain conditions for uniqueness. Finally, we propose two simple consistent estimators. We revisit the empirical analyses of teenage smoking and peer effects of Lee, Li, and Lin (2014) and of entry into airline markets of Ciliberto and Tamer (2009). Our reanalyses showcase the main interests of the linear framework and suggest that the estimations in these two studies suffer from endogeneity problems. |
| Keywords: | Binary Outcomes,Linear Probability Model,Peer Effects,Econometrics of Games |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-03031767&r=all |
| By: | Péter Bayer (TSE - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Ani Guerdjikova (GAEL - Laboratoire d'Economie Appliquée de Grenoble - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA [2020-....] - Université Grenoble Alpes [2020-....] - CNRS - Centre National de la Recherche Scientifique - UGA [2020-....] - Université Grenoble Alpes [2020-....]) |
| Abstract: | We analyze a model of endogenous two-sided network formation where players are affected by uncertainty in their opponents' decisions. We model this uncertainty using the notion of equilibrium under ambiguity (Eichberger and Kelsey, 2014). Unlike the set of Nash equilibria, the set of equilibria under ambiguity does not always include underconnected and thus inefficient networks such as the empty network. On the other hand, it may include networks with unreciprocated, one-way links, which comes with an efficiency loss as linking efforts are costly. We characterize equilibria under ambiguity and provide conditions under which increased player optimism comes with an increase in efficiency in equilibrium. Next, we analyze the dynamic situation with one-sided, myopic updating with regular optimistic shocks and derive a global stability condition of benefit-maximizing equilibrium networks. |
| Keywords: | network formation,ambiguity,equilibrium selection,Pareto-optimality,optimism,pessimism |
| Date: | 2020–11–13 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03005107&r=all |
| By: | Peter G Moffatt (School of Economics, University of East Anglia, Norwich.); Ganna Pogrebna (The Alan Turing Institute, The University of Sydney); Graciela Zevallos-Porles (School of Economics, University of East Anglia, Norwich.) |
| Abstract: | In the context of guessing games, we propose the Sophisticated Reasoning Model (SRM) which includes a “sophisticated†type. A parameter ps represents the proportion of sophisticated players in the population. Asophisticated player is one who forms a belief (eps) of the proportion of the population who are sophisticated (following the same cognitive process as themselves) and best responds to this belief. The model nests the standard Level-k and cognitive hierarchy models (when eps = 0) and also Nash behaviour (when eps = 1). Moreover, a sophisticated player with correct beliefs (eps = ps) has best response equal to the winning guess. The model is extended to allow heterogeneity in beliefs. When applied to field data from a guessing game, only 9% of players are estimated to be sophisticated, but these players greatly over-estimate the proportion who are of the same type. This is interpreted as a manifestation of the Dunning-Kruger effect. |
| Keywords: | Beauty contest game; Sophisticated reasoning model; Level k-model; Cognitive hierarchy model; Dunning-Kruger effect. |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:uea:wcbess:20-06&r=all |
| By: | Louis Abraham |
| Abstract: | We study two questions related to competition on the OTC CDS market using data collected as part of the EMIR regulation. First, we study the competition between central counterparties through collateral requirements. We present models that successfully estimate the initial margin requirements. However, our estimations are not precise enough to use them as input to a predictive model for CCP choice by counterparties in the OTC market. Second, we model counterpart choice on the interdealer market using a novel semi-supervised predictive task. We present our methodology as part of the literature on model interpretability before arguing for the use of conditional entropy as the metric of interest to derive knowledge from data through a model-agnostic approach. In particular, we justify the use of deep neural networks to measure conditional entropy on real-world datasets. We create the $\textit{Razor entropy}$ using the framework of algorithmic information theory and derive an explicit formula that is identical to our semi-supervised training objective. Finally, we borrow concepts from game theory to define $\textit{top-k Shapley values}$. This novel method of payoff distribution satisfies most of the properties of Shapley values, and is of particular interest when the value function is monotone submodular. Unlike classical Shapley values, top-k Shapley values can be computed in quadratic time of the number of features instead of exponential. We implement our methodology and report the results on our particular task of counterpart choice. Finally, we present an improvement to the $\textit{node2vec}$ algorithm that could for example be used to further study intermediation. We show that the neighbor sampling used in the generation of biased walks can be performed in logarithmic time with a quasilinear time pre-computation, unlike the current implementations that do not scale well. |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2012.01883&r=all |
| By: | Chukwudi Henry Dike |
| Abstract: | This paper models interactions of firms in a pre-trading(fixed network of lending/borrowing) period whereby firms set fixed lending rates given loan management cost. We show strategic substitution in the rate each firm sets and more fundamentally, propose that the rates charged to debtors by a creditor firm is likened to results from a private provision of public good in networks game. We then highlight specific core-periphery network properties in relation to interdependence and Nash rate charged by firms. For welfare policies, we find neutrality of intervention policies that create or reduce transaction cost and improvement based on policies that provide administrative subsidies thus creating an avenue for cost effective resource transfer policy. Lastly, we find significant relationship between a firms centrality measured by weaker negative externality and welfare improvement due to such subsidy. |
| JEL: | C72 D44 D85 E43 H23 |
| Date: | 2020–12–09 |
| URL: | http://d.repec.org/n?u=RePEc:jmp:jm2020:pdi579&r=all |
| By: | Johannes Hörner; Nicolas Klein; Sven Rady |
| Abstract: | This paper considers a class of experimentation games with Lévy bandits encompassing those of Bolton and Harris (1999) and Keller, Rady and Cripps (2005). Its main result is that efficient (perfect Bayesian) equilibria exist whenever players’ payoffs have a diffusion component. Hence, the trade-offs emphasized in the literature do not rely on the intrinsic nature of bandit models but on the commonly adopted solution concept (MPE). This is not an artifact of continuous time: we prove that such equilibria arise as limits of equilibria in the discrete-time game. Furthermore, it suffices to relax the solution concept to strongly symmetric equilibrium. |
| Keywords: | Two-Armed Bandit, Bayesian Learning, Strategic Experimentation, Strongly Symmetric Equilibrium |
| JEL: | C73 D83 |
| Date: | 2019–11 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2019_135v1&r=all |
| By: | Aureo de Paula; Xun Tang |
| Abstract: | We study testable implications of multiple equilibria in discrete games with incomplete information. Unlike de Paula and Tang (2012), we allow the players' private signals to be correlated. In static games, we leverage independence of private types across games whose equilibrium selection is correlated. In dynamic games with serially correlated discrete unobserved heterogeneity, our testable implication builds on the fact that the distribution of a sequence of choices and states are mixtures over equilibria and unobserved heterogeneity. The number of mixture components is a known function of the length of the sequence as well as the cardinality of equilibria and unobserved heterogeneity support. In both static and dynamic cases, these testable implications are implementable using existing statistical tools. |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2012.00787&r=all |
| By: | Jens Gudmundsson (Department of Food and Resource Economics, University of Copenhagen); Jens Leth Hougaard (NYU-Shanghai, China; Department of Food and Resource Economics, University of Copenhagen) |
| Abstract: | We introduce a reciprocity protocol, an innovative approach to coordinating and sharing rewards in blockchains. Inherently decentralized and easy to implement, it puts emphasis on incentives rather than forcing specific sharing rules from the outset. Analyzing the non-cooperative game the protocol induces, we identify a robust, strict, and Pareto-dominant symmetric equilibrium. In it, even self-centered participants show extensive reciprocity to one another. Thus, despite a setting that is generally unfavorable to reciprocal behavior, the protocol manages to build trust between the users by taking on a role akin to a social contract. |
| Keywords: | Blockchain, reciprocity, protocol design, Nash equilibrium |
| JEL: | C62 C72 D02 D63 D91 |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:foi:wpaper:2020_14&r=all |
| By: | Dietzenbacher, Bas (Tilburg University, School of Economics and Management) |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiutis:6caea8c0-1dcd-4038-88da-bbf034bd65b6&r=all |
| By: | Stephan Lauermann; Asher Wolinsky |
| Abstract: | This paper analyzes a common-value, …rst-price auction with state-dependent participation. The number of bidders, which is unobservable to them, depends on the true value. For exogenously given participation patterns that involve many bidders in each state, the bidding equilibrium may be of a “pooling” type—with high probability, the winning bid is the same across states and is below the ex-ante expected value—or of a “partially revealing” type—with no signi…cant atoms in the winning bid distribu- tion and an expected winning bid increasing in the true value. Which of these forms will arise is determined by the likelihood ratio at the top of the signal distribution and the participation across states. When the state-dependent participation is endogenized as the strategic solicitation by an informed seller who bears a small cost for each solicited bidder, an equilibrium of the partially revealing type always exists and is unique of this type; for certain signal distributions there also exist equilibria of the pooling type. |
| Keywords: | Search, Auctions, Adverse Selection |
| JEL: | C78 D83 |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2018_063v2&r=all |
| By: | Garcia, Arturo; Leal, Mariel; Lee, Sang-Ho |
| Abstract: | We study the firm's strategic choice of corporate social responsibility (CSR) in a managerial delegation framework where a multiproduct corporation competes against a single plant firm. We examine simultaneous-move versus sequential-move in output choices when CSR decisions are simultaneous. We show that both firms adopt CSR in a simultaneous-move game, whereas only the follower firm adopts CSR (but not the leader firm) in sequential-move games. We also consider an endogenous timing game in output choices between the two firms and show that a simultaneous-move is an equilibrium when the products are substitutes or weak complements, while a single plant firm's leadership is an equilibrium when the products are sufficiently strong complements. Our findings can explain the widely observed phenomenon, in the real world, of different industries in which firms' CSR activities are more or less (even non-CSR or negative CSR) commonly widespread. It also partially helps us understand CSR's strategic motives and its relations with the firm's profits. |
| Keywords: | corporate social responsibility; managerial delegation; multiproduct corporation; endogenous timing game |
| JEL: | D21 L13 L22 M14 |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:104431&r=all |
| By: | Sebasti\'an Morales; Charles Thraves |
| Abstract: | In an election campaign, candidates must decide how to optimally allocate their efforts/resources optimally among the regions of a country. As a result, the outcome of the election will depend on the players' strategies and the voters' preferences. In this work, we present a zero-sum game where two candidates decide how to invest a fixed resource in a set of regions, while considering their sizes and biases. We explore the Majority System (MS) as well as the Electoral College (EC) voting systems. We prove equilibrium existence and uniqueness under MS in a deterministic model; in addition, their closed form expressions are provided when fixing the subset of regions and relaxing the non-negative investing constraint. For the stochastic case, we use Monte Carlo simulations to compute the players' payoffs, together with its gradient and hessian. For the EC, given the lack of Equilibrium in pure strategies, we propose an iterative algorithm to find Equilibrium in mixed strategies in a subset of the simplex lattice. We illustrate numerical instances under both election systems, and contrast players' equilibrium strategies. Finally, we show that polarization induces candidates to focus on larger regions with negative biases under MS, whereas candidates concentrate on swing states under EC. |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2012.02856&r=all |
| By: | Goncalo dos Reis; Vadim Platonov |
| Abstract: | We study a portfolio management problem featuring many-player and mean-field competition, investment and consumption, and relative performance concerns under the forward performance processes (FPP) framework. We focus on agents using power (CRRA) type FPPs for their investment-consumption optimization problem an under common noise Merton market model and we solve both the many-player and mean-field game providing closed-form expressions for the solutions where the limit of the former yields the latter. In our case, the FPP framework yields a continuum of solutions for the consumption component as indexed to a market parameter we coin "market consumption intensity". The parameter permits the agent to set a preference for their consumption going forward in time that, in the competition case, reflects a common market behaviour. We show the FPP framework, under both competition and no-competition, allows the agent to disentangle his risk-tolerance and elasticity of intertemporal substitution (EIS) just like Epstein-Zin preferences under recursive utility framework and unlike the classical utility theory one. This, in turn, allows a finer analysis on the agent's consumption "income" and "substitution" regimes, and, of independent interest, motivates a new strand of economics research on EIS under the FPP framework. We find that competition rescales the agent's perception of consumption in a non-trivial manner in addition to a time-dependent "elasticity of conformity" of the agent to the market's consumption intensity. |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2012.01235&r=all |
| By: | D'Exelle, Ben (University of East Anglia); Gutekunst, Christine (University of East Anglia); Riedl, Arno (Maastricht University) |
| Abstract: | Men and women negotiate differently, which might create gender inequality in access to resources as well as efficiency losses due to disagreement. We study the role of gender and gender pairing in bilateral bargaining, using a lab-in-the-field experiment in which pairs of participants bargain over the division of a fixed amount of resources. We vary the gender composition of the bargaining pairs as well as the disclosure of the participants' identities. We find gender differences in earnings, agreement and demands, but only when the identities are disclosed. Women in same-gender pairs obtain higher earnings than men and women in mixed-gender pairs. This is the result of the lower likelihood of disagreement among women-only pairs. Women leave more on the bargaining table, conditional on their beliefs, which contributes to the lower disagreement and higher earnings among women-only pairs. |
| Keywords: | bargaining, gender, gender pairing, beliefs, experiment |
| JEL: | C9 J16 O12 |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp13916&r=all |
| By: | Christoph Belak; Daniel Hoffmann; Frank T. Seifried |
| Abstract: | We formulate and analyze a mathematical framework for continuous-time mean field gameswith finitely many states and common noise, including a rigorous probabilistic constructionof the state process. The key insight is that we can circumvent the master equation andreduce the mean field equilibrium to a system of forward-backward systems of (random)ordinary differential equations by conditioning on common noise events. In the absenceof common noise, our setup reduces to that of Gomes, Mohr and Souza [GMS13] andCecchin and Fischer [CF20]. |
| Keywords: | mean field games, common noise, Markov chains, regime shifts |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:trr:qfrawp:202005&r=all |
| By: | Stefan Ambec (TSE - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) |
| Abstract: | Environmental markets distribute tradable rights on natural resources that are available for free on the earth such as water, biomass or clean air. In a framework where users differ solely in respect of their access to the resource, I investigate the allocation of rights that are accepted in the sense that, after trading, users obtain at least what they can achieve by sharing the resources they control. I show that, among all accepted rights, the more egalitarian ones do not allow any redistribution among users. Consequently, compared to an efficient allocation of resources, the net trading of rights always increases inequality. |
| Keywords: | Common-pool resources,Environmental externalities,Property rights,Cooperative game,Fairness,Tradable quotas,Emission permits |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02945513&r=all |
| By: | Liyang Han; Jalal Kazempour; Pierre Pinson |
| Abstract: | When energy customers schedule loads ahead of time, this information, if acquired by their energy retailer, can improve the retailer's load forecasts. Better forecasts lead to wholesale purchase decisions that are likely to result in lower energy imbalance costs, and thus higher profits for the retailer. Therefore, this paper monetizes the value of the customer schedulable load data by quantifying the retailer's profit gain from adjusting the wholesale purchase based on such data. Using a cooperative game theoretic approach, the retailer translates their increased profit in expectation into the value of cooperation, and redistributes a portion of it among the customers as monetary incentives for them to continue providing their load data. Through case studies, this paper demonstrates the significance of the additional profit for the retailer from using the proposed framework, and evaluates the long-term monetary benefits to the customers based on different payoff allocation methods. |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2012.05519&r=all |