
on Game Theory 
By:  Lijun Bo; Shihua Wang; Xiang Yu 
Abstract:  This paper studies the equilibrium consumption under external habit formation in a large population of agents. We first formulate problems under two types of conventional habit formation preferences, namely linear and multiplicative external habit formation, in a mean field game framework. In a lognormal market model with the asset specialization, we characterize one mean field equilibrium in analytical form in each problem, allowing us to understand some quantitative properties of the equilibrium strategy and conclude distinct financial implications caused by different consumption habits from a mean field perspective. In each problem with $n$ agents, we then construct an approximate Nash equilibrium for the $n$player game using the obtained mean field equilibrium when $n$ is sufficiently large. The explicit convergence order in each problem can also be obtained. 
Date:  2022–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2206.13341&r= 
By:  Yurong Chen; Xiaotie Deng; Yuhao Li 
Abstract:  To take advantage of strategy commitment, a useful tactic of playing games, a leader must learn enough information about the follower's payoff function. However, this leaves the follower a chance to provide fake information and influence the final game outcome. Through a carefully contrived payoff function misreported to the learning leader, the follower may induce an outcome that benefits him more, compared to the ones when he truthfully behaves. We study the follower's optimal manipulation via such strategic behaviors in extensiveform games. Followers' different attitudes are taken into account. An optimistic follower maximizes his true utility among all game outcomes that can be induced by some payoff function. A pessimistic follower only considers misreporting payoff functions that induce a unique game outcome. For all the settings considered in this paper, we characterize all the possible game outcomes that can be induced successfully. We show that it is polynomialtime tractable for the follower to find the optimal way of misreporting his private payoff information. Our work completely resolves this follower's optimal manipulation problem on an extensiveform game tree. 
Date:  2022–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2206.13119&r= 
By:  Blázquez, Mario (Dept. of Business and Management Science, Norwegian School of Economics); Koptyug, Nikita (Research Institute of Industrial Economics) 
Abstract:  In HawkDove games with mulitiplicity of equilibria, we study which equilibria are selected using various equilibrium selection methods. Using a uniform price auction as an illustrative example, we apply the tracing procedure method of Harsanyi and Selten (1988), the robustness to strategic uncertainty method of Andersson, Argenton and Weibull (2014), and the quantal response method of McKelvey and Palfrey (1998) to predict which equilibrium is selected by the players and how changes to the various model parameters impact the selected equilibria. 
Keywords:  HawkDove games; equilibrium selection; tracing procedure method; robustness to strategic uncertainty method; quantal response method 
JEL:  C72 C79 D44 D47 
Date:  2022–06–29 
URL:  http://d.repec.org/n?u=RePEc:hhs:nhhfms:2022_012&r= 
By:  Raouf Boucekkine (ESC Rennes School of Business  ESC Rennes School of Business); Carmen Camacho (PSE  Paris School of Economics  UP1  Université Paris 1 PanthéonSorbonne  ENSPSL  École normale supérieure  Paris  PSL  Université Paris sciences et lettres  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE  Paris Jourdan Sciences Economiques  UP1  Université Paris 1 PanthéonSorbonne  ENSPSL  École normale supérieure  Paris  PSL  Université Paris sciences et lettres  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Weihua Ruan (Purdue University Northwest); Benteng Zou (University of Luxembourg [Luxembourg]) 
Abstract:  We use a parsimonious twostage differential game setting where the duration of the first stage, the coalition stage, depends on the will of a particular player to leave the coalition through an explicit timing variable. By specializing in a standard linearquadratic environmental model augmented with a minimal constitutional setting for the coalition (payoff share parameter), we are able to analytically extract several nontrivial findings. Three key aspects drive the results: the technological gap as an indicator of heterogeneity across players, the constitution of the coalition and the intensity of the public bad (here, the pollution damage). We provide with a full analytical solution to the twostage differential game. In particular, we characterize the intermediate parametric cases leading to optimal finite time splitting. A key characteristic of these finitetimelived coalitions is the requirement of the payoff share accruing to the splitting country to be large enough. Incidentally, our twostage differential game setting reaches the conclusion that splitting countries are precisely those which use to benefit the most from the coalition. Constraining the payoff share to be low by Constitution may lead to optimal everlasting coalitions only provided initial pollution is high enough, which may cover the emergency cases we are witnessing nowadays. 
Keywords:  Coalition splitting,Constitutional vs technological heterogeneity,Environmental agreements,Multistage optimal control Coalition splitting,Differential games 
Date:  2022–05 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs03676670&r= 
By:  Michela Chessa; Nobuyuki Hanaki; Aymeric Lardon; Takashi Yamada 
Abstract:  In this experiment, we compare three implementations of the Winter demand commitment bargaining mechanism: a oneperiod implementation, a twoperiod implementation with low delay costs, and a twoperiod implementation with high delay costs. Despite the different theoretical predictions, our results show that the three different implementations result in similar outcomes in all our investigation domains: namely, coalition formation, alignment with the Shapley value prediction, and satisfaction of the axioms. Our results suggest that a lighter bargaining implementation with only one period is often sufficient in providing allocations that sustain the Shapley value as an appropriate cooperative solution concept, while saving unnecessary time and resource costs. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:dpr:wpaper:1152r&r= 
By:  Vincent Leon; S. Rasoul Etesami; Rakesh Nagi 
Abstract:  We consider the diffusion of innovation in social networks using a gametheoretic approach. Each individual plays a coordination game with its neighbors and decides what alternative product to adopt to maximize its payoff. As products are used in conjunction with others and through repeated interactions, individuals are more interested in their longterm benefits and tend to show trustworthiness to others to maximize their longterm payoffs. To capture such trustworthy behavior, we deviate from the expected utility theory and use a new notion of rationality based on limitedtrust equilibrium (LTE). By incorporating such notion into the diffusion model, we analyze the convergence of emerging dynamics to their equilibrium points using a meanfield approximation. We study the equilibrium state and the convergence rate of the diffusion process using the absorption probability and the expected absorption time of a reducedsize absorbing Markov chain. We also show that the LTE diffusion model under the bestresponse strategy can be converted to the wellknown linear threshold model. Simulations show that when agents behave trustworthily, their longterm payoffs will increase significantly compared to the case when they are solely selfinterested. Moreover, the Markov chain analysis provides a good estimation of the convergence property over random networks. 
Date:  2022–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2206.06318&r= 
By:  Leonardo Massai; Giacomo Como; Fabio Fagnani 
Abstract:  We study the equilibrium state of an energy market composed of producers who compete to supply energy to different markets and want to maximize their profits. The energy market is modeled by means of a graph that represents a constrained power network where nodes represent the markets and links are the physical lines with a finite capacity connecting them. Producers play a networked Cournot game on such a network together with a centralized authority, called market maker, that facilitates the trade between geographically separate markets via the constrained power network and aims to maximize a certain welfare function. We study existence of uniqueness of the Nash equilibria and prove a connection between capacity bottlenecks in the power network and the emergence of price differences between different markets that are separated by bottlenecked lines. 
Date:  2022–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2206.08133&r= 
By:  Alexei Parakhonyak; Anton Sobolev 
Abstract:  We consider an information design problem when the sender faces ambiguity regarding the probability distribution over the states of the world, the utility function and the prior of the receiver. The solution concept is minimax loss (regret), that is, the sender minimizes the distance from the full information benchmark in the worstcase scenario. We show that in the binary states and binary actions setting the optimal strategy involves a mechanism with a continuum of messages, which admits a representation as a randomization over mechanisms consisting of two messages. A small level of uncertainty regarding the re ceiver’s prior makes the sender more truthful than in the full information benchmark, but as uncertainty increases at some point the sender starts to lie more. If the sender either knows the probability distribution over the states of the world, or knows that the receiver knows it, then the maximal loss is bounded from above by 1/e. This result generalizes to an infinite state model, provided that the set of admissible mechanisms is limited to cutoff strategies. 
Keywords:  Persuasion, Robustness, Multiple priors, Minimax regret 
JEL:  D81 D82 D83 
Date:  2022–07 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2022_359&r= 
By:  Gong, Doudou (RS: GSBE other  not themerelated research, Quantitative Economics); Dietzenbacher, Bas (RS: GSBE other  not themerelated research, QE Math. Economics & Game Theory); Peters, Hans (RS: FSE DKE Mathematics Centre Maastricht, QE Math. Economics & Game Theory) 
Abstract:  A mechanism allocates one unit of an infinitely divisible commodity among agents reporting a number between zero and one. Nash, Pareto optimal Nash, and strong equilibria are analyzed for the case where the agents have singledipped preferences. One of the main results is that when the mechanism is anonymous, monotonic, standard, and order preserving, then the Pareto optimal Nash and strong equilibria coincide and assign Pareto optimal allocations that are characterized by socalled maximal coalitions: members of a maximal coalition prefer an equal coalition share over obtaining zero, whereas the outside agents prefer zero over obtaining an equal share from joining the coalition. 
JEL:  C72 D71 
Date:  2022–07–18 
URL:  http://d.repec.org/n?u=RePEc:unm:umagsb:2022007&r= 
By:  Davide Bosco; Luca Portoghese 
Abstract:  This paper presents a stylised socialinteraction game where the implementation of a lockdown policy is delegated to the decentralised, uncoordinated decisionmaking of a large population of atomistic agents â€“ assumed riskneutral and demographically heterogeneous. Compliance with policy prescriptions is socially beneficial but individually costly. In the static, it determines the individual risk of contagion in social interactions (at the microlevel) and the number of new infections (at the macro). Over time, it affects the peak prevalence of the disease and the duration of the epidemic. Albeit atomistic, agents act strategically, for they rationally anticipate othersâ€™ behaviour when deciding (not) to comply. Three are the key results of our analysis. First, the strategic incentives faced by the agents coevolve with the epidemic. When prevalence is low, compliance is a dominated strategy. When prevalence is high, individual decisions to comply are strategic substitutes: older/weaker agents selfprotect by implementing social distancing and younger/healthier ones freeride. Second, the strategic incentives faced by the agents coevolve, too, with their beliefs about susceptibility. When they disregard any information about their past behaviour and use the aggregates to estimate susceptibility, strategic substitutability prevails. When beliefs are pathdependent, both complementarity and substitutability may arise. Third, we show that SIRbased models that fail to account for the endogenous response to policy prescriptions may substantially overestimate the effectiveness of lockdowns. Incidentally, we highlight that myopic behaviour may cease to be rational in a dynamic setting where agentsâ€™ beliefs about susceptibility are pathdependent. 
Keywords:  COVID19, Contagion, Social distancing, Collective action, Strategic complements and substitutes 
JEL:  C72 D71 H41 I13 
Date:  2022–06 
URL:  http://d.repec.org/n?u=RePEc:mib:wpaper:500&r= 
By:  Maria Gabriella Graziano (University of Naples Federico II and CSEF.); Vincenzo Platino (University of Naples Federico II and CSEF.) 
Abstract:  In this paper we consider a production economy and adopt a cooperative approach to equilibrium analysis which allows each individual to cooperate with others and to form a coalition whose members have access to the available technologies. Our definition of the core requires a blocking coalition to take account of the consequences of its blocking for the production of the countercoalition. Following Montesano (2002), we introduce a measure of social loss with respect to the core of the economy which characterizes the corresponding core allocations. Our characterization holds in the presence of consumption externalities and an optimistic attitude of coalition agents with respect to the behavior of outsiders. 
Keywords:  production economy, core, social loss, externalities. 
JEL:  C71 D11 D21 D62 D64 
Date:  2022–07–13 
URL:  http://d.repec.org/n?u=RePEc:sef:csefwp:649&r= 
By:  Marek Weretka (University of WisconsinMadison; Group for Research in Applied Economics (GRAPE)); Daniel Quint (University of WisconsinMadison) 
Abstract:  We present a learningbased selection argument for Linear Bayesian Nash equilibrium in a Walrasian auction. Endowments vary stochastically; traders model residual supply as linear, estimate its slope from past trade data, and periodically update these estimates. With quadratic preferences, this learning process converges to the unique LBN. In an example with nonquadratic preferences, it converges to a steady state close to a particular equilibrium of the corresponding deterministic setting; strategies played are not an equilibrium, but utility sacrificed is negligible. Anonymity and statistical learning therefore support use of LBN under quadratic utility, and motivate a related concept under nonquadratic utility. 
Keywords:  Walrasian auction, anonymous thin markets, price impacts 
JEL:  D43 D52 L13 L14 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:fme:wpaper:64&r= 
By:  Joshua S. Gans; Richard T. Holden 
Abstract:  Blockchain consensus is a state whereby each node in a network agrees on the current state of the blockchain. Existing protocols achieve consensus via a contest or voting procedure to select one node as a dictator to propose new blocks. However, this procedure can still lead to potential attacks that make consensus harder to achieve or lead to coordination issues if multiple, competing chains (i.e., forks) are created with the potential that an untruthful fork might be selected. We explore the potential for mechanisms to be used to achieve consensus that are triggered when there is a dispute impeding consensus. Using the feature that nodes stake tokens in proof of stake (POS) protocols, we construct revelation mechanisms in which the unique (subgame perfect) equilibrium involves validating nodes propose truthful blocks using only the information that exists amongst all nodes. We construct operationally and computationally simple mechanisms under both Byzantine Fault Tolerance and a Longest Chain Rule, and discuss their robustness to attacks. Our perspective is that the use of simple mechanisms is an unexplored area of blockchain consensus and has the potential to mitigate known tradeoffs and enhance scalability. 
JEL:  D02 D47 D82 D86 
Date:  2022–06 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:30189&r= 
By:  Patrick Rey; Yossi Spiegel; Konrad O. Stahl 
Abstract:  We study the feasibility and profitability of predation in a parsimonious infinitehorizon, complete information setting where an incumbent may face an entrant, in which case it needs to decide whether to accommodate or predate it. If the entrant exits, a new entrant is born with positive probability. We show that there always exists a Markov perfect equilibrium, which can be of three types: accommodation, predation with no future entry, and predation with hitandrun entry. We use the model to study alternative antitrust policies, derive the best rules for these policies, and compare their welfare effects. 
Keywords:  predation, accommodation, entry, legal rules, Markov perfect equilibrium 
JEL:  D43 L41 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_9819&r= 