
on Game Theory 
By:  Philippe De Donder; Humberto Llavador; Stefan Penczynski; John E. Roemer; Roberto Vélez 
Abstract:  Whether or not to vaccinate one's child is a decision that a parent may approach in several ways. The vaccination game, in which parents must choose whether to vaccinate a child against a disease, is one with positive externalities (herd immunity). In some societies, not vaccinating is an increasingly prevalent behavior, due to deleterious side effects that parents believe may accompany vaccination. The standard gametheoretic approach assumes that parents make decisions according to the Nash behavioral protocol, which is individualistic and noncooperative. Because of the positive externality that each child's vaccination generates for others, the Nash equilibrium suffers from a freerider problem. However, in more solidaristic societies, parents may behave cooperatively they may optimize according to the Kantian protocol, in which the equilibrium is efficient. We test, on a sample of six countries, whether childhood vaccination behavior conforms better to the individualistic or cooperative protocol. In order to do so, we conduct surveys of parents in these countries, to ascertain the distribution of beliefs concerning the subjective probability and severity of deleterious side effects of vaccination. We show that in all the countries of our sample the Kant model dominates the Nash model. We conjecture that, due to the freerider problem inherent in the Nash equilibrium, a social norm has evolved, quite generally, inducing parents to vaccinate with higher probability than they would in the noncooperative solution. Kantian equilibrium offers one precise version of such a social norm. 
Keywords:  Kantian equilibrium, Nash equilibrium, vaccination, social norm 
JEL:  C72 D62 D63 I12 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:upf:upfgen:1808&r= 
By:  Dominik Grafenhofer; Wolfgang Kuhle 
Abstract:  We study Bayesian coordination games where agents receive noisy private information over the game's payoffs, and over each others' actions. If private information over actions is of low quality, equilibrium uniqueness obtains in a manner similar to a global games setting. On the contrary, if private information over actions (and thus over the game's payoff coefficient) is precise, agents can coordinate on multiple equilibria. We argue that our results apply to phenomena such as bankruns, currency crises, recessions, or riots and revolutions, where agents monitor each other closely. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.10554&r= 
By:  Paul Belleflamme; Martin Peitz; Eric Toulemonde 
Abstract:  We introduce asymmetries across platforms in the linear model of competing twosided platforms with singlehoming on both sides and fully characterize the price equilibrium. We identify market environments in which one platform has a larger market share on both sides while obtaining a lower profit than the other platform. This platform enjoys a competitive advantage on one or both sides. Our finding raises further doubts on using market shares as a measure of market power in platform markets. 
Keywords:  Twosided platforms, market share, market power, oligopoly, network effects, antitrust 
JEL:  D43 L13 L86 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2020_204v1&r= 
By:  Moritz, KarlHeinz; Stadtmann, Georg 
Abstract:  A gametheoretic setting is used to illuminate the conflict between vaccination proponents and vaccination opponents. A central result is that vaccination proponents could in principle persuade vaccination opponents to vaccinate by means of subsidization. Such a subsidy could increase benefits for both groups. Deeper analysis provides numerous further insights regarding the stability of these results. 
Keywords:  vaccination,corona,covid,game theory,moral hazard 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:zbw:euvwdp:426&r= 
By:  Anibal Sanjab; H\'el\`ene Le Cadre; Yuting Mou 
Abstract:  In this paper, a transmissiondistribution systems flexibility market is introduced, in which system operators (SOs) jointly procure flexibility from different systems to meet their needs (balancing and congestion management) using a common market. This common market is, then, formulated as a cooperative game aiming at identifying a stable and efficient split of costs of the jointly procured flexibility among the participating SOs to incentivize their cooperation. The nonemptiness of the core of this game is then mathematically proven, implying the stability of the game and the naturallyarising incentive for cooperation among the SOs. Several cost allocation mechanisms are then introduced, while characterizing their mathematical properties. Numerical results focusing on an interconnected system (composed of the IEEE 14bus transmission system and the Matpower 18bus, 69bus, and 141bus distributions systems) showcase the cooperationinduced reduction in systemwide flexibility procurement costs, and identifies the varying costs borne by different SOs under various cost allocations methods. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.12830&r= 
By:  Claire Mouminoux (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); Christophe Dutang (CEREMADE  CEntre de REcherches en MAthématiques de la DEcision  CNRS  Centre National de la Recherche Scientifique  Université Paris DauphinePSL  PSL  Université Paris sciences et lettres); Stéphane Loisel (SAF  Laboratoire de Sciences Actuarielle et Financière  UCBL  Université Claude Bernard Lyon 1  Université de Lyon); Hansjoerg Albrecher (UNIL  Université de Lausanne) 
Abstract:  In this paper, we extend the noncooperative oneperiod game of Dutang et al. (2013) to model a nonlife insurance market over several periods by considering the repeated (oneperiod) game. Using Markov chain methodology, we derive general properties of insurer portfolio sizes given a price vector. In the case of a regulated market (identical premium), we are able to obtain convergence measures of long run market shares. We also investigate the consequences of the deviation of one player from this regulated market. Finally, we provide some insights of longterm patterns of the repeated game as well as numerical illustrations of leadership and ruin probabilities. 
Keywords:  Markov chains Mathematics Subject Classification (2010): MSC 60J10,solvency constraint,noncooperative game,consumers' price sensitivity,game theory,Markov chains Mathematics Subject Classification (2010): MSC 91G05,Markov chains Mathematics Subject Classification (2010): MSC 91A20 
Date:  2021–10–29 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03448339&r= 
By:  Flavio M. Menezes (School of Economics, University of Queensland, Brisbane, Australia); John Quiggin (School of Economics, University of Queensland, Brisbane, Australia) 
Abstract:  A number of writers have modelled imperfect markets using games in which the strategies are supply functions, that is, mappings from prices to quantities produced. Two representations of this problem have beenanalyzed, which may be referred to as ex ante and ex post, depending on whether strategies are chosen before or after demand shocks are observed. In this paper, we examine the relationship between equilibria in supply curves derived using the ex ante and ex post approaches. We derive conditions under which a linear ex ante solution coincides with the ex post solution. These conditions generalize the case of linear demand and quadratic cost, analyzed by Klemperer and Meyer. We demonstrate that all ex ante solutions derived in this way are unique. 
Date:  2021–11–16 
URL:  http://d.repec.org/n?u=RePEc:qld:uq2004:649&r= 
By:  Sihua Ding; Marcin DziubiÅ„ski; Sanjeev Goyal (Division of Social Science) 
Abstract:  A recurring theme in the study of society is the concentration of inï¬‚uence and power that is driven through unequal membership of groups and associations. In some instances these bodies constitute a small world while in others they are fragmented into distinct cliques. This paper presents a new model of clubs and networks to understand the sources of individual marginalization and the origins of diï¬€erent club networks. In our model, individuals seek to become members of clubs while clubs wish to have members. Club value is increasing in its size and in the strength of ties with other clubs. We show that a stable membership proï¬ le exhibits marginalization of individuals and that this is generally not welfare maximizing. Our second result shows that if returns from strength of ties are convex (concave) then stable memberships support fragmented networks with strong ties (small worlds held together by weak ties). We illustrate the value of these theoretical results through case studies of interlocking directorates, boards of editors of journals, and defence and R&D alliances. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:nad:wpaper:20210073&r= 
By:  Hanna Halaburda; Zhiguo He; Jiasun Li 
Abstract:  In recent years, the designs of many new blockchain applications have been inspired by the Byzantine fault tolerance (BFT) problem. While traditional BFT protocols assume that most system nodes are honest (in that they follow the protocol), we recognize that blockchains are deployed in environments where nodes are subject to strategic incentives. This paper develops an economic framework for analyzing such cases. Specifically, we assume that 1) nonByzantine nodes are rational, so we explicitly study their incentives when participating in a BFT consensus process; 2) nonByzantine nodes are ambiguity averse, and specifically, Knightian uncertain about Byzantine actions; and 3) decisions/inferences are all based on local information. The consensus game then resembles one with preplay “cheap talk” communications. We characterize all equilibria, some of which feature rational leaders withholding messages from some nodes in order to achieve consensus. These findings enrich those from traditional BFT algorithms, where an honest leader always sends messages to all nodes. We also study how the progress of communication technology (i.e., potential message losses) affects the equilibrium consensus outcome. 
JEL:  D02 D82 D85 G14 G29 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:29515&r= 
By:  Masaaki Fujii (Graduate School of Economics, The University of Tokyo); Akihiko Takahashi (Graduate School of Economics, The University of Tokyo) 
Abstract:  We study an equilibriumbased continuous asset pricing problem for the securities mar ket. In the previous work [16], we have shown that a certain price process, which is given by the solution to a forward backward stochastic differential equation of conditional McKean Vlasov type, asymptotically clears the market in the large population limit. In the current work, under suitable conditions, we show the existence of a finite agent equilibrium and its strong convergence to the corresponding meanfield limit given in [16]. As an important byproduct, we get the direct estimate on the difference of the equilibrium price between the two markets; the one consisting of heterogeneous agents of finite population size and the other of homogeneous agents of infinite population size. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:tky:fseres:2021cf1180&r= 
By:  Giovanni Di Bartolomeo; Martin Dufwenberg; Stefano Papa 
Abstract:  Building on a partnerswitching mechanism, we experimentally test two theories that posit different reasons why promises breed trust and cooperation. The expectationbased explanation (EBE) operates via beliefdependent guilt aversion, while the commitmentbased explanation (CBE) suggests that promises offer commitment power via a (beliefindependent) preference to keep one's word. Previous research performed a similar test, which we however argue should be interpreted as concerning informal agreements rather than (unilateral) promises. 
Keywords:  Promises; Partnerswitching, Expectations, Commitment, Guilt, Informal agreements 
JEL:  A13 C91 D01 D64 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:sap:wpaper:wp215&r= 
By:  DELBONO Flavio; REGGIANI Carlo (European Commission – JRC); SANDRINI Luca 
Abstract:  The unprecedented access of firms to consumer level data facilitates more precisely targeted individual pricing. We study the incentives of a data broker to sell data about a segment of the market to three competing firms. The segment only includes a share of the consumers in the market around one of the firms. Data are never sold exclusively. Despite the data are particularly tailored to the potential clientele of one of the firms, we show that the data broker has incentives to sell the list to its competitors. Such market outcome is not socially optimal, and a regulator that aims to maximise consumers and social welfare should consider mandating data sharing. 
Keywords:  data markets, personalised pricing, price discrimination, oligopoly, selling mechanisms 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:ipt:decwpa:202105&r= 
By:  Gagan Aggarwal; Kshipra Bhawalkar; Guru Guruganesh; Andres Perlroth 
Abstract:  We study the mechanism design problem of selling $k$ items to unitdemand buyers with private valuations for the items. A buyer either participates directly in the auction or is represented by an intermediary, who represents a subset of buyers. Our goal is to design robust mechanisms that are independent of the demand structure (i.e. how the buyers are partitioned across intermediaries), and perform well under a wide variety of possible contracts between intermediaries and buyers. We first study the case of $k$ identical items where each buyer draws its private valuation for an item i.i.d. from a known $\lambda$regular distribution. We construct a robust mechanism that, independent of the demand structure and under certain conditions on the contracts between intermediaries and buyers, obtains a constant factor of the revenue that the mechanism designer could obtain had she known the buyers' valuations. In other words, our mechanism's expected revenue achieves a constant factor of the optimal welfare, regardless of the demand structure. Our mechanism is a simple postedprice mechanism that sets a takeitorleaveit peritem price that depends on $k$ and the total number of buyers, but does not depend on the demand structure or the downstream contracts. Next we generalize our result to the case when the items are not identical. We assume that the item valuations are separable. For this case, we design a mechanism that obtains at least a constant fraction of the optimal welfare, by using a menu of posted prices. This mechanism is also independent of the demand structure, but makes a relatively stronger assumption on the contracts between intermediaries and buyers, namely that each intermediary prefers outcomes with a higher sum of utilities of the subset of buyers represented by it. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.10472&r= 