
on Game Theory 
By:  Toomas Hinnosaar 
Abstract:  Most products are produced and sold by supply chain networks, where an interconnected network of producers and intermediaries set prices to maximize their profits. I show that there exists a unique equilibrium in a pricesetting game on a network. The key distortion reducing both total profits and social welfare is multiplemarginalization, which is magnified by strategic interactions. Individual profits are proportional to influentiality, which is a new measure of network centrality defined by the equilibrium characterization. The results emphasize the importance of the network structure when considering policy questions such as mergers or trade tariffs. 
Keywords:  price setting, networks, sequential games, multiplemarginalization, supply chains, mergers, tariffs, trade, centrality. 
JEL:  C72 L14 D43 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:cca:wpaper:618&r=all 
By:  Brams, Steven J.; Ismail, Mehmet S. 
Abstract:  It is wellknown that Nash equilibria may not be Paretooptimal; worse, a unique Nash equilibrium may be Paretodominated, as in Prisoners’ Dilemma. By contrast, we prove a previously conjectured result: Every finite normalform game of complete information and common knowledge has at least one Paretooptimal nonmyopic equilibrium (NME) in pure strategies, which we define and illustrate. The outcome it gives, which depends on where play starts, may or may not coincide with that given by a Nash equilibrium. We use some simple examples to illustrate properties of NMEs—for instance, that NME outcomes are usually, though not always, maximin—and seem likely to foster cooperation in many games. Other approaches for analyzing farsighted strategic behavior in games are compared with the NME analysis. 
Keywords:  Game theory, theory of moves, twoperson games, cooperation 
JEL:  C70 D74 F50 
Date:  2021–03–21 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:106718&r=all 
By:  Changxia Ke; Florian Morath; Anthony Newell; Lionel Page 
Abstract:  In standard coalition games, players try to form a coalition to secure a prize and a coalition agreement specifies how the prize is to be split among its members. However, in practical situations where coalitions are formed, the actual split of the prize often takes place after the coalition formation stage. This creates the possibility for some players to ask for a renegotiation of the initial split. We predict that, in such situations, a player can suffer from being "too strong". Our experimental results confirm that, when the actual split of the prize is delayed, a player's strength can turn into a strategic disadvantage: a greater voting power in forming a winning coalition is undermined by the threat of being overly powerful at the stage when a split is determined. This result is relevant to many real world situations where "too strong" players find it paradoxically hard to partner with weaker players to win the game. 
Keywords:  Shapley Value, (Non) Binding Agreement, Balance of Power, Communication 
JEL:  C71 C92 D72 D74 
Date:  2021–09 
URL:  http://d.repec.org/n?u=RePEc:inn:wpaper:202109&r=all 
By:  Yuhki Hosoya; Chaowen Yu 
Abstract:  We consider a game in which the action set of each player is uncountable, and show that, from weak assumptions on the common prior, for any mixed strategy there exists a pure strategy that is approximately equivalent to it. The assumption of this result can be further weakened if we consider a purification of an Nash equilibrium. Combined with the existence theorem for a Nash equilibrium, we derive an existence theorem for pure strategy approximated Nash equilibrium under sufficiently weak assumptions. All pure strategies we derive in this paper can take a finite number of possible actions. 
Date:  2021–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2103.07736&r=all 
By:  Axel Anderson (Department of Economics, Georgetown University); Jeremy Rosen (Topspin Shot Research); John Rust (Department of Economics, Georgetown University); KinPing Wong (Digonex) 
Abstract:  Are the serves of the world’s best tennis pros consistent with the theoretical prediction of Nash equilibrium in mixed strategies? We analyze their serve direction choices (to the returner’s left, right or body) with data from an online database called the Match Charting Project. Using a new methodology, we test and decisively reject a key implication of a mixed strategy Nash equilibrium, namely, that the probability of winning a service game is the same for all serve directions. We also use dynamic programming (DP) to numerically solve for the bestresponse serve strategies to probability models of service game outcomes estimated for individual serverreturner pairs, such as Novak Djokovic serving to Rafael Nadal. We show that for most elite pro servers, the DP serve strategy significantly increases their service game win probability compared to the mixed strategies they actually use, which we estimate using flexible reducedform logit models. Stochastic simulations verify that our results are robust to estimation error. Classification C61, C73, L21 
Keywords:  tennis, games, Nash equilibrium, Minimax theorem, constant sum games, mixed strategies, dynamic directional games, binary Markov games, dynamic programming, structural estimation, muscle memory 
Date:  2021–03–16 
URL:  http://d.repec.org/n?u=RePEc:geo:guwopa:gueconwpa~212107&r=all 
By:  Yun Kuen Cheung; Stefanos Leonardos; Georgios Piliouras 
Abstract:  We study learning dynamics in distributed production economies such as blockchain mining, peertopeer file sharing and crowdsourcing. These economies can be modelled as multiproduct Cournot competitions or allpay auctions (Tullock contests) when individual firms have market power, or as Fisher markets with quasilinear utilities when every firm has negligible influence on market outcomes. In the former case, we provide a formal proof that Gradient Ascent (GA) can be LiYorke chaotic for a step size as small as $\Theta(1/n)$, where $n$ is the number of firms. In stark contrast, for the Fisher market case, we derive a Proportional Response (PR) protocol that converges to market equilibrium. The positive results on the convergence of the PR dynamics are obtained in full generality, in the sense that they hold for Fisher markets with \emph{any} quasilinear utility functions. Conversely, the chaos results for the GA dynamics are established even in the simplest possible setting of two firms and one good, and they hold for a wide range of price functions with different demand elasticities. Our findings suggest that by considering multiagent interactions from a market rather than a gametheoretic perspective, we can formally derive natural learning protocols which are stable and converge to effective outcomes rather than being chaotic. 
Date:  2021–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2103.08529&r=all 
By:  Michel Le Breton (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); Alexander Shapoval (Unknown); Shlomo Weber (Unknown) 
Abstract:  In this paper we examine a gametheoretical generalization of the landscape theory introduced by Axelrod and Bennett (1993). In their twobloc setting each player ranks the blocs on the basis of the sum of her individual evaluations of members of the group. We extend the Axelrod–Bennett setting by allowing an arbitrary number of blocs and expanding the set of possible deviations to include multicountry gradual deviations. We show that a Pareto optimal landscape equilibrium which is immune to profitable gradual deviations always exists. We also indicate that while a landscape equilibrium is a stronger concept than Nash equilibrium in pure strategies, it is weaker than strong Nash equilibrium. 
Keywords:  Landscape theory,Landscape equilibrium,Blocs,Gradual deviation,Potential functions,Hedonic games 
Date:  2021–01 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03156677&r=all 
By:  Françoise Forges (LEDa  Laboratoire d'Economie de Dauphine  IRD  Institut de Recherche pour le Développement  Université Paris DauphinePSL  PSL  Université Paris sciences et lettres  CNRS  Centre National de la Recherche Scientifique, Université Paris DauphinePSL  PSL  Université Paris sciences et lettres); Jérôme Renault (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  INRA  Institut National de la Recherche Agronomique  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique, UT1  Université Toulouse 1 Capitole) 
Abstract:  We consider a senderreceiver game with an outside option for the sender. After the cheap talk phase, the receiver makes a proposal to the sender, which the latter can reject. We study situations in which the sender's approval is crucial to the receiver. We show that a partitional, (perfect Bayesian Nash) equilibrium exists if the sender has only two types or if the receiver's preferences over decisions do not depend on the type of the sender as long as the latter participates. The result does not extend: we construct a counterexample (with three types for the sender and typedependent affine utility functions) in which there is no mixed equilibrium. In the three type case, we provide a full characterization of (possibly mediated) equilibria. 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal02440627&r=all 
By:  David Lowing (GATE Lyon SaintÉtienne  Groupe d'analyse et de théorie économique  ENS Lyon  École normale supérieure  Lyon  UL2  Université Lumière  Lyon 2  UCBL  Université Claude Bernard Lyon 1  Université de Lyon  UJM  Université Jean Monnet [SaintÉtienne]  Université de Lyon  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  We consider multichoice cooperative games with a permission tree structure. Multichoice games are a generalization of a cooperative transferable utility games in which each player has several activity levels. In addition, a permission tree structure models a situation in which a player needs permission from another player to cooperate. In this framework, the influence of a permission structure on the possibility of cooperation may have several interpretations depending on the context. In this paper, we investigate several of these interpretations and introduce for each of them a new allocation rule that we axiomatically characterize. 
Keywords:  Multichoice games,Multichoice Permission value,Permission (tree) structures Multichoice games,Permission (tree) structures 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs03121514&r=all 
By:  Florian O. O. Wagener; Aart de Zeeuw; Florian O.O. Wagener 
Abstract:  Tipping of a natural system, entailing a loss of ecosystem services, may be prevented by stable partial cooperation. The presence of tipping points reverses the grim story that a high level of cooperation is hard to achieve and leaves large possible gains of cooperation. We investigate a tipping game with constant emissions and a piecewise linear response, and the wellknown lake system with concaveconvex dynamics and timedependent emissions. Tipping back, leading to a gain in services, can also be induced by stable partial cooperation, but is harder to achieve. A physically reversible natural system may prove to be socially irreversible. 
Keywords:  tipping points, multiple Nash equilibria, stable partial cooperation, ecological systems 
JEL:  C70 Q20 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_8944&r=all 
By:  Pierfrancesco Guarino; Gabriel Ziegler 
Abstract:  We provide a theory of strategic interactions in static games in the presence of ignorance, i.e., when players cannot produce beliefs as probability measures (or similia) concerning the uncertain elements present in the interaction they are involved in. Assuming only players' ordinal preferences as transparent, we investigate players that are either optimistic or pessimistic, that we deem tropical players. To explicitly formalize these attitudes, we employ tools from interactive epistemology, by defining the corresponding epistemic events in epistemic possibility structures, which are the counterpart of epistemic type structures suited for our analysis in the presence of ignorance, We show that the behavioral implications related to common belief in these events have algorithmic counterparts in terms of iterative deletion procedures. While optimism is related to Point Rationalizability, to capture pessimism we introduce a new algorithm, deemed Wald Rationalizability. We show that the algorithmic procedure capturing optimism selects a subset of the strategies selected by the algorithmic procedure capturing pessimism. Additionally, we compare both algorithmic procedures to an analogous algorithm based on B\"orgers dominance, deemed B\"orgers Rationalizability, and we show that in generic static games both Point Rationalizability and Wald Rationalizability select a subset of the actions selected by B\"orgers Rationalizability. More generally, while we prove that dropping the genericity assumption does not change the relation between Point Rationalizability and B\"orgers Rationalizability, we show that Wald and B\"orgers Rationalizability are not comparable in their behavioral implications, and we shed light on why this difference emerges. Finally, we explore connections to strategic wishful thinking. 
Date:  2021–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2103.08319&r=all 
By:  Lorenzo Bastianello; Mehmet S. Ismail 
Abstract:  We prove the existence of an equilibrium concept for noncooperative games in which a strategy of a player is a function from the other players' actions to her own actions. 
Date:  2021–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2103.06928&r=all 
By:  Emma Jagu (LGI  Laboratoire Génie Industriel  CentraleSupélec  Université ParisSaclay, IFP School, IFPEN  IFP Energies nouvelles  IFPEN  IFP Energies nouvelles); Olivier Massol (IFP School, IFPEN  IFP Energies nouvelles  IFPEN  IFP Energies nouvelles, City University London) 
Abstract:  This paper examines the deployment of a shared CO2 transportation infrastructure needed to support the combined emergence of Bioenergy with Carbon Capture and Storage (BECCS) and Fossil energy with Carbon Capture and Storage (CCS). We develop a cooperative gametheoretic approach to: (i) examine the conditions needed for its construction to be decided, and (ii) determine the breakeven CO2 value needed to build such a shared infrastructure. In particular, we highlight that, as biogenic emissions are overlooked in currentlyimplemented carbon accounting frameworks, BECCS and CCS emitters face asymmetric conditions for joining a shared infrastructure. We thus further examine the influence of these carbon accounting considerations by assessing and comparing the breakeven CO2 values obtained under alternative accounting rules. We apply this modeling framework to a large contemporary BECCS/CCS casestudy in Sweden. Our results indicate that sustainable and incentivecompatible cooperation schemes can be implemented if the value of CO2 is high enough and show how that value varies depending on the carbon accounting framework retained for negative emissions and the nature of the infrastructure operators. In the most advantageous scenario, the CO2 value needs to reach 112€/tCO2, while the current Swedish carbon tax amounts to 110€/tCO2. Overall, these findings position pragmatic policy recommendations for local BECCS deployment. 
Date:  2021–01–22 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03118399&r=all 
By:  Bloch, Francis (Universite Paris 1 and Paris School of Economics); Chatterjee, Kalyan (Pennsylvania State University); Dutta, Bhaskar (University of Warwick and Ashoka University) 
Abstract:  This paper studies a game of attack and interception in a network, where a single attacker chooses a target and a path, and each node chooses a level of protection. We show that the Nash equilibrium of the game exists and is unique. It involves a mixed strategy of the attacker except when one target has a very high value relative to others. We characterize equilibrium attack paths and attack distributions as a function of the underlying network and target values. We also show that adding a link or increasing the value of a target may harm the attacker  a comparative statics e ect which is reminiscent of Braess's paradox in transportation economics. Finally, we contrast the Nash equilibrium with the equilibria of two variations of the model : one where nodes make sequential protection decisions upon observing the arrival of a suspicious object, and one where all nodes cooperate in defense. 
Keywords:  Keywords: Network interdiction ; Networks ; Attack and defense ; Inspection 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:wrk:warwec:1338&r=all 
By:  Stefano Matta 
Abstract:  The motivation of this note is to show how singular values affect local unique ness. More precisely, Theorem 3.1 shows how to construct a neighborhood (a ball) of a regular equilibrium whose diameter represents an estimate of local uniqueness, hence providing a measure of how isolated a (local) unique equilibrium can be. The result, whose relevance in terms of comparative statics is evident, is based on reasonable and natural assumptions and hence is applicable in many different settings, ranging from pure exchange economies to noncooperative games. 
Date:  2021–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2103.04968&r=all 
By:  Francesca Busetto; Giulio Codognato; Sayantan Ghosal; Damiano Turchet 
Abstract:  We address the problem of monopoly in general equilibrium in a mixed version of a monopolistic twocommodity exchange economy where the monopolist, represented as an atom, is endowed with one commodity and "small traders," represented by an atomless part, are endowed only with the other. We provide a theoretical foundation of the monopoly solution in this bilateral framework through a formalization of an explicit trading process inspired by Pareto (1896) for an exchange economy with a finite number of commodities. Then, we provide a game theoretical foundation of our monopoly solution through a twostage reformulation of our model. This allows us to prove that the set of the allocations corresponding to a monopoly equilibrium and the set of the allocations corresponding to a subgame perfect equilibrium of the twostage game coincide. Finally, we give the conditions under which our monopoly solution coincides with that defined by Kats (1974) and those, more restrictive, under which it has the geometric characterization proposed by Schydlowsky and Siamwalla (1966). Moreover, we establish the formal relationships between our concept of a monopoly equilibrium and that proposed by Pareto (1896), by redefining the latter in terms of our bilateral exchange setting. 
JEL:  D42 D51 
Date:  2021–03 
URL:  http://d.repec.org/n?u=RePEc:gla:glaewp:2021_04&r=all 
By:  Alessandro De Chiara (Universitat de Barcelona, BEAT); Marco A. Schwarz (University of Innsbruck, CESifo) 
Abstract:  Firms often try to influence individuals that, like regulators, are tasked with advising or deciding on behalf of a third party. In a dynamic regulatory setting, we show that a firm may prefer to capture regulators through the promise of a lucrative future job opportunity (i.e., the revolvingdoor channel) than through a hidden payment (i.e., a bribe). This is because the revolving door publicly signals the firm's eagerness and commitment to rewarding lenient regulators, which facilitates collusive equilibria. We find that opening the revolving door conditional on the regulator's report is usually more efficient than a blanket ban on postagency employment and may increase social welfare. This insight extends to a variety of applications and can also be used to determine the optimal length of coolingoff periods. 
Keywords:  Corruption, dynamic games, regulatory capture, revolving door. 
JEL:  D73 D86 H11 J45 L51 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:ewp:wpaper:410web&r=all 
By:  Ingela Alger (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:  Why are some societies monogamous and others polygynous? Most theories of polygyny invoke male heterogeneity as an explanation. Arguing that such heterogeneity depends on men's willingness to compete against each other in the first place, I propose an evolutionary game to model the evolution of this trait. Lack of competitiveness (and the associated monogamous unions) is shown to be compatible with evolution if male reproductive success decreases with the number of wives. In a model where the man and his spouse(s) make fertility and child care choices that aim at maximizing reproductive success, I show that, due to men's involvement in child care and female agency over her fertility, male reproductive success is decreasing in the number of wives under certain conditions and increasing in others. The model thus sheds light on the variation in polygyny rates across space and time in human societies. 
Keywords:  Malemale competition,Competitiveness,Evolution,Monogamy,Polygyny,Parental care 
Date:  2021–03–16 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03171126&r=all 
By:  Federico Innocenti; Domenico Menicucci 
Abstract:  This paper examines the issue of product compatibility in an oligopoly with three multiproduct firms. Whereas most of the existing literature focuses on the extreme cases of full compatibility or full incompatibility, we look at asymmetric settings in which some firms make their products compatible with a standard technology and others do not. Our analysis reveals each firm’s individual incentive to adopt the standard, and allows to study a twostage game in which first each firm chooses its technological regime (compatibility or incompatibility), then price competition occurs given the regime each firm has selected at stage one. When firms are ex ante symmetric, we find that for each firm, compatibility weakly dominates incompatibility. In a setting in which a firm’s products have higher quality than its rivals’ products, individual incentives to make products incompatible emerge, first for the firm with higher quality products, then also for the other firms, as the quality difference increases. This paper sheds lights on markets in which some firms adopt the standard technology but other firms use proprietary systems. 
Keywords:  Compatibility, Spatial competition, Vertical differentiation, Asymmetric equilibrium, Competitive Bundling 
JEL:  D43 L13 
Date:  2021–03 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2021_278&r=all 
By:  Géraldine Bouveret (NTU  Nanayang Technological University  Nanayang Technological University); Antoine Mandel (CES  Centre d'économie de la Sorbonne  UP1  Université Paris 1 PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  We investigate the containment of epidemic spreading in networks from a normative point of view. We consider a susceptible/infected model in which agents can invest in order to reduce the contagiousness of network links. In this setting, we study the relationships between social efficiency, individual behaviours and network structure. First, we characterise individual and socially efficient behaviour using the notions of communicability and exponential centrality. Second, we show, by computing the Price of Anarchy, that the level of inefficiency can scale up to linearly with the number of agents. Third, we prove that policies of uniform reduction of interactions satisfy some optimality conditions in a vast range of networks. In setting where no central authority can enforce such stringent policies, we consider as a type of secondbest policy the implementation of cooperation frameworks that allow agents to subsidise prophylactic investments in the global rather than in the local network. We then characterise the scope for Pareto improvement opened by such policies through a notion of Price of Autarky, measuring the ratio between social welfare at a global and a local equilibrium. Overall, our results show that individual behaviours can be extremely inefficient in the face of epidemic propagation but that policy can take advantage of the network structure to design welfare improving containment policies. 
Keywords:  Network,Price of Anarchy,Epidemic Spreading,Public Good 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs03165772&r=all 