
on Game Theory 
By:  Mauleon, Ana (Université catholique de Louvain, LIDAM/CORE, Belgium); Nanumyan, Mariam; Schopohl, Simon (Université catholique de Louvain, LIDAM/CORE, Belgium); Vannetelbosch, Vincent (Université catholique de Louvain, LIDAM/CORE, Belgium) 
Abstract:  We study network games with social and private dissonance where each player in the network exerts some costly efforts. We allow for cooperative behavior in the sense that players may belong to unions and members of each union choose their efforts by maximizing the joint utility of the union. Each player not only benefits from the aggregate effort and efforts of network neighbors are strategic complements, but also suffers disutility when her effort differs from her neighbors’ efforts or is inconsistent with her ideal effort. We characterize the unique Nash equilibrium of the network game with unions and we define a union intercentrality measure for finding the key player whose removal has the highest impact on the aggregate effort level. In addition, we explore the role of unions in fostering effort levels and we consider two alternative policies: the key addition to an existing union (the player who increases the most the aggregate effort by joining the union) and the key union that generates the highest total effort. Finally, we investigate the stability of unions. 
Keywords:  Social networks ; peer effects ; key players ; unions ; social and private dissonance 
JEL:  A14 C72 D85 L14 
Date:  2023–04–27 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2023012&r=gth 
By:  Aviad Heifetz; Enrico Minelli; Herakles Polemarchakis 
Abstract:  Purely affective interaction allows the welfare of an individual to depend on her own actions and on the profile of welfare levels of others. Under an assumption on the structure of mutual affection that we interpret as "nonexplosive mutual affection, " we show that equilibria of simultaneousmove affective interaction are Pareto optimal independently of whether or not an induced standard game exists. Moreover, if purely affective interaction induces a standard game, then an equilibrium profile of actions is a Nash equilibrium of the game, and this Nash equilibrium and Pareto optimal profile of strategies is locally dominant. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.10165&r=gth 
By:  Gilles, Robert P.; Mallozzi, Lina 
Abstract:  We investigate Gately's solution concept for cooperative games with transferable utilities. Gately's conception is a bargaining solution and minimises the maximal quantified 'propensity to disrupt' the negotiation of the players over the allocation of the generated collective payoffs. Gately's solution concept is welldefined for a broad class of games. We consider a generalisation based on a parameterbased quantification of the propensity to disrupt. Furthermore, we investigate the relationship of these generalised Gately values with the Core. Gately's solution is in the Core for all regular 3player games. We identify precise conditions under which generalised Gately values are Core imputations for arbitrary regular cooperative games. We devise an axiomatisation of the Gately value for the class of regular cooperative games. We conclude the paper with an application of the Gately value to the measurement of power in hierarchical social networks. 
Keywords:  Cooperative TUgame, sharing values, Gately point, Core 
JEL:  C71 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:zbw:qmsrps:202206&r=gth 
By:  Dehez, Pierre (Université catholique de Louvain, LIDAM/CORE, Belgium) 
Abstract:  A cooperative product game is a transferable utility game defined by associating the product of given players' weights to coalitions. This idea has been introduced by Rosales (2014) in an unpublished memo. Here we analyze a modified version and cover the Shapley value to which we provide an axiomatic foundation. 
Date:  2023–03–01 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2023010&r=gth 
By:  Dokka, Trivikram; Bruno, Jorge; SenGupta, Sonali; Anwar, Sakib 
Abstract:  We study equilibria in an Electric Vehicle (EV) charging game, a cost minimization game inherent to decentralized charging control strategy for EV power demand management. In our model, each user optimizes its total cost which is sum of direct power cost and the indirect dissatisfaction cost. We show that, taking player specific price independent dissatisfaction cost into account, contrary to popular belief, herding only happens at lower EV uptake. Moreover, this is true for both linear and logistic dissatisfaction functions. We study the question of existence of price profiles to induce a desired equilibrium. We define two types of equilibria, distributed and nondistributed equilibria, and show that under logistic dissatisfaction, only nondistributed equilibria are possible by feasibly setting prices. In linear case, both type of equilibria are possible but price discrimination is necessary to induce distributed equilibria. Finally, we show that in the case of symmetric EV users, mediation cannot improve upon Nash equilibria. 
Keywords:  Electric Vehicles, Pricing, Nash equilibrium, Coarse correlated equilibrium, Mediation, Herding, Dissatisfaction cost 
JEL:  C61 C72 D4 D11 D82 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:zbw:qmsrps:202210&r=gth 
By:  Anwar, Sakib; Bruno, Jorge; SenGupta, Sonali 
Abstract:  We model a dynamic public good contribution game, where players are (naturally) formed into groups. The groups are exogenously placed in a sequence, with limited information available to players about their groups' position in the sequence. Contribution decisions are made by players simultaneously and independently, and the groups' total contribution is made sequentially. We try to capture both inter and intragroup behaviors and analyze different situations where players observe partial history about total contributions of their predecessor groups. Given this framework, we show that even when players observe a history of defection (no contribution), a cooperative outcome is achievable. This is particularly interesting in the situation when players observe only their immediate predecessor groups' contribution, where we observe that players play an important role in motivating others to contribute. 
Keywords:  Social Dilemmas, Public Goods, Position Uncertainty, Voluntary Contributions, Fundraising, Groups 
JEL:  C72 D82 H41 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:zbw:qmsrps:202207&r=gth 
By:  Srinivas Arigapudi; Yuval Heller; Amnon Schreiber 
Abstract:  Coordination games admit two types of equilibria: pure equilibria, where all players successfully coordinate their actions, and mixed equilibria, where players frequently experience miscoordination. The existing literature shows that under many evolutionary dynamics, populations converge to a pure equilibrium from almost any initial distribution of actions. By contrast, we show that under plausible learning dynamics, where agents observe the actions of a random sample of their opponents and adjust their strategies accordingly, stable miscoordination can arise when there is heterogeneity in the sample sizes. This occurs when some agents make decisions based on small samples (anecdotal evidence) while others rely on large samples. Finally, we demonstrate the empirical relevance of our results in a bargaining application. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.10301&r=gth 
By:  Martin Palovic 
Abstract:  We analyse incentive problems in coordination of network operators that purchase services for electricity networks from distributed resources. Such services are often associated with externalities that make the social optimum costly against the individual one. However, a costly reaction of other operators occurs when the social optimum is missed. Regular network situations result in gametheoretical problems like prisoner’s dilemma or chicken that are played in a random order in an infinitely repeated game. The outcome of this complex gametheoretical setting, i.e. adopted strategies, is difficult to predict. Adjustments to network regulation aiming to internalize external effects are discussed as a remedy. 
Keywords:  network operator coordination, game theory, network regulation 
JEL:  D42 K23 L51 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:bei:00bewp:0040&r=gth 
By:  Elpiniki Bakaouka (Universitat de les Illes Balears); Marc EscrihuelaVillar (Universitat de les Illes Balears); Walter Ferrarese (Universitat de les Illes Balears) 
Abstract:  We discuss the effect of horizontal mergers in homogeneous goods industries when firms compete à la Bertrand with increasing marginal costs of production. We set up a twostage game where in the first stage firms decide whether to join the merger or to remain outside and in the second stage market competition takes place. We identify necessary and sufficient conditions for a market structure where a merger did occur to be coalition proof. We find that such market structure could be consumer surplus enhancing as it could arise even for lower postmerger prices with respect to the premerger scenario. This is in sharp contrast with the findings under both price and quantity competition where, absent efficiency gains, mergers unambiguously harm consumers. 
Keywords:  Homogeneous Goods; Horizontal Mergers; Bertrand Competition; Coalition Proof Nash Equilibrium. 
JEL:  C72 D43 G34 L13 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:ubi:deawps:96&r=gth 
By:  Dollinger, Jérôme (Université catholique de Louvain, LIDAM/CORE, Belgium); Mauleon, Ana (Université catholique de Louvain, LIDAM/CORE, Belgium); Vannetelbosch, Vincent (Université catholique de Louvain, LIDAM/CORE, Belgium) 
Abstract:  We analyze the formation of R&D alliances and market sharing (MS) agreements by which firms commit not to enter in each other’s territory in oligopolistic markets. We show that R&D alliance structures are stable only in the presence of MS agreements. Thus, long lasting R&D alliances could signal the existence of some MS agreement in the industry. We characterize the set of stable symmetric pairs of coalition structures with identical R&D and MS structure. In addition, we show the stability of a class of asymmetric pairs of coalition structures where the most efficient firms form both an R&D and a MS agreement while the other firms do not form any MS agreement but form two smaller R&D alliances. Even though MS agreements are detrimental for consumers, we show that stable cooperation in terms of R&D is yet a better outcome for consumers than no cooperation at all. 
Keywords:  R&D alliances ; Market sharing agreements ; Oligopoly ; Cournot competition ; Stability 
JEL:  C70 L13 L40 
Date:  2023–01–20 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2023004&r=gth 
By:  de Callatay, Pierre (Université catholique de Louvain, LIDAM/CORE, Belgium); Mauleon, Ana (Université catholique de Louvain, LIDAM/CORE, Belgium); Vannetelbosch, Vincent (Université catholique de Louvain, LIDAM/CORE, Belgium) 
Abstract:  We propose the concept of localk farsighted consistent network for analysing network formation games where players only consider a limited number of feasible networks. A network g is said to be localk farsightedly consistent if, for any network g' within the distancek neighbourhood of g, either g is not defeated by g' , or g defeats g' . We show that if the utility function is (componentwise) egalitarian or satisfies reversibility or excludes externalities across components, then localk farsightedness is more likely to be a good proxy for what would happen when players have full knowledge of all feasible networks. 
Keywords:  Networks ; local farsightedness ; stability 
JEL:  A14 C70 D20 
Date:  2023–01–20 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2023003&r=gth 
By:  Galit AshkenaziGolan (LSE  London School of Economics and Political Science); Yevgeny Tsodikovich (BarIlan University [Israël], AMSE  AixMarseille Sciences Economiques  EHESS  École des hautes études en sciences sociales  AMU  Aix Marseille Université  ECM  École Centrale de Marseille  CNRS  Centre National de la Recherche Scientifique); Yannick Viossat (CEREMADE  CEntre de REcherches en MAthématiques de la DEcision  Université Paris DauphinePSL  PSL  Université Paris sciences et lettres  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  A common practice in many auctions is to offer bidders an opportunity to improve their bids, known as a best and final offer stage. This improved bid can depend on new information either about the asset or about the competitors. This paper examines the effects of new information regarding competitors, seeking to determine what information the auctioneer should provide assuming the set of allowable bids is discrete. The rational strategy profile that maximizes the revenue of the auctioneer is the one where each bidder makes the highest possible bid that is lower than his valuation of the item. This strategy profile is an equilibrium for a large enough number of bidders, regardless of the information released. We compare the number of bidders needed for this profile to be an equilibrium under different information structures. We find that it becomes an equilibrium with fewer bidders when less additional information is made available to the bidders regarding the competition. It follows that when the number of bidders is a priori unknown, there are some advantages to the auctioneer not revealing information and conducting a onestage auction instead. 
Keywords:  Auctions, Multistage auctions, BAFO, Information utilization 
Date:  2023–04–06 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal04099021&r=gth 
By:  Anwar, Sakib; Matros, Alexander; SenGupta, Sonali 
Abstract:  We present a model of public good provision with a distributor. Our main result describes a symmetric mixedstrategy equilibrium, where all agents contribute to a common fund with probability p and the distributor provides either a particular amount of public goods or nothing. A corollary of this finding is the efficient public good provision equilibrium where all agents contribute to the common fund, all agents are expected to contribute, and the distributor spends the entire common fund for the public good provision. 
Keywords:  Public goods, Embezzlement, Distributor 
JEL:  D73 H40 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:zbw:qmsrps:202208&r=gth 
By:  Simon K. Schnyder; John J. Molina; Ryoichi Yamamoto; Matthew S. Turner 
Abstract:  During epidemics people reduce their social and economic activity to lower their risk of infection. Such social distancing strategies will depend on information about the course of the epidemic but also on when they expect the epidemic to end, for instance due to vaccination. Typically it is difficult to make optimal decisions, because the available information is incomplete and uncertain. Here, we show how optimal decision making depends on knowledge about vaccination timing in a differential game in which individual decision making gives rise to Nash equilibria, and the arrival of the vaccine is described by a probability distribution. We show that the earlier the vaccination is expected to happen and the more precisely the timing of the vaccination is known, the stronger is the incentive to socially distance. In particular, equilibrium social distancing only meaningfully deviates from the novaccination equilibrium course if the vaccine is expected to arrive before the epidemic would have run its course. We demonstrate how the probability distribution of the vaccination time acts as a generalised form of discounting, with the special case of an exponential vaccination time distribution directly corresponding to regular exponential discounting. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.13618&r=gth 
By:  Felix Brandt; Matthias Greger; Erel SegalHalevi; Warut Suksompong 
Abstract:  Charity is typically done either by individual donors, who donate money to the charities that they support, or by centralized organizations such as governments or municipalities, which collect the individual contributions and distribute them among a set of charities. On the one hand, individual charity respects the will of the donors but may be inefficient due to a lack of coordination. On the other hand, centralized charity is potentially more efficient but may ignore the will of individual donors. We present a mechanism that combines the advantages of both methods by distributing the contribution of each donor in an efficient way such that no subset of donors has an incentive to redistribute their donations. Assuming Leontief utilities (i.e., each donor is interested in maximizing an individually weighted minimum of all contributions across the charities), our mechanism is groupstrategyproof, preferencemonotonic, contributionmonotonic, maximizes Nash welfare, and can be computed using convex programming. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.10286&r=gth 
By:  Abheek Ghosh; Paul W. Goldberg 
Abstract:  We study the convergence of bestresponse dynamics in lottery contests. We show that bestresponse dynamics rapidly converges to the (unique) equilibrium for homogeneous agents but may not converge for nonhomogeneous agents, even for two nonhomogeneous agents. For $2$ homogeneous agents, we show convergence to an $\epsilon$approximate equilibrium in $\Theta(\log\log(1/\epsilon))$ steps. For $n \ge 3$ agents, the dynamics is not unique because at each step $n1 \ge 2$ agents can make nontrivial moves. We consider a model where the agent making the move is randomly selected at each time step. We show convergence to an $\epsilon$approximate equilibrium in $O(\beta \log(n/(\epsilon\delta)))$ steps with probability $1\delta$, where $\beta$ is a parameter of the agent selection process, e.g., $\beta = n$ if agents are selected uniformly at random at each time step. Our simulations indicate that this bound is tight. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.10881&r=gth 