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on Game Theory |
| By: | Mohamed Belhaj (AMSE - Aix-Marseille 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); Frédéric Deroïan (AMSE - Aix-Marseille 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); Shahir Safi (AMSE - Aix-Marseille 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) |
| Abstract: | We consider agents organized in an undirected network of local complementarities. A principal with a limited budget offers costly bilateral contracts in order to increase the sum of agents' effort. We study excess-effort linear payment schemes, i.e. contracts rewarding effort in excess to the effort made in absence of principal. The analysis provides the following main insights. First, for all contracting costs, the optimal unit returns offered to every targeted agent are positive and generically heterogeneous. This heterogeneity is due to the presence of outsiders, who create asymmetric interaction between contracting agents. Second, when contracting costs are low, it is optimal to contract with everyone and optimal unit returns are identical for all agents. Third, when contracting costs are sufficiently high, it becomes optimal to target a subset of agents, and optimal targeting can lead to NP-hard problems. In particular, when the intensity of complementarities is sufficiently low, a correspondence is established between optimal targeting and the densest k subgraph problem. Overall, the optimal targeting problem involves a trade-off between centrality and budget spending-central agents are influential, but are also more budget-consuming. These considerations can lead the principal to not target central agents. |
| Keywords: | networked synergies,aggregate effort,optimal group targeting,linear contract |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-02558397&r=all |
| By: | Raouf Boucekkine (Aix-Marseille University, CNRS and EHESS); Carmen Camacho (Paris School of Economics, CNRS); Benteng Zou (CREA, Université du Luxembourg) |
| Abstract: | In this paper, we tackle a generic optimal regime switching problem where the decision making process is not the same from a regime to another. Precisely, we consider a simple model of optimal switching from competition to cooperation. To this end, we solve a two- stage optimal control problem. In the first stage, two players engage in a dynamic game with a common state variable and one control for each player. We solve for open-loop strategies with a linear state equation and linear-quadratic payoffs. More importantly, the players may also consider the possibility to switch at finite time to a cooperative regime with the associated joint optimization of the sum of the individual payoffs. Using theoretical analysis and numerical exercises, we study the optimal switching strategy from competition to cooperation. We also discuss the reverse switching. |
| Keywords: | Cooperation, competition, dynamic games, multi-stage optimal control. |
| JEL: | C61 D71 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:luc:wpaper:20-02&r=all |
| By: | Mitra, Manipushpak (Economic Research Unit, Indian Statistical Institute); Ray, Indrajit (Cardiff Business School); Roy, Souvik (Economic Research Unit, Indian Statistical Institute,) |
| Abstract: | We provide a full characterisation of the set of trading equilibria (in which all goods are traded at a positive price) in a strategic market game (as introduced by Shapley and Shubik), for both the Òbuy and sellÓ and the Òbuy or sellÓ versions of this model under standard assumptions on the utility functions. We also interpret and illustrate our main equilibrium-characterising condition, using simple examples. |
| Keywords: | strategic market game, trading equilibrium, buy and sell, buy or sell. |
| JEL: | C72 D44 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:cdf:wpaper:2020/8&r=all |
| By: | Márton Benedek (Institute of Economics, Centre for Economic and Regional Studies,Toth Kalman utca 4, 1097 Budapest, Hungary Corvinus University of Budapest, Fõvám tér 8., Budapest, 1093, Hungary,Budapest University of Technology and Economics, Egry József u. 1., Budapest, 1111, Hungary); Jörg Fliege (Mathematical Sciences, University of Southampton, University Road, Southampton, SO17 1BJ, United Kingdom); Tri-Dung Nguyen (Mathematical Sciences, Business School and CORMSIS, University of Southampton, Southampton, SO17 1BJ, United Kingdom) |
| Abstract: | The nucleolus offers a desirable payoff-sharing solution in cooperative games, thanks to its attractive properties. Although computing the nucleolus is very challenging, the Kohlberg criterion offers a method for verifying whether a solution is the nucleolus in relatively small games (number of players n at most 15). This approach becomes more challenging for larger games as the criterion involves possibly exponentially large collections of coalitions, with each collection being potentially exponentially large. The aim of this work is twofold. First, we develop an improved Kohlberg criterion that involves checking the `balancedness' of at most (n-1) sets of coalitions. Second, we exploit these results and introduce a novel descent-based constructive algorithm to find the nucleolus efficiently. We demonstrate the performance of the new algorithms by comparing them with existing methods over different types of games. Our contribution also includes the first open-source code for computing the nucleolus of moderately large games. |
| Keywords: | nucleolus, cooperative games, Kohlberg criterion, computation |
| JEL: | C71 C61 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:2021&r=all |
| By: | Isaksen, Elisabeth Thuestad; Brekke, Kjell Arne; Richter, Andries |
| Abstract: | We investigate whether positive framing increases cooperation in three social dilemmas with slightly different properties: a linear public goods (PG) game, a non-linear PG game, and a common pool resource (CPR) game. Results from our laboratory experiments show that contributions to a linear PG are higher if the externality is framed positively, rather than negatively, corroborating earlier findings by Andreoni (1995). By contrast, we find no such framing effects in the non-linear PG game or the CPR game. In these games, the best response in the material payoffs is to contribute less if others contribute more, counteracting effects of pro-social preferences. Positive framing therefore does not help to solve the tragedy of the commons. |
| JEL: | C72 C92 D70 |
| Date: | 2019–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:90607&r=all |
| By: | Giuseppe Attanasi (Université Côte d'Azur; CNRS, GREDEG, France); Claire Rimbaud (Université Lyon 2; GATE CNRS); Marie-Claire Villeval (Université Lyon 2; GATE CNRS) |
| Abstract: | From the literature we know that contextual factors modulate guilt aversion, such as pre-play communication and social closeness. In this study, we investigate whether a particular feature of the game itself = the vulnerability of the co-players = affects a player's guilt aversion. We deem that a co-player is (i) ex-post vulnerable when her final payoff depends on the decision-maker's actions, and (ii) ex-ante vulnerable when the use of her initial endowment depends on the decision-maker's actions. In a laboratory experiment, we introduce four (new) three-player trust games played within-subjects, varying whether the trustees can condition their decision on the belief of another player who is ex-post vulnerable and/or ex-ante vulnerable. We put forward a portable model of lexicographic altruism and role-dependent guilt, where the trustee can only be altruistic toward the most disadvantaged player and can feel guilty simply because of his role in the game. We find that trustees' guilt aversion is insensitive to the opponents' vulnerability and to the role of the vulnerable player. |
| Keywords: | Guilt aversion, vulnerability, psychological game theory, experiment |
| JEL: | C72 C91 D91 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:gre:wpaper:2020-15&r=all |
| By: | P. Jean-Jacques Herings (Department of Economics, Maastricht University, P.O. Box 616, 6200 MD, Maastricht, The Netherlands.); László Á. Kóczy (Institute of Economics, Centre for Economic and Regional Studies, Tóth Kálmán u. 4., 1097 Budapest, Hungary And Department of Finance, Faculty of Economics and Social Sciences, Budapest University of Technology and Economics, Magyar tudósok körútja 2, 1117 Budapest, Hungary) |
| Abstract: | In cooperative games, the coalition structure core is, despite its potential emptiness, one of the most popular solutions. While it is a fundamentally static concept, the consideration of a sequential extension of the underlying dominance correspondence gave rise to a selection of non-empty generalizations. Among these, the payoff-equivalence minimal dominant set and the myopic stable set are defined by a similar set of conditions. We identify some problems with the payoff-equivalence minimal dominant set and propose an appropriate reformulation called the minimal dominant set. We show that replacing asymptotic external stability by sequential weak dominance leaves the myopic stable set unaffected. The myopic stable set is therefore equivalent to the minimal dominant set. |
| Keywords: | coalition structure core; sequential dominance |
| JEL: | C71 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:2022&r=all |
| By: | Federica Alberti (University of Portsmouth); Werner Güth (LUISS Guido Carli and Max Planck Institute for Research on Collective Goods); Kei Tsutsui (University of Bath) |
| Abstract: | We experimentally investigate corporate governance of a co-determined firm. The experimental setup confronts the firm’s manager with three employees as stakeholders. There are two investment opportunities, each of which could affect the stakeholders either positively or negatively. First, the manager states his or her demand of the total value of each investment. Then the three stakeholders, knowing the manager’s demands, state their claims via bidding. The bidding rule is procedurally fair by treating all three stakeholders equally as long as stakeholders truthfully state their own values, but offers underbidding incentives. We find that most stakeholder-participants do underbid. The total bids are not significantly different from the managers’ claims. Contrary to game theoretical prediction, manager-participants demand a fair share of the value rather than almost the entire investment value. |
| Keywords: | corporate management, co-determination, procedural fairness, laboratory experiments |
| JEL: | J52 J54 C92 |
| Date: | 2020–05–29 |
| URL: | http://d.repec.org/n?u=RePEc:pbs:ecofin:2020-10&r=all |
| By: | Mickaël Beaud (CEE-M - Centre d'Economie de l'Environnement - Montpellier - FRE2010 - INRA - Institut National de la Recherche Agronomique - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier); Mathieu Lefebvre (BETA - Bureau d'Économie Théorique et Appliquée - INRA - Institut National de la Recherche Agronomique - CNRS - Centre National de la Recherche Scientifique - UL - Université de Lorraine - UNISTRA - Université de Strasbourg); Julie Rosaz (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - CNRS - Centre National de la Recherche Scientifique - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UL2 - Université Lumière - Lyon 2 - ENS Lyon - École normale supérieure - Lyon) |
| Abstract: | This paper investigates if and how other-regarding preferences governing giving decisions in dictator games are affected in risky environments in which the payoff of the recipient is random. We demonstrate that, whenever the risk is actuarially neutral, the donation of dictators with a purely ex post view of fairness should, in general, be affected by the riskyness of the recipient's payoff, while dictators with a purely ex ante view should not be. Our experimental data give weak empirical support to the purely ex post view of fairness. |
| Keywords: | ex ante and ex post views of fairness,impure altruism,Laboratory experiments dictator games,background risk,other-regarding preferences,Inequality aversion |
| Date: | 2018–09–11 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpceem:halshs-01872072&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); Chiu Yu Ko (Department of Economics, National University of Singapore) |
| Abstract: | We examine a chain of sequential losses: an agent causes a loss to another, which triggers a loss to a third, and so forth. Our objective is to devise a fair distribution of liability, taking into account that the chain turns “victim” to “injurer” in its subsequent step. This opens up for many interpretations of the notion of strict liability: should agents merely be responsible for the direct loss they cause or also bear some of the indirect losses they trigger? Through an axiomatic approach, we characterize the parametric class of fixed-fraction rules. These hold each agent accountable for a fixed fraction of the direct harm she causes while the initiator — the root cause of the loss chain — is liable for the residual. We then explore the case in which individual losses are contested while agreement remains on the total loss and the order of liability. We extend the principle of equalizing losses to equalizing distances to ideal allocations. In particular, we find that liability always can be distributed equidistant to every agent’s ideal allocation. Interestingly, this fair allocation coincides with the intermediate fixed-fraction rule when individual losses are identical. |
| Keywords: | Sequential losses, Strict liability, Ordered liability, Fair allocation, Cost allocation |
| JEL: | K12 C7 D6 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:foi:wpaper:2020_05&r=all |
| By: | Deepanshu Vasal |
| Abstract: | We consider the problem of dynamic information design with one sender and one receiver where the sender observers a private state of the system and takes an action to send a signal based on its observation to a receiver. Based on this signal, the receiver takes an action that determines rewards for both the sender and the receiver and controls the state of the system. In this technical note, we show that this problem can be considered as a problem of dynamic game of asymmetric information and its perfect Bayesian equilibrium (PBE) and Stackelberg equilibrium (SE) can be analyzed using the algorithms presented in [1], [2] by the same author (among others). We then extend this model when there is one sender and multiple receivers and provide algorithms to compute a class of equilibria of this game. |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2005.07267&r=all |
| By: | Castillo, Marco (Texas A&M University); Dickinson, David L. (Appalachian State University) |
| Abstract: | When group outcomes depend on minimal effort (e.g., disease containment, work teams, or indigenous hunt success), a classic coordination problem exists. Using a well-established paradigm, we examine how a common cognitive state (insufficient sleep) impacts coordination outcomes. Our data indicate that insufficient sleep increases coordination failure costs, which suggests that the sleep or, more generally, cognitive composition of a group might determine its ability to escape from a trap of costly miscoordination and wasted cooperative efforts. These findings are first evidence of the potentially large externality of a commonly experienced biological state (insufficient sleep) that has infiltrated many societies. |
| Keywords: | coordination games, sleep, cooperative dilemma |
| JEL: | C91 D91 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp13242&r=all |
| By: | Garfinkel, Michelle (University of California, Irvine); Syropoulos, Constantinos (Drexel University) |
| Abstract: | On the basis of a single-period, guns-versus-butter, complete-information model in which two agents dispute control over an insecure portion of their combined output, we study the choice between a peace agreement that maintains the status quo without arming (or unarmed peace) and open conflict (or war) that is possibly destructive. With a focus on outcomes that are immune to both unilateral deviations and coalitional deviations, we find that, depending on war's destructive effects, the degree of output security and the initial distribution of resources, peace can, but need not necessarily, emerge in equilibrium. We also find that, while ex ante resource transfers without commitment can improve the prospects for peace, war remains the unique equilibrium in pure strategies when the initial distribution of resources is sufficiently uneven. |
| Keywords: | Disputes; output insecurity; destructive wars; peaceful settlement; unarmed peace |
| JEL: | D30 D74 F51 |
| Date: | 2020–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:ris:drxlwp:2020_007&r=all |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Benjamin Brooks (Dept. of Economics, University of Chicago); Stephen Morris (Dept. of Economics, MIT) |
| Abstract: | We study price discrimination in a market in which two ï¬ rms engage in Bertrand competition. Some consumers are contested by both ï¬ rms, and other consumers are “captive†to one of the ï¬ rms. The market can be divided into segments, which have different relative shares of captive and contested consumers. It is shown that the revenue-maximizing segmentation involves dividing the market into “nested†markets, where exactly one ï¬ rm may have captive consumers. |
| Keywords: | Price Competition, Bertrand Competition, Price Count, Price Quote, Information Structure, Bayes Correlated Equilibrium |
| JEL: | D41 D42 D43 D83 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2234&r=all |
| By: | Rodolphe Dos Santos Ferreira (Strasbourg University; BETA CNRS) |
| Abstract: | In his 1961 seminal paper, Muth applied his "rational expectations" hypothesis to a simple model of a competitive market for a homogeneous good produced under random shocks. The hypothesis goes beyond the Marshallian expectational approach to equilibrium in attributing to entrepreneurs the capacity to form theory-based price predictions. We find this capacity already in Cournot (1838), although in a model without explicit fundamental uncertainty. The purpose of this note is to show within the same model that oligopolistic competition adds indeterminacy, hence market uncertainty, to the picture, weakening in some sense the rational expectations hypothesis. Before equilibrium is realised, each entrepreneur stands in a hawkish-dovish superposition, very much as the Schrödinger's cat is in a dead-living superposition. |
| Keywords: | rational expectations, market uncertainty, oligopoly, equilibrium indeterminacy, competitive toughness |
| JEL: | B21 D43 D84 L13 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:gre:wpaper:2020-22&r=all |
| By: | Dotti, Valerio |
| Abstract: | I propose a model of legislative bargaining among endogenous political parties over multiple policy dimensions. I provide a characterization of (i) the partition of the legislature into parties, (ii) the policy reforms that parties propose (if any), and (iii) the policy outcome attained from these proposals. I show that - depending on the position of the status quo - either (1) the presence of parties does not affect the policy outcome and a median voter theorem holds, or (2) a party representing legislators with extreme and opposite political views - i.e., a coalition of extremes - can successfully block reforms that would be feasible if parties did not exist. Lastly, I show that the extent to which the existence of parties can increase the set of possible policy reforms is severely limited or null. |
| Keywords: | Multidimensional policy space, Political parties, Policy reforms |
| JEL: | C71 D72 |
| Date: | 2019–10–23 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:100227&r=all |
| By: | Berliant, Marcus |
| Abstract: | Workers generally commute on a daily basis, so we model commuting as a repeated game. The folk theorem implies that for sufficiently large discount factors the repeated commuting game has as a Nash equilibrium any strategy profile that is at least as good as the maximin strategy for a commuter in the one shot game, including the efficient ones. This result applies whether the game is static, in the sense that only routes are chosen as a strategy by commuters, or dynamic, where both routes and times of departure are chosen. Our conclusions pose a challenge to congestion pricing. We examine evidence from St. Louis to determine what equilibrium strategies are actually played in the repeated commuting game. |
| Keywords: | Repeated game; Nash equilibrium; Commuting; Folk theorem |
| JEL: | R41 |
| Date: | 2020–05–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:100169&r=all |
| By: | Christmann, Robin; Kirstein, Roland |
| Abstract: | The prosecution of criminals is costly, and subject to errors. In contrast to adversarial court procedures, the prosecutor is regarded as an impartial investigator and aide to the judge in inquisitorial justice systems. We show in a sequential prosecution game of a Bayesian court that a strategic interaction between these two benevolent enforcement agents exists where each player hopes to freeride on the other one´s investigative effort. This gives rise to inefficient equilibria with excessive operating and error costs. Moreover, we will demonstrate that our results are sensitive to the applied standard of proof and that, more disturbingly, the inefficient outcome becomes more probable when the conviction threshold is raised. Applying the concept of ‘beyond reasonable doubt’, we analyze the impact of the standard of proof and other legal policy instruments on type I and type II errors and operating costs. |
| Keywords: | criminal justice, reasonable doubt, litigation, court errors |
| JEL: | K14 K41 |
| Date: | 2020–04–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:99686&r=all |