
on Game Theory 
By:  Bergantiños, Gustavo; Lorenzo, Leticia 
Abstract:  A planner wants to carry out a project involving several firms. In many cases the planner, for instance the Spanish Administration, includes in the contract a penalty clause that imposes a payment per day if the firms do not complete their activities or the project on time. We discuss two ways of including such penalty clauses in contracts. In the first the penalty applies only when the whole project is delayed. In the second the penalty applies to each firm that incurs a delay even if the project is completed on time. We compare the two penalty systems and find that the optimal penalty (for the planner) is larger in the second method, the utility of the planner is always at least as large or larger in the second case and the utility of the firms is always at least as large or larger in the first. Surprisingly, the final delay in the project is unrelated to which penalty system is chosen. 
Keywords:  game theory; PERT; delays; penalties 
JEL:  C72 
Date:  2019–01–25 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:91718&r=all 
By:  Mitri Kitti (University of Turku) 
Abstract:  This paper considers subgame perfect equilibria of continuoustime repeated games with perfect monitoring when immediate reactions to deviations are allowed. The set of subgame perfect equilibrium payoffs is shown to be a fixedpoint of a setvalued operator introduced in the paper. For a large class of discrete time games the closure of this set corresponds to the limit payoffs of when the discount factors converge to one. It is shown that in the continuoustime setup pure strategies are sufficient for obtaining all equilibrium payoffs supported by the players' minimax values. Moreover, the equilibrium payoff set is convex and satisfies monotone comparative statics when the ratios of players' discount rates increase. 
Keywords:  repeated game, continuous time, subgame perfection, equilibrium payoff set 
JEL:  C72 C73 
Date:  2018–10 
URL:  http://d.repec.org/n?u=RePEc:tkk:dpaper:dp120&r=all 
By:  Arribillaga, Pablo; Bergantiños, Gustavo 
Abstract:  In the knapsack problem a group of agents want to fill a knapsack with several goods. Two issues should be considered. Firstly, to decide optimally the goods selected for the knapsack, which has been studied in many papers. Secondly, to divide the total revenue among the agents, which has been studied in few papers (including this one). We assign to each knapsack problem several cooperative games. For some of them we prove that the core is nonempty. Later, we follow the axiomatic approach. We propose two rules. The first one is based on the optimal solution of the knapsack problem. The second one is the Shapley value of the so called optimistic game. We offer axiomatic characterizations of both rules. 
Keywords:  Knapsack problem; axiomatic; cooperative games 
JEL:  C71 
Date:  2019–01–25 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:91719&r=all 
By:  Seungjin Han 
Abstract:  This paper studies prematch investment competition with upper and lower bounds on feasible transfers to sellers in a general signaling environment, where the types of buyers and sellers are private information and the surplus may depend on both types and investments. Bounded transfers create methodological challenges  e.g., externalities in the bottom match, limits of a separate investment reward (or market utility) schedule for each side  that would be present even in a large market. To overcome such challenges, this paper proposes a notion of equilibrium that incorporates strategic behavior of a continuum of agents. Given our notion of equilibrium with bounded transfers, our model explains remarkably well why sellers and buyers in the bottom tail of the match distribution are stuck in a vicious cycle of a rat race, and how stars who stand out from the rest endogenously arise through prematch investment competition. 
Keywords:  bounded transfers, prematch investment, matching, rat race, rise of stars 
JEL:  C72 C78 D40 D82 
Date:  2019–01 
URL:  http://d.repec.org/n?u=RePEc:mcm:deptwp:201901&r=all 
By:  Tanaka, Yasuhito 
Abstract:  We study a Stackelberg type symmetric dynamic threeplayers zerosum game. One player is the leader and two players are followers. All players have symmetric payoff functions. The game is a twostages game. In the first stage the leader determines the value of its strategic variable. In the second stage the followers determine the values of their strategic variables given the value of the leader's strategic variable. On the other hand, in the static game all players simultaneously determine the values of their strategic variables. We show that if and only if the game is fully symmetric, the Stackelberg equilibrium and the static equilibrium are equivalent. 
Keywords:  zerosum game, Stackelberg equilibrium, leader and follower 
JEL:  C72 
Date:  2019–02–03 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:91934&r=all 
By:  Tanaka, Yasuhito 
Abstract:  We study a Stackelberg type symmetric dynamic multiplayers zerosum game. One player is the leader and other players are followers. All players have symmetric payoff functions. The game is a twostages game. In the first stage the leader determines the value of its strategic variable. In the second stage the followers determine the values of their strategic variables given the value of the leader's strategic variable. On the other hand, in the static game all players simultaneously determine the values of their strategic variables. We show that if and only if the game is fully symmetric, the Stackelberg equilibrium and the static equilibrium are equivalent. 
Keywords:  Stackelberg equilibrium, static equilibrium, multiplayers zerosum game 
JEL:  C72 
Date:  2019–02–02 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:91897&r=all 
By:  Jeanne Hagenbach (CES  Centre d'économie de la Sorbonne  UP1  Université PanthéonSorbonne  CNRS  Centre National de la Recherche Scientifique); Frédéric Koessler (PSE  Paris School of Economics, PJSE  Paris Jourdan Sciences Economiques  UP1  Université PanthéonSorbonne  ENS Paris  École normale supérieure  Paris  INRA  Institut National de la Recherche Agronomique  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  This paper proposes an equilibrium concept, LanguageBased Expectation Equilibrium , which accounts for partial language understanding in senderreceiver cheap talk games. Each player is endowed with a privately known language competence which represents all the messages that he understands. For the messages he does not understand, he has correct but only coarse expectations about the equilibrium strategies of the other player. In general, a languagebased expectation equilibrium outcome differs from Nash and communication equilibrium outcomes, but is always a Bayesian solution. Partial language competence of the sender rationalizes information transmission and lies in pure persuasion problems, and facilitates information transmission from a moderately biased sender. 
Keywords:  Analogybased expectations,Bayesian solution,bounded rationality,cheap talk,language,pure persuasion,strategic information transmission 
Date:  2019–01 
URL:  http://d.repec.org/n?u=RePEc:hal:psewpa:halshs01988076&r=all 
By:  Mathieu Martin; Zéphirin Nganmeni (Université de CergyPontoise, THEMA) 
Abstract:  In this paper, we focus on a result stated by Bräuninger that the fi nagle point is within the Ɛcore in a spatial voting game with Euclidean individual preferences. Through a counterex ample with 7 players, we show that Bräuninger's result is not valid. 
Keywords:  Spatial voting, majority game, dominance, core, fi nagle. 
JEL:  C62 C70 D71 D72 
Date:  2019 
URL:  http://d.repec.org/n?u=RePEc:ema:worpap:201903&r=all 
By:  Vincent Martinet (Economie Publique, AgroParisTech, Inra, Universtié Paris Saclay); Pedro Gajardo; Michel De Lara 
Abstract:  We frame sustainability problems as bargaining problems among stakeholders who have to agree on a common development path. For infinite alternatives, the set of feasible payoffs is unknown, limiting the possibility to apply classical bargaining theory and mechanisms. We define a framework accounting for the economic environment, which specifies how the set of alternatives and payoff structure underlie the set of feasible payoffs and disagreement point. A mechanism satisfying the axioms of Independence of NonEfficient Alternatives and Independence of Redundant Alternatives can be applied to a reduced set of alternatives producing all Paretoefficient outcomes of the initial problem, and produces the same outcome. We exhibit monotonicity conditions under which such a subset of alternatives is computable. We apply our framework to dynamic sustainability problems. We characterize a « satisficing'' decision rule achieving any Paretoefficient outcome. This rule is renegotiationproof and generates a timeconsistent path under the axiom of Individual Rationality. 
Keywords:  social choice, axiomatic bargaining theory, economic environment, monotonicity, sustainability 
JEL:  C70 Q01 
Date:  2019–01 
URL:  http://d.repec.org/n?u=RePEc:fae:wpaper:2019.02&r=all 
By:  Mathieu Martin; Zéphirin Nganmeni; Craig A. Tovey (Université de CergyPontoise, THEMA) 
Abstract:  We introduce a dominance relationship in spatial voting with Euclidean preferences, by treating voter ideal points as balls of radius δ. Values δ > 0 model imprecision or ambiguity as to voter preferences, or caution on the part of a social planner. The winning coalitions may be any consistent monotonic collection of voter subsets. We characterize the minimum value of δ for which the δcore, the set of undominated points, is nonempty. In the case of simple majority voting, the core is the yolk center and δ is the yolk radius. Thus the δcore both generalizes and provides a new characterization of the yolk. We then study relationships between the δcore and two other concepts: the Ɛcore and the finagle point. We prove that every fi nagle point must be within 2.32472 yolk radii of every yolk center, in all dimensions m ≥ 2. 
Keywords:  Spatial voting, dominance, core, yolk, fi nagle. 
JEL:  C62 C70 D71 D72 
Date:  2019 
URL:  http://d.repec.org/n?u=RePEc:ema:worpap:201902&r=all 
By:  Abhijit Banerjee; Emily Breza; Arun G. Chandrasekhar; Markus Mobius 
Abstract:  The DeGroot model has emerged as a credible alternative to the standard Bayesian model for studying learning on networks, offering a natural way to model naive learning in a complex setting. One unattractive aspect of this model is the assumption that the process starts with every node in the network having a signal. We study a natural extension of the DeGroot model that can deal with sparse initial signals. We show that an agent's social influence in this generalized DeGroot model is essentially proportional to the number of uninformed nodes who will hear about an event for the first time via this agent. This characterization result then allows us to relate network geometry to information aggregation. We identify an example of a network structure where essentially only the signal of a single agent is aggregated, which helps us pinpoint a condition on the network structure necessary for almost full aggregation. We then simulate the modeled learning process on a set of real world networks; for these networks there is on average 21.6% information loss. We also explore how correlation in the location of seeds can exacerbate aggregation failure. Simulations with real world network data show that with clustered seeding, information loss climbs to 35%. 
JEL:  D8 D83 D85 O1 O12 Z13 
Date:  2019–01 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:25497&r=all 
By:  David Spector (PSE  ParisJourdan Sciences Economiques  CNRS  Centre National de la Recherche Scientifique  ENPC  École des Ponts ParisTech  EHESS  École des hautes études en sciences sociales  INRA  Institut National de la Recherche Agronomique  ENS Paris  École normale supérieure  Paris, PJSE  Paris Jourdan Sciences Economiques  UP1  Université PanthéonSorbonne  ENS Paris  École normale supérieure  Paris  INRA  Institut National de la Recherche Agronomique  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  Many collusive agreements involve the exchange of selfreported sales data between competitors, which use them to monitor compliance with a target market share allocation. Such communication may facilitate collusion even if it is unverifiable cheap talk and the underlying information becomes publicly available with a delay. The exchange of sales information may allow firms to implement incentivecompatible market share reallocation mechanisms after unexpected swings, limiting the recourse to price wars. Such communication may allow firms to earn profits that could not be earned in any collusive, symmetric purestrategy equilibrium without communication. 
Date:  2019–01 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs01983037&r=all 
By:  Mitri Kitti (University of Turku); Matti Pihlava (University of Turku); Hannu Salonen (University of Turku) 
Abstract:  We study axiomatically recursive clustering methods for networks. Such methods can be used to identify community structures of a network. One of the methods is based on identifying a node subset that maximizes the average degree within this subset. Once such a subset is found, the method is applied on the subnetwork whose node set is the complement of the first cluster, and so on recursively. The method produces an ordered partition of the node set of the original network. We give a list of axioms that this method satisfies, and show that any recursive clustering method satisfying the same set of axioms must produce the same or a coarser partition than our method. 
Keywords:  networks; clustering; community structure 
JEL:  C71 D85 
Date:  2018–10 
URL:  http://d.repec.org/n?u=RePEc:tkk:dpaper:dp118&r=all 
By:  Bobba, Matteo; Flabbi, Luca; Levy, Santiago; Tejada, Mauricio 
Abstract:  We develop a search and matching model where firms and workers produce output that depends both on matchspecific productivity and on workerspecific human capital. The human capital is accumulated while working but depreciates while searching for a job. Jobs can be formal or informal and firms post the formality status. The equilibrium is characterized by an endogenous steady state distribution of human capital and by an endogenous formality rate. The model is estimated on longitudinal labor market data for Mexico. Human capital accumulation onthejob is responsible for more than half of the overall value of production and upgrades more quickly while working formally than informally. Policy experiments reveal that the dynamics of human capital accumulation magnifies the negative impact on productivity of the labor market institutions that give raise to informality. 
Keywords:  Labor market frictions; Search and matching; Nash bargaining; Informality; OntheJob human capital accumulation 
JEL:  J24 J3 J64 O17 
Date:  2019–01 
URL:  http://d.repec.org/n?u=RePEc:tse:wpaper:33230&r=all 
By:  Bergantiños, Gustavo; Massó, Jordi; Neme, Alejandro 
Abstract:  We study individually rational rules to be used to allot, among a group of agents, a perfectly divisible good that is freely available only in whole units. A rule is individually rational if, at each preference profile, each agent finds that her allotment is at least as good as any whole unit of the good. We study and characterize two individually rational and efficient rules, whenever agents' preferences are symmetric singlepeaked on the set of possible allotments. The two rules are in addition envyfree, but they differ on wether envyfreeness is considered on losses or on awards. Our main result states that (i) the constrained equal losses rule is the unique individually rational and efficient rule that satisfies justified envyfreeness on losses and (ii) the constrained equal awards rule is the unique individually rational and efficient rule that satisfies envyfreeness on awards. 
Keywords:  Division problem; Singlepeaked preferences; Individual rationality; Efficiency; Strategyproofness; Envyfreeness 
JEL:  C78 
Date:  2019–01–25 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:91721&r=all 
By:  Bergantiños, Gustavo; Navarro, Adriana 
Abstract:  We consider minimum cost spanning tree problems with multiple sources. We propose a cost allocation rule based on a painting procedure. Agents paint the edges on the paths connecting them to the sources. We prove that the painting rule coincides with the folk rule. Finally, we provide an axiomatic characterization. 
Keywords:  }minimum cost spanning tree problems with multiple sources, painting rule, axiomatic characterization. 
JEL:  C71 
Date:  2019–01–25 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:91723&r=all 
By:  Sarah Bensalem (SAF  Laboratoire de Sciences Actuarielle et Financière  UCBL  Université Claude Bernard Lyon 1  Université de Lyon); Nicolás Hernández Santibáñez (Department of Mathematics  University of Michigan  University of Michigan [Ann Arbor]); Nabil KaziTani (SAF  Laboratoire de Sciences Actuarielle et Financière  UCBL  Université Claude Bernard Lyon 1  Université de Lyon) 
Abstract:  This paper studies an equilibrium model between an insurance buyer and an insurance seller, where both parties' risk preferences are given by convex risk measures. The interaction is modeled through a Stackelberg type game, where the insurance seller plays first by offering prices, in the form of safety loadings. Then the insurance buyer chooses his optimal proportional insurance share and his optimal prevention effort in order to minimize his risk measure. The loss distribution is given by a family of stochastically ordered probability measures, indexed by the prevention effort. We give special attention to the problems of selfinsurance and selfprotection. We prove that the formulated game admits a unique equilibrium, that we can explicitly solve by further specifying the agents criteria and the loss distribution. In selfinsurance, we consider also an adverse selection setting, where the type of the insurance buyers is given by his loss probability, and study the screening and shutdown contracts. Finally, we provide case studies in which we explicitly apply our theoretical results. 
Keywords:  Coherent risk measures,Stackelberg game,Prevention,Selfinsurance,Selfprotection 
Date:  2019–01–16 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal01983433&r=all 
By:  Serdarevic, Nina (University of Bergen, Department of Economics); Strømland, Eirik (University of Bergen, Department of Economics); Tjøtta, Sigve (University of Bergen, Department of Economics) 
Abstract:  This paper contributes to the experimental literature by examining the causal effect of partnerchoice opportunities on the earnings of different cooperative types. We first elicit cooperative types and then randomly assign subjects to a repeated prisoner’s dilemma game with either mutual partner choice or random matching. In each round, the individual who fails to attain a partner is excluded from the group. This design allows us to study the causal effect of partner choice on earnings and exclusion. The results from two experiments show that partner choice allows cooperators to outperform free riders, cooperators earn more than free riders, and cooperators are less frequently excluded. 
Keywords:  cooperation; commitment; partner choice; punishment 
JEL:  C91 C92 D02 
Date:  2018–09–13 
URL:  http://d.repec.org/n?u=RePEc:hhs:bergec:2018_012&r=all 
By:  Mark Whitmeyer 
Abstract:  We examine the classic "BeerQuiche" game from Cho and Kreps (1987), and relax the assumption that the order placed by the sender is completely observable. Under the optimal degree of transparency, the receiver achieves a higher payoff than with full transparency. Partial obfuscation of the sender's choice encourages separation: committing to a less informative signal about the sender's choice affects the endogenous information generation process such that the receiver thereby secures himself more information. 
Date:  2019–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1902.00976&r=all 