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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 continuous-time repeated games with perfect monitoring when immediate reactions to deviations are allowed. The set of subgame perfect equilibrium payoffs is shown to be a fixed-point of a set-valued 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 continuous-time 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 non-empty. 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 pre-match 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 pre-match investment competition. |
| Keywords: | bounded transfers, pre-match 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:2019-01&r=all |
| By: | Tanaka, Yasuhito |
| Abstract: | We study a Stackelberg type symmetric dynamic three-players zero-sum game. One player is the leader and two players are followers. All players have symmetric payoff functions. The game is a two-stages 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: | zero-sum 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 multi-players zero-sum game. One player is the leader and other players are followers. All players have symmetric payoff functions. The game is a two-stages 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, multi-players zero-sum 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 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Frédéric Koessler (PSE - Paris School of Economics, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Panthéon-Sorbonne - 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, Language-Based Expectation Equilibrium , which accounts for partial language understanding in sender-receiver 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 language-based 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: | Analogy-based 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:halshs-01988076&r=all |
| By: | Mathieu Martin; Zéphirin Nganmeni (Université de Cergy-Pontoise, THEMA) |
| Abstract: | In this paper, we focus on a result stated by Bräuninger that the fi nagle point is within the Ɛ-core 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:2019-03&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 Non-Efficient Alternatives and Independence of Redundant Alternatives can be applied to a reduced set of alternatives producing all Pareto-efficient 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 Pareto-efficient outcome. This rule is renegotiation-proof and generates a time-consistent 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 Cergy-Pontoise, 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 δ-core, 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 δ-core both generalizes and provides a new characterization of the yolk. We then study relationships between the δ-core and two other concepts: the Ɛ-core 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:2019-02&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 - Paris-Jourdan 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 Panthéon-Sorbonne - 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 self-reported 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 incentive-compatible 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 pure-strategy equilibrium without communication. |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-01983037&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 match-specific productivity and on worker-specific 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 on-the-job 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; On-the-Job 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 single-peaked on the set of possible allotments. The two rules are in addition envy-free, but they differ on wether envy-freeness 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 envy-freeness on losses and (ii) the constrained equal awards rule is the unique individually rational and efficient rule that satisfies envy-freeness on awards. |
| Keywords: | Division problem; Single-peaked preferences; Individual rationality; Efficiency; Strategy-proofness; Envy-freeness |
| 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 Kazi-Tani (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 self-insurance and self-protection. 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 self-insurance, 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,Self-insurance,Self-protection |
| Date: | 2019–01–16 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01983433&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 "Beer-Quiche" 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 |