nep-mic New Economics Papers
on Microeconomics
Issue of 2012‒01‒03
24 papers chosen by
Jing-Yuan Chiou
IMT Lucca Institute for Advanced Studies

  1. Selfconfirming Equilibrium and Uncertainty By Pierpaolo Battigalli; Simone Cerreia-Vioglio; Fabio Maccheroni; Massimo Marinacci
  2. Regularity and Stability in Monotone Bayesian Games By A.W. Beggs
  3. Full Disclosure in Decentralized Organizations By Jeanne Hagenbach; Frédéric Koessler
  4. Existence of equilibrium in OLG economies with increasing returns By Jean-Marc Bonnisseau; Lalaina Rakotonindrainy
  5. Ensuring the boundedness of the core of games with restricted cooperation By Michel Grabisch
  6. Subjective Evaluations with Performance Feedback By Jan Zabojnik
  7. A Note on Contribution Games with Loss Functions By Giuseppe Russo
  8. Existence of Optimal Mechanisms in Principal-Agent Problems By Ohad Kadan; Philip J. Reny; Jeroen Swinkels
  9. Nash Equilibria in 2 × 2 × 2 Trimatrix Games with Identical Anonymous Best-Replies By Gonzalez-Alcon, C.; Borm, P.E.M.; Hendrickx, R.L.P.
  10. Lying about what you know or about what you do? (replaces CentER DP 2010-033) By Serra Garcia, M.; Damme, E.E.C. van; Potters, J.J.M.
  11. Subgame-Perfection in Free Transition Games By Flesch J.; Kuipers J.; Schoenmakers G.; Vrieze K.
  12. Update Monotone Preference Rules By Can Burak; Storcken Ton
  13. Reasoning about Strategies and Rational Play in Dynamic Games By Bonanno, Giacomo
  14. Context and Decision: Utility on a Union of Mixture Spaces By O’Callaghan, Patrick
  15. Seeking Harmony Amidst Diversity: Consensus Building with Network Externalities By Junichiro Ishida; Chia-Hui Chen
  16. Game-theoretic pragmatics under conflicting and common interests By Kris De Jaegher; Robert van Rooij
  17. A geometric approach to mechanism design By Jacob K. Goeree; Alexey Kushnir
  18. Implementation of Reduced Form Mechanisms: A Simple Approach and a New Characterization By Sergiu Hart; Philip J. Reny
  19. On the optimal management of teams under budget constraints By Dunia López-Pintado; Juan D. Moreno-Ternero
  20. Sandbagging By Matthias Kräkel
  21. Peer punishment with third-party approval in a social dilemma game By Tan, Fangfang; Xiao, Erte
  22. Optimality of linearity with collusion and renegotiation By Barlo, Mehmet; Ozdogan, Ayca
  23. Strategic behavior in non-atomic games By Barlo, Mehmet; Carmona, Guilherme
  24. Commitment and optimal incentive By Liu, Taoxiong; Zhou, Bihua

  1. By: Pierpaolo Battigalli; Simone Cerreia-Vioglio; Fabio Maccheroni; Massimo Marinacci
    Abstract: We propose to bring together two conceptually complementary ideas: (1) selfconfi?rming equilibrium (SCE): at a rest point of learning dynamics in a game played recurrently, agents best respond to confi?rmed beliefs, i.e. beliefs consistent with the evidence they accumulate, and (2) ambiguity aversion: agents, coeteris paribus, prefer to bet on events with known rather than unknown probabilities, more generally, agents distinguish objective from subjective uncertainty, which is captured by their ambiguity attitudes. Using as a workhorse the ?smooth ambiguity model of Klibanoff, Marinacci and Mukerji (2005), we provide a de?nition of "smooth SCE" which generalizes the traditional concept of Fudenberg and Levine (1993a,b), called Bayesian SCE, and admits Waldean (maxmin) SCE as a limit case. We show that the set of equilibria expands as ambiguity aversion increases. The intuition is simple: by playing the same "status-quo" strategy in a stable state an agent learns the implied objective probabilities of payoffs, but alternative strategies yield payoffs with unknown probabilities; keeping beliefs ?fixed, increased aversion to ambiguity makes such strategies less appealing. We rely on this core intuition to show that different notions of equilibrium are nested in a simple way, from ?ner to coarser: Nash, Bayesian SCE, Smooth SCE and Waldean SCE. We also prove some equivalence results, under special assumptions about the information structure.
    Date: 2011
  2. By: A.W. Beggs
    Abstract: This paper defines regular and weakly regular equilibria for monotone Bayesian games with one-dimensional actions and types. It proves an index theorem and provides applications to uniqueness of equilibrium. It also provides analyses of stability with respect to perturbations and dynamic stability.
    Keywords: Bayesian games, Monotone strategies, Index theory, Stability, Uniqueness, Regularity
    JEL: C72 D83
    Date: 2011
  3. By: Jeanne Hagenbach (Ecole Polytechnique - Ecole Polytechnique); Frédéric Koessler (PSE - Paris-Jourdan Sciences Economiques - CNRS : UMR8545 - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - Ecole des Ponts ParisTech - Ecole Normale Supérieure de Paris - ENS Paris - INRA, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)
    Abstract: We characterize sufficient conditions for full and decentralized disclosure of hard information in organizations with asymmetrically informed and self interested agents with quadratic loss functions. Incentive conflicts arise because agents have different (and possibly interdependent) ideal actions and different incentives to coordinate with each others. A fully revealing sequential equilibrium exists in the disclosure game if each player's ideal action is monotonic in types and types are independently distributed, but may fail to exist with non-monotonic ideal actions or correlated types. When biases between players' ideal actions are constant across states, complete information is the Pareto dominant information structure. In that case, there is a fully revealing sequential equilibrium in which informational incentive constraints are satisfied ex-post, so it exists for all possible prior beliefs, even when players' types are correlated. This existence result applies whether information disclosure is private or public, and is extended to partial certifiability of information.
    Keywords: Certifiable types ; Coordination ; Information disclosure ; Multi-divisional organizations
    Date: 2011–12
  4. By: Jean-Marc Bonnisseau (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Lalaina Rakotonindrainy (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)
    Abstract: We consider a standard overlapping generation economy with a simple demographic structure with a new cohort of agents at each period with an economic activity extended over two successive periods and finitely many firms active forever. The production possibilities are described by a sequence of production mapping and the main innovation comes from the fact that we allow for increasing returns to scale of more general type of non-convexities. To describe the behavior of the firms, we consider loss-free pricing rules, which covers the case of the average pricing rule, the competitive behavior when the firms have convex production sets, and the competitive behavior with quantity constraints à la Dehez-Drèze. We prove the existence of an equilibrium under assumptions, which are at the same level of generality than the ones for the existence in an exchange economy.
    Keywords: Overlapping generation model, increasing returns to scale, loss-free pricing rules, equilibrium, existence.
    Date: 2011–11
  5. By: Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)
    Abstract: The core of a cooperative game on a set of players $N$ is one of the most popular concepts of solution. When cooperation is restricted (feasible coalitions form a subcollection $\cF$ of $2^N$), the core may become unbounded, which makes its usage questionable in practice. Our proposal is to make the core bounded by turning some of the inequalities defining the core into equalities (additional efficiency constraints). We address the following mathematical problem: can we find a minimal set of inequalities in the core such that, if turned into equalities, the core becomes bounded? The new core obtained is called the restricted core. We completely solve the question when $\cF$ is a distributive lattice, introducing also the notion of restricted Weber set. We show that the case of regular set systems amounts more or less to the case of distributive lattices. We also study the case of weakly union-closed systems and give some results for the general case.
    Date: 2011
  6. By: Jan Zabojnik (Queen's University)
    Abstract: This paper models two key roles of subjective performance evaluations: their incentive role and their feedback role. The paper shows that the feedback role makes subjective pay feasible even without repeated interaction, as long as there exists some verifiable measure of performance. It also shows that while subjective pay is helpful, it cannot achieve full efficiency. However, fully efficient incentives are achievable if the firm can commit to a forced distribution of evaluations and employs a continuum of workers. With a small number of workers, a forced distribution is valuable only if the verifiable measure is poor.
    Keywords: Subjective Evaluations, Performance Feedback, Optimal Contracts
    JEL: D82 D86 M52
    Date: 2011–11
  7. By: Giuseppe Russo (University of Salerno and CSEF)
    Abstract: Decisions on joint funding of continuous public goods between two agents often involve heterogeneous targets. We introduce loss functions in a contribution game in order to study the effect of this conflict. Unlike Varian (1994), joint contribution occurs only if the players’ targets are sufficiently close and the sequential game reduces free riding problems, while total contribution is higher in the simultaneous game.
    Keywords: Public Goods, Intergovernmental Relations
    JEL: H41 H77
    Date: 2011–12–20
  8. By: Ohad Kadan (Washington University in St. Louis - Olin School of Business); Philip J. Reny (University of Chicago - Department of Economics); Jeroen Swinkels (Northwestern University - Kellogg School of Management)
    Abstract: We provide general conditions under which principal-agent problems admit mechanisms that are optimal for the principal. Our result covers as special cases those in which the agent has no private information –i.e., pure moral hazard –as well as those in which the agent’s only action is a participation decision – i.e., pure adverse selection. We allow multi-dimensional actions and signals, as well as both …nancial and non-…nancial rewards. Beyond measurability, we require no a priori restrictions on the space of mechanisms. Consequently, our optimal mechanisms are optimal among all measurable mechanisms. A key to obtaining our result is to permit randomized mechanisms. We also provide conditions under which randomization is unnecessary.
    Date: 2011–01
  9. By: Gonzalez-Alcon, C.; Borm, P.E.M.; Hendrickx, R.L.P. (Tilburg University, Center for Economic Research)
    Abstract: This paper introduces the class of 2 × 2 × 2 trimatrix games with identical anonymous best-replies. For this class a complete classification on the basis of the Nash equilibrium set is provided.
    Keywords: trimatrix games;Nash equilibrium;best-reply correspondences;symmetric games.
    JEL: C72
    Date: 2011
  10. By: Serra Garcia, M.; Damme, E.E.C. van; Potters, J.J.M. (Tilburg University, Center for Economic Research)
    Abstract: We compare communication about private information to communication about actions in a one- shot 2-person public good game with private information. The informed player, who knows the exact return from contributing and whose contribution is unobserved, can send a message about the return or her contribution. Theoretically, messages can elicit the uninformed player's contribution, and allow the informed player to free-ride. The exact language used is not expected to matter. Experimentally, however, we find that free-riding depends on the language: the informed player free-rides less, and thereby lies less frequently, when she talks about her contribution than when she talks about the return. Further experimental evidence indicates that it is the promise component in messages about the contribution that leads to less free-riding and less lying.
    Keywords: Information transmission;lying;communication;experiment.
    JEL: C72 D82 D83
    Date: 2011
  11. By: Flesch J.; Kuipers J.; Schoenmakers G.; Vrieze K. (METEOR)
    Abstract: We prove the existence of a subgame-perfect epsilon-equilibrium, for every epsilon> 0, in a classof multi-player games with perfect information, which we call free transition games. The noveltyis that a non-trivial class of perfect information games is solved for subgame-perfection, withmultiple non-terminating actions, in which the payoff structure is generally not semi-continuous.Due to the lack of semi-continuity, there is no general rule of comparison between the payoffsthat a player can obtain by deviating a large but finite number of times or, respectively,infinitely many times. We introduce new techniques to overcome this difficulty. Our constructionrelies on an iterative scheme which is independent of epsilon and terminates in polynomial timewith the following output: for all possible histories h, a pure action a(1,h) or in some cases twopure actions a(2,h) and b(2,h) for the active player at h. The subgame-perfect epsilon-equilibriumthen prescribes for every history h that the active player plays a(1,h) with probability 1 orrespectively plays a(2,h) with probability 1-delta and b(2,h) with probability delta. Here, deltais arbitrary as long as it is positive and small compared to epsilon, so the strategies can bemade “almost” pure.
    Keywords: mathematical economics;
    Date: 2011
  12. By: Can Burak; Storcken Ton (METEOR)
    Abstract: Collective decisions are modeled by preference correspondences (rules). In particular, we focus ona new condition: "update monotonicity" for preference rules. Although many so-called impossibilitytheorems for the choice rules are based on -or related to- monotonicity conditions, this appealingcondition is satisfied by several non-trivial preference rules. In fact, in case of pairwise,Pareto optimal, neutral, and consistent rules; the Kemeny-Young rule is singled out by thiscondition. In case of convex valued, Pareto optimal, neutral and replication invariant rules;strong update monotonicity implies that the rule equals the union of preferences which extend allpreference pairs unanimously agreed upon by k agents, where k is related to the number ofalternatives and agents. In both cases, it therewith provides a charaterization of these rules.
    Keywords: microeconomics ;
    Date: 2011
  13. By: Bonanno, Giacomo (University of CA, Davis)
    Abstract: We discuss a number of conceptual issues that arise in attempting to capture, in dynamic games, the notion that there is "common understanding" among the players that they are all rational.
    Date: 2011–11
  14. By: O’Callaghan, Patrick (University of Warwick)
    Abstract: Suppose a decision-maker is willing to make statements of the form : I prefer to choose alternative a when in context p, than to choose alternative b when in context q”. Contexts p and q may refer to given probability distributions over a set of states, and b and c to alternatives such as: “turn left” or “turn right” at a junction. In such decision problems, the set of alternatives is discrete and there is a continuum of possible contexts. I assume there is a is a mixture operation on the space of contexts (eg. convex combinations of lotteries), and propose a model that defines preferences over a collection of mixture spaces indexed by a discrete set. The model yields a spectrum of possibilities: some decision-makers are well represented by a standard von Neumann–Morgenstern type of utility function; whilst for others, utility across some or all the mixture spaces is only ordinally comparable. An application to the decision problem of Karni and Safra (2000) leads to a generalization, and shows that state-dependence and comparability are distinct concepts. A final application provides a novel way modeling incomplete preferences and explaining the Allais paradox.
    Date: 2011
  15. By: Junichiro Ishida; Chia-Hui Chen
    Abstract: A group of individuals, with a potential conflict of interest, face a choice among alternatives. There is a network externality such that the chosen alternative yields value only if sufficiently many individuals get on board. Their preferences for each alternative and the benefit derived from a successfully formed network are known only privately and might vary between the players who determine whether to make their choices early or late. We characterize the equilibrium timing of adoption as well as the efficient timing which maximizes the total expected payoff. We also show that the efficient timing of adoption can be implemented by a simple fee scheme. The analysis gives an insight into why consensus is often hard-won in some societies and suggests a potential role of social norms in improving the efficiency.
    Date: 2011–12
  16. By: Kris De Jaegher; Robert van Rooij
    Abstract: This paper combines a literature overview of existing literature in game-theoretic pragmatics, with new models that fill some voids in the literature. We start with an overview of signaling games with a conflict of interest between sender and receiver, and show that the literature on such games can be classified into models with direct, costly, noisy and imprecise signals. We then argue that this same subdivision can be used to classify signaling games with common interests, where we fill some voids in the literature. For each of the signaling games treated, we show how equilibrium- refinement arguments and evolutionary arguments can be interpreted in the light of pragmatic inference.
    Keywords: Signaling games, pragmatics, equilibrium refinements, evolutionary game theory
    JEL: D82 D83
    Date: 2011–12
  17. By: Jacob K. Goeree; Alexey Kushnir
    Abstract: An important result in convex analysis is the duality between a closed convex set and its support function. We exploit this duality to develop a novel geometric approach to mechanism design. For a general class of social choice problems we characterize the feasible set, which is closed and convex, and its support function. We next provide a geometric interpretation of incentive compatibility and refine the support function to include incentive constraints using arguments from majorization theory. The optimal mechanism can subsequently be derived from the support function using Hotelling's lemma. We first assume that values are linear in types and types are independent, private, and one-dimensional. For this environment we provide a simple geometric proof that Bayesian and dominant strategy implementation are equivalent by showing that the feasible sets that remain after imposing either type of incentive constraints coincide. Furthermore, we derive the optimal mechanism for any social choice problem and any linear objective, including revenue and surplus maximization. As an illustration, we determine the optimal multi-unit auction for a class of value functions that exhibit decreasing marginal valuations. Other types of constraints, such as capacity constraints and budget balancedness, can be interpreted geometrically as well, which facilitates a unified approach to a range of social choice problems, including auctions, bargaining, and public goods provision. We discuss how our geometric approach extends to environments with value interdependencies, non-linear valuations, and correlated or multi-dimensional types. Specifically, we illustrate that with interdependent valuations the equivalence between Bayesian and dominant strategy implementation breaks down, and our approach naturally produces the second-best outcomes for both types of incentive constraints.
    Keywords: Convex sets, support functions, majorization, Hotelling's lemma, mechanism design, revenue equivalence, BIC-DIC equivalence, multi-unit auctions, bargaining, public goods provision, capacity constraints, budget balance, interdependent values, second best efficiency
    JEL: D44
    Date: 2011–12
  18. By: Sergiu Hart; Philip J. Reny
    Date: 2011–12–21
  19. By: Dunia López-Pintado (Department of Economics, Universidad Pablo de Olavide; CORE, Université catholique de Louvain); Juan D. Moreno-Ternero (Department of Economics, Universidad Pablo de Olavide; CORE, Université catholique de Louvain)
    Abstract: We study optimal wage schemes for teams, under the presence of budget constraints, in a model in which agents’ effort decisions are mapped into the probability of the team’s success. We show that (first-best) efficiency can only be attained with complex contracts that are vulnerable to ex post manipulations and off-equilibrium path violations of the budget constraints. Within the domain of simple (and budget-balanced) contracts, an interesting scheme, which treats equal members of the team unequally, emerges as optimal
    Keywords: Team production, budget constraints, efficiency, manipulability, impartiality
    JEL: C70 D23 D78
    Date: 2011–12
  20. By: Matthias Kräkel
    Abstract: Participants of dynamic competition games may prefer to play with the rules of the game by systematically withholding e¤ort in the beginning. Such behavior is referred to as sandbagging. I consider a two-period con- test between heterogeneous players and analyze potential sandbagging of high-ability participants in the first period. Such sandbagging can be ben- eficial to avoid second-period matches against other high-ability opponents. I characterize the conditions under which sandbagging leads to a coordina- tion problem, similar to that of the battle-of-the sexes game. Moreover, if players' abilities have a stronger impact on the outcome of the first-period contest than e¤ort choices, mutual sandbagging by all high-ability players can arise.
    Keywords: ecoordination problem, dynamic contest, heterogeneous contestants, withholding e¤ort
    JEL: C72 D72
    Date: 2011–11
  21. By: Tan, Fangfang; Xiao, Erte
    Abstract: This paper investigates how punishment promotes cooperation when the punishment enforcer is a third party independent of the implicated parties who propose the punishment. In a prisoner's dilemma experiment, we find an independent third party vetoes not only punishment to the cooperators but punishment to the defectors as well. Compared with the case when the implicated parties are allowed to punish each other, both the cooperation rate and the earnings are lower when the enforcement of punishment requires approval from an independent third party.
    Keywords: Social dilemmas; third party; punishment; cooperation; experiment
    JEL: D63 C92 C72
    Date: 2011–12–21
  22. By: Barlo, Mehmet; Ozdogan, Ayca
    Abstract: This study analyzes a continuous-time N-agent Brownian hidden-action model with exponential utilities, in which agents' actions jointly determine the mean and the variance of the outcome process. In order to give a theoretical justi¯cation for the use of linear contracts, as in Holmstrom and Milgrom (1987), we consider a variant of its generalization given by Sung (1995), into which collusion and renegotiation possibilities among agents are incorporated. In this model, we prove that there exists a linear and stationary optimal compensation scheme which is also immune to collusion and renegotiation.
    Keywords: Principal-agent problems; moral hazard; linear contracts; continuous-time model; Brownian motion martingale method; collusion;; renegotiation; team
    JEL: D86 D82 C61 C73
    Date: 2011–12–13
  23. By: Barlo, Mehmet; Carmona, Guilherme
    Abstract: In order to remedy the possible loss of strategic interaction in non-atomic games with a societal choice, this study proposes a refinement of Nash equilibrium, strategic equilibrium. Given a non-atomic game, its perturbed game is one in which every player believes that he alone has a small, but positive, impact on the societal choice; and a distribution is a strategic equilibrium if it is a limit point of a sequence of Nash equilibrium distributions of games in which each player's belief about his impact on the societal choice goes to zero. After proving the existence of strategic equilibria, we show that all of them must be Nash. Moreover, it is displayed that in many economic applications, the set of strategic equilibria coincides with that of Nash equilibria of large finite games.
    Keywords: Strategic equilibrium; Games with a continuum of players; Equilibrium distributions
    JEL: C72
    Date: 2011–12–13
  24. By: Liu, Taoxiong; Zhou, Bihua
    Abstract: We propose an extended principal-agent model considering employee commitment and describe how to motivate committed agent, who not only shows regard for his own income but also cares the organizational benefit. The principal also would like to provide support to such an agent and his utility depends on both the final profit and the payoff to the agent. There are some interesting insights into the characteristic of optimal contracts: First, commitment is an effective motivator and committed employee needs less monetary inducement to perform his job well than one who not. More specifically, undifferentiated pay is sufficient in incentivizing committed agent to implement high effort in some cases. Second, commitment and wage differential are substitutable to each other in the optimal incentive compensation design. Third, commitment is not always good for organizational efficiency when the increase in employee commitment relies on the principal’s support. Our model's finding is consistent with employee incentive in some organizations, and also help to incentive mechanism design under wages differential constraints and understanding excessive compensation.
    Keywords: Commitment; Organizational support; Optimal Incentive; Contract
    JEL: D23 J33
    Date: 2011–12–08

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