nep-gth New Economics Papers
on Game Theory
Issue of 2009‒10‒10
eleven papers chosen by
Laszlo A. Koczy
Budapest Tech and Maastricht University

  1. Strategic Effects of Incomplete and Renegotiation-Proof Contracts By Levent Kockesen; Emanuele Gerratana
  2. On reciprocal Behavior in Prisoner Dilemma game By Ahmed Doghmi; Miloudi Kobiyh
  3. Share the Gain, Share the Pain? Almost Transferable Utility, changes in production possibilities, and bargaining solutions By Elisabeth Gugl; Justin Leroux
  4. Context-Dependent Forward Induction Reasoning By Pierpaolo Battigalli; Amanda Friedenberg
  5. House Allocation with Overlapping Agents: A Dynamic Mechanism Design Approach By Morimitsu Kurino
  6. Making the World a better Place: Experimental evidence from the generosity Game By Werner Güth; M. Vittoria Levati; Matteo Ploner
  7. Inequity and Risk Aversion in Sequential Public Good Games By Sabrina Teyssier
  8. A weighted position value By Amandine Ghintran
  9. Faulty Nash Implementation in Exchange Economies with Single-peaked Preferences By Ahmed Doghmi; Abderrahmane Ziad
  10. Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation By Roberto Serrano; Rajiv Vohra
  11. Contracts as Threats: on a Rationale For Rewarding A while Hoping For B By Elisabetta Iossa; Giancarlo Spagnolo

  1. By: Levent Kockesen (Koc University); Emanuele Gerratana
    Abstract: It is well known that non-renegotiable contracts with third parties may have an effect on the outcome of a strategic interaction and thus serve as a commitment device. We address this issue when contracts are renegotiable. More precisely, we analyze the equilibrium outcomes of twostage games with renegotiation-proof third-party contracts in relation to the equilibrium outcomes of the same game without contracts. We assume that one of the parties in the contractual relationship is unable to observe everything that happens in the game when played by the other party. This implies that contracts are incomplete and we show that such incompleteness restricts the set of equilibrium outcomes to a subset of Nash equilibrium outcomes of the game without contracts. Introducing renegotiation, in general, imposes further constraints and in some games implies that only subgame perfect equilibrium outcomes can be supported. However, there is a large class of games in which non-subgame perfect equilibriumoutcomes can also be supported, and hence, third-party contracts still have strategic implications even when they are renegotiable.
    Keywords: Third-Party Contracts, Strategic Delegation, Incomplete Contracts, Renegotiation
    JEL: C72 C78 D86 L13
    Date: 2009–09
  2. By: Ahmed Doghmi (Strategic Interaction Group, Max Planck Institute of Economics, Jena, Germany); Miloudi Kobiyh (Center for Research in Economics and Management, University of Caen, France)
    Abstract: In this paper, we introduce the concept of payoffi distortion in the standard prisoner's dilemma game when strategies are driven by psychological behaviors. This concept enables to take account each player's assessment of the other player's behavior and the asymmetry of information. We determine the conditions which allow that mutual cooperation constitutes the equilibrium. we particularly focus on the reciprocity in case of complete and incomplete information about the payoffi distortion. We show that mutual cooperation is a Nash equilibrium with complete information and is a Bayesian equilibrium when each player believes that his opponent behaves with "large" reciprocity in incomplete information environment.
    Keywords: Reciprocity, Behavior, Cooperation, prisoner's dilemma game.
    JEL: C7 A13
    Date: 2009–09–25
  3. By: Elisabeth Gugl; Justin Leroux (IEA, HEC Montréal)
    Abstract: We consider an n-person economy in which efficiency is independent of distribution but the cardinal properties of the agents’ utility functions preclude transferable utility (a property we call "Almost TU"). We show that Almost TU is a necessary and sufficient condition for all agents to either benefit jointly or suffer jointly with any change in production possibilities under well-behaved generalized utilitarian bargaining solutions (of which the Nash Bargaining and the utilitarian solutions are special cases). We apply the result to household decision making in the context of the Rotten Kid Theorem and in evaluating a change in family taxation.
    Keywords: Axiomatic Bargaining, Solidarity, Transferable Utility, Family Taxation, Rotten Kid Theorem
    JEL: C71 D63 D13
    Date: 2009–08
  4. By: Pierpaolo Battigalli; Amanda Friedenberg
    Abstract: This paper studies the case where a game is played in a particular context. The context influences what beliefs players hold. As such, it may affect forward induction reasoning: If players rule out specific beliefs, they may not be able to rationalize observed behavior. The effects are not obvious. Context-laden forward induction may allow outcomes precluded by context-free forward induction. At the formal level, forward induction and contextual reasoning are defined within an epistemic structure. In particular, we represent contextual forward induction reasoning as rationality and common strong belief of rationality”(RCSBR) within an arbitrary type structure. (The concept is due to Battigalli-Siniscalchi [6, 2002].) We ask: What strategies are consistent with RCSBR (across all type structures)? We show that the RCSBR is characterized by a solution concept we call Extensive Form Best Response Sets (EFBRS’s). We go on to study the EFBRS concept in games of interest.
    Date: 2009
  5. By: Morimitsu Kurino (Max Planck Institute of Economics, Jena, Germany)
    Abstract: Many real-life applications of house allocation problems are dynamic. For example, in the case of on-campus housing for college students, each year freshmen apply to move in and graduating seniors leave. Each student stays on campus for a few years only. A student is a "newcomer" in the beginning and then becomes an "existing tenant". Motivated by this observation, we introduce a model of house allocation with overlapping agents. In terms of dynamic mechanism design, we examine two representative static mechanisms of serial dictatorship (SD) and top trading cycles (TTC), both of which are based on an ordering of agents and give an agent with higher order an opportunity to obtain a better house. We show that for SD mechanisms, the ordering that favors existing tenants is better than the one that favors newcomers in terms of Pareto efficiency. Meanwhile, this result holds for TTC mechanisms under time-invariant preferences in terms of Pareto efficiency and strategy-proofness. We provide another simple dynamic mechanism that is strategy-proof and Pareto efficient.
    Keywords: house allocation, overlapping agents, dynamic mechanism, top trading cycles, serial dictatorship
    JEL: C71 C78 D71 D78
    Date: 2009–09–25
  6. By: Werner Güth (Max Planck Institute of Economics); M. Vittoria Levati (Max Planck Institute of Economics); Matteo Ploner (Max Planck Institute of Economics)
    Abstract: We study ultimatum and dictator experiments where the first mover chooses the amount of money to be distributed between the players within a given interval, knowing that her own share is ?xed. Thus, the first mover is faced with scarcity, but not with the typical trade-off between her own and the other's payoff. Removing the trade-off inspires significant generosity, which is not affected by the second mover's veto power. On the whole our results con?rm heterogeneity in behavior, but point to efficiency concerns as the predominant motive.
    Keywords: Ultimatum, Dictator, Social Preferences
    JEL: C70 C91 D63
    Date: 2009–09–25
  7. By: Sabrina Teyssier (Thurgau Institute of Economics, Kreuzlingen, Switzerland; University of Konstanz, Department of Economics, Germany)
    Abstract: This paper analyzes which type of intrinsic preferences drive an agent’s behavior in a sequential public good game depending on whether the agent is ï¬rst or second mover. Theoretical predictions are based on heterogeneity of individuals in terms of social and risk preferences. We modelize preferences according to the inequity aversion model of Fehr and Schmidt (1999) and to the assumption of constant relative risk aversion. Risk aversion is signiï¬cantly and negatively correlated with the contribution decision of ï¬rst movers. Second movers with sufficiently high advantageous inequity aversion free-ride less and reciprocate more than others. Both results are predicted by our model. Nevertheless, no effect of disadvantageous inequity aversion of ï¬rst movers is found in the data while theory predicted it. Our results underline the importance of taking into account the order of agents’ play to correctly understand which type of preferences influences cooperation in voluntary contribution mechanisms. They suggest that individuals’ behavior can be consistent between different experimental games.
    Keywords: inequity aversion, risk aversion, public good game, conditional contribution
    JEL: C72 C91 D63 D81 H41
    Date: 2009
  8. By: Amandine Ghintran (GATE Lyon Saint-Etienne - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines)
    Abstract: We provide a generalization of the position value (Meessen 1988) that allows players to benefit from transfers of worth by investing in communication links. The player who invests the most in a communication link obtains transfers of worth from the second one. We characterize this new allocation rule on the class of cycle free graphs by means of four axioms. The first two axioms, component efficiency and superfluous link property, are used to characterize the position value (Meessen (1988), Borm, Owen, and Tijs (1992)). Quasi-additivity is a weak version of the standard additivity axiom. The weighting axiom captures the fact that the allocation of players should be increasing with their level of investment.
    Keywords: Weighted position value; Monotonicity
    Date: 2009–09–16
  9. By: Ahmed Doghmi (Strategic Interaction Group, Max Planck Institute of Economics, Jena, Germany); Abderrahmane Ziad (Center for Research in Economics and Management, University of Caen, France)
    Abstract: In this paper, we reexamine Eliaz's results (2002) of fault tolerant implementation on one hand and we extend theorems 1 and 2 of Doghmi and Ziad (2008a) to bounded rationality environments, on the other. We identify weak versions of the k-no veto power condition, in conjunction with unanimity and variants of k-monotonicity, are sufficient for implementability in k- Fault Tolerant Nash equilibria (k-FTNE). In addition, these new conditions are stable by intersection which makes it possible to check directly the k-FTNE implementability of the social choice correspondences. We apply these results to exchange economies with single -peaked preferences, to ?nite allocation problems, and to equilibrium theory. Firstly, we note that our conditions are satis?ed by all monotonic solutions contrary to Eliaz's results (2002). Secondly, in exchange economy when preferences are single-peaked, the k-monotonicity is sufficient for the k-FTNE implementation for the correspondences and both necessary and sufficient for the functions. However, the results are negatives for the no-monotonic solutions.
    Keywords: Faulty Nash implementation, Bounded rationality, Exchange economies, Single-peaked preferences
    JEL: C72 D71
    Date: 2009–09–25
  10. By: Roberto Serrano (Brown University and IMDEA Social Sciences); Rajiv Vohra (Brown University)
    Abstract: We characterize full implementation of social choice sets in mixed strategy Bayesian equilibrium. Our results concern both exact and virtual mixed implementation. For exact implementation, we identify a strengthening of Bayesian monotonicity, which we refer to as mixed Bayesian monotonicity. It is shown that, in economic environments with at least three agents, mixed Bayesian implementation is equivalent to mixed Bayesian monotonicity, incentive compatibility and closure. For implementing a social choice function, the case of two-agents is also covered by these conditions and mixed Bayesian monotonicity reduces to Bayesian monotonicity. Following parallel steps, mixed virtual implementation is shown to be equivalent to mixed virtual monotonicity, incentive compatibility and closure. The key condition, mixed virtual monotonicity, is argued to be very weak. In particular, it is weaker than Abreu-Matsushima\'s measurability, there by implying that: (1) virtual implementation in mixed Bayesian equilibrium is more permissive than virtual implementation in iteratively undominated strategies, and (2) non-regular mechanisms are essential for the implementation of rules in that gap.
    Keywords: exact implementation; approximate implementation; incomplete information; incentive compatibility; monotonicity
    JEL: C72 D78 D82
    Date: 2009–09–21
  11. By: Elisabetta Iossa (Faculty of Economics, University of Rome "Tor Vergata"); Giancarlo Spagnolo (Faculty of Economics, University of Rome "Tor Vergata")
    Abstract: In this paper we explore theoretically the relationship between explicit and implicit/relational contracting distinguishing between the ex-ante decision to sign an explicit contract and the ex-post decision wheter to actually apply it. We show, among other things, that the relational efficient explicit contract tends to display overcontracting on tasks or qualitative requirements (A) that are verifiable but apparently of little use for the principal. The ex-post (non) implementation of such explicit contract can then be discretionally exchanged against the provision of non contractible tasks (B) that are highly valuable for the principal. An empirical implication of the result, consistent with casual observation in procurement, is that penalties for infringements established by explicit contracts are seldom exercised, even though violations take place and are easy to monitor and verify.
    Keywords: Implicit contracts, incomplete contracts, repeated games
    JEL: C73 D86
    Date: 2009–09–30

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