nep-gth New Economics Papers
on Game Theory
Issue of 2012‒02‒01
thirteen papers chosen by
Laszlo A. Koczy
Hungarian Academy of Sciences and Obuda University

  1. Once Beaten, Never Again: Imitation in Two-Player Potential Games By Duersch, Peter; Oechssler, Jorg; Schipper, Burkhard C.
  2. Beliefs and rationalizability in games with complementarities By Mathevet, Laurent
  3. A simple axiomatics of dynamic play in repeated games By Mathevet, Laurent
  4. Discounted Stochastic Games with Voluntary Transfers By Sebastian Kranz
  5. Finding Maxmin Allocations in Cooperative and Competitive Fair Division By Marco Dall'Aglio; Camilla Di Luca
  6. A New Class of Welfare Maximizing Stable Sharing Rules for Partition Function Games with Externalities By Eyckmans, Johan; Finus, Michael; Mallozzi, Lina
  7. An Uninterpreted Spatial Version of the Trust Game: Evidence of Reciprocity without Suggestive Words, Evidence of Iterated Dominance Self-Taught By Talbot Page; Louis Putterman
  8. Efficient Auctions and Interdependent Types By Dirk Bergemann; Stephen Morris; Satoru Takahashi
  9. Bounded Rationality in Principal‐Agent Relationships By Mathias Erlei; Heike Schenk-Mathes
  10. Bluffing as a Mixed Strategy By Thomas W.L. Norman
  11. Evolutionary strategic beliefs and financial markets By Elyès Jouini; Clotilde Napp; Yannick Viossat
  12. Complexity and Endogenous Instability By Sami Al-Suwailem
  13. On the (non) existence of a price equilibrium in delegation games with relative performance compensation By M. Kopel; L. Lambertini

  1. By: Duersch, Peter (University of Heidelberg); Oechssler, Jorg (University of Heidelberg); Schipper, Burkhard C. (University of CA, Davis)
    Abstract: We show that in symmetric two-player exact potential games, the simple decision rule "imitate-if-better" cannot be beaten by any strategy in a repeated game by more than the maximal payoff difference of the one-period game. Our results apply to many interesting games including examples like 2x2 games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games.
    JEL: C72 C73 D43
    Date: 2011–12
  2. By: Mathevet, Laurent
    Abstract: We propose two characteristics of players' beliefs and study their role in shaping the set of rationalizable strategy profiles in games with incomplete information. The first characteristic, type-sensitivity, is related to how informative a player thinks his type is. The second characteristic, optimism, is related to how "favorable" a player expects the outcome of the game to be. The paper has two main results: the first result provides an upper bound on the size of the set of rationalizable strategy profiles, the second gives a lower bound on the change of location of this set. These bounds have explicit and relatively simple expressions that feature type-sensitivity, optimism, and properties of the payoffs. Our results generalize and clarify the well-known uniqueness result of global games (Carlsson and van Damme (1993)). They imply new uniqueness results and allow to study rationalizability in new environments. We provide applications to supermodular mechanism design (Mathevet (2010)) and non-Bayesian updating (Epstein (2006)).
    Keywords: Complementarities; rationalizability; beliefs; type-sensitivity; optimism; global games; equilibrium uniqueness
    JEL: D82 D83 C72
    Date: 2012–01–05
  3. By: Mathevet, Laurent
    Abstract: This paper proposes an axiomatic approach to study two-player infinitely repeated games. A solution is a correspondence that maps the set of stage games into the set of infinite sequences of action profiles. We suggest that a solution should satisfy two simple axioms: individual rationality and collective intelligence. The paper has three main results. First, we provide a classification of all repeated games into families, based on the strength of the requirement imposed by the axiom of collective intelligence. Second, we characterize our solution as well as the solution payoffs in all repeated games. We illustrate our characterizations on several games for which we compare our solution payoffs to the equilibrium payoff set of Abreu and Rubinstein (1988). At last, we develop two models of players' behavior that satisfy our axioms. The first model is a refinement of subgame-perfection, known as renegotiation proofness, and the second is an aspiration-based learning model.
    Keywords: Axiomatic approach; repeated games; classification of games; learning; renegotiation
    JEL: C71 C72 C73
    Date: 2012–01–17
  4. By: Sebastian Kranz (Dept. of Economics, University of Bonn, Institute for Energy Economics, University of Cologne)
    Abstract: This paper studies discounted stochastic games perfect or imperfect public monitoring and the opportunity to conduct voluntary monetary transfers. We show that for all discount factors every public perfect equilibrium payoff can be implemented with a simple class of equilibria that have a stationary structure on the equilibrium path and optimal penal codes with a stick and carrot structure. We develop algorithms that exactly compute or approximate the set of equilibrium payoffs and find simple equilibria that implement these payoffs.
    Keywords: Stochastic games, Monetary transfers, Computation, Imperfect public monitoring, Public perfect equilibria
    JEL: C73 C61 C63
    Date: 2012–01
  5. By: Marco Dall'Aglio (LUISS University Rome, Italy); Camilla Di Luca ("G. D'Annunzio" University Pescara, Italy)
    Abstract: We consider upper and lower bounds for maxmin allocations of a completely divisible good in both competitive and cooperative strategic contexts. We then derive a subgradient algorithm to compute the exact value up to any fixed degree of precision.
    Keywords: Fair Division, Maxmin Allocation, Kalai Bargaining Solution, Cooperative Game Theory
    JEL: D63 C61 C71 C78
    Date: 2011–12
  6. By: Eyckmans, Johan (Hogeschool-Universiteit Brussel (HUB), Belgium); Finus, Michael (University of Exeter Business School,UK); Mallozzi, Lina (University of Naples Federico II, Italy)
    Abstract: We propose a class of sharing rules for the distribution of the gains from cooperation for partition function games with externalities. We show that this class of sharing rules is characterized by three axioms: coalitional efficiency, additivity and anonimity which are adapted to the context of partition function games. The sharing rules stabilize, in the sense of d'Aspremont et al. (1983), the coalition which generates the highest global welfare among the set of potentially internally stable coalitions. The new class of sharing rules is particularly powerful for economic problems that are characterized by positive externalities from coalition formation (outsiders benefit from the expansion of the coalition) and which therefore often suffer from free-riding.
    Keywords: partition function; coalition formation; externalities; surplus
    JEL: C70 C71
    Date: 2011–07
  7. By: Talbot Page; Louis Putterman
    Abstract: In this working paper we report on two trust games: a BDM-like game which is interpreted through its use of the possibly suggestive words “show up fee,” “sends,” “tripled,” “send back”; and an uninterpreted spatial game that does not use these words suggestive or not. In the spatial game we found a considerable amount of reciprocity, which implies the words are not necessary for reciprocity. For further comparison we designed the two games to have a correspondence relation (the relation extends to the original BDM trust game). We focused on two “variables” – interpreted or uninterpreted and spatial or word-based. We also designed “constants” which were identical or near identical in the two games. We did this to reduce confounding in statistical comparisons. We found the frequency of reciprocity in the spatial game, without the suggestive words, was about the same as the frequency of reciprocity in the BDM-like game, with the suggestive words. We found iterated dominance in the spatial game was 5.5 times higher than in the BDM-like game. And we found sending the full endowment was significantly more frequent in the BDM-like game than in the spatial game.
    Keywords: #
    Date: 2012
  8. By: Dirk Bergemann (Cowles Foundation, Yale University); Stephen Morris (Dept. of Economics, Princeton University); Satoru Takahashi (Dept. of Economics, Princeton University)
    Abstract: We consider the efficient allocation of a single good with interdependent values in a quasi-linear environment. We present an approach to modelling interdependent preferences distinguishing between "payoff types" and "belief types" and report a characterization of when the efficient allocation can be partially Bayesian implemented on a finite type space. The characterization can be used to unify a number of sufficient conditions for efficient partial implementation in this classical auction setting. We report how a canonical language for discussing interdependent types -- developed in a more general setting by Bergemann, Morris and Takahashi (2011) -- applies in this setting and note by example that this canonical language will not allow us to distinguish some types in the payoff type -- belief type language.
    Keywords: Mechanism Design, Robust mechanism design, Efficient auctions, Interdepedent types, Partial implementation, Full implementation
    JEL: C79 D82
    Date: 2012–01
  9. By: Mathias Erlei; Heike Schenk-Mathes (Abteilung für Volkswirtschaftslehre, Technische Universität Clausthal (Department of Economics, Technical University Clausthal))
    Abstract: We conducted six treatments of a standard moral hazard experiment with hidden action. All treatments had identical Nash equilibria. However, the behavior in all treatments and periods was inconsistent with established agency theory (Nash equilibrium). In the early periods of the experiment, behavior differed significantly between treatments. This difference largely vanished in the final periods. We used logit equilibrium (LE) as a device to grasp boundedly rational behavior and found the following: (1) LE predictions are much closer to subjects’ behavior in the laboratory; (2) LE probabilities of choosing between strategies and experimental behavior show remarkably similar patterns; and (3) profit‐maximizing contract offers according to the LE are close to those derived from regressions.
    Keywords: experiment, logit equilibrium, moral hazard, hidden action
    JEL: C72 C92 J31 L14
    Date: 2012
  10. By: Thomas W.L. Norman
    Abstract: In von Neumann and Morgenstern’s sample model of poker, equilibrium has the first player bet with high and low hands, and check with intermediate hands. The second player then calls if his hand is sufficiently high. Betting by the low hands is interpreted as bluffing, and is a pure strategy. Here we show that this equilibrium is nongeneric, in the sense that it ceases to exist if the first player is allowed to choose among many possible bets, rather than just one. Moreover, Newman’s solution for this case - which also has pure-strategy bluffing - is shown not to be a sequential equilibrium. However, a modified solution - where low hands bluff using mixed strategies - is a sequential equilbrium.
    Keywords: Poker, Game theory, Mixed strategies, Perfect Bayesian equilibrum, Sequential equilibrium
    JEL: C73
    Date: 2012
  11. By: Elyès Jouini (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris IX - Paris Dauphine); Clotilde Napp (CREST - Centre de Recherche en Économie et Statistique - INSEE - École Nationale de la Statistique et de l'Administration Économique, DRM - Dauphine Recherches en Management - CNRS : UMR7088 - Université Paris IX - Paris Dauphine); Yannick Viossat (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris IX - Paris Dauphine)
    Abstract: We provide a discipline for belief formation through a model of subjective beliefs, in which agents hold strategic beliefs. More precisely, we consider beliefs as a strategic variable that agents can choose (consciously or not) in order to maximize their utility at the equilibrium. These strategic beliefs result from an evolutionary process. We find that evolutionary strategic behavior leads to belief subjectivity and heterogeneity. Optimism (resp. overconfidence) as well as pessimism (resp. doubt) both emerge from the evolution process. Furthermore, we obtain a positive correlation between pessimism (rep. doubt) and risk-tolerance. We analyse the equilibrium characteristics. Under reasonable assumptions, the consensus belief is pessimistic and, as a consequence, the risk premium is higher than in a standard setting.
    Keywords: Beliefs formation, strategic beliefs, optimal beliefs, distorded beliefs, pessimism, risk premium
    Date: 2012–01–03
  12. By: Sami Al-Suwailem
    Abstract: The global financial crisis proved the critical impact of the gap between individual rationality and group rationality. This gap is not supposed to arise in a Neoclassical world, but it frequently arises in a world as complex as ours. The paper explores how endogenous instability might arise due to such a gap, and what behavioral rules might help to mitigate its impact.
    Keywords: fallacy of composition, empathy, n-person prisoner’s dilemma games, n-person zero-sum games, symmetry, the golden rule.
    JEL: C70 D03 D87 G01
    Date: 2012
  13. By: M. Kopel; L. Lambertini
    Abstract: We show that Miller and Pazgal.s (2001) model of strategic delegation, in which managerial incentives are based upon relative performance, is affected by a non-existence problem which has impact on the price equilibrium. The undercutting incentives generating this result are indeed similar to those affecting the stability of price cartels.
    JEL: C73 L13
    Date: 2012–01

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