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on Game Theory |
| By: | George J. Mailath (University of Pennsylvania); Larry Samuelson (Yale University) |
| Abstract: | People reason with incomplete models. How do people hampered by different, incomplete views learn from each other? We introduce a model of ``model-based inference.'' Model-based reasoners partition an otherwise hopelessly complex state space into a manageable model. Unless the differences in agents' models are trivial, interactions will often not lead agents to common beliefs, and the correct-model belief will typically lie outside the convex hull of the agents' beliefs. However, if the agents' models have enough in common, then interacting will lead agents to similar beliefs, even if their models also exhibit bizarre idiosyncrasies and their information is widely dispersed. |
| Keywords: | Information aggregation, model-based reasoning |
| JEL: | D8 |
| Date: | 2019–09–30 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:19-018&r=all |
| By: | Aïd, René; Basei, Matteo; Callegaro, Giorgia; Campi, Luciano; Vargiolu, Tiziano |
| Abstract: | We consider a general nonzero-sum impulse game with two players. The main mathemat- ical contribution of the paper is a verification theorem which provides, under some regularity conditions, a suitable system of quasi-variational inequalities for the payoffs and the strate- gies of the two players at some Nash equilibrium. As an application, we study an impulse game with a one-dimensional state variable, following a real-valued scaled Brownian motion, and two players with linear and symmetric running payoffs. We fully characterize a family of Nash equilibria and provide explicit expressions for the corresponding equilibrium strategies and payoffs. We also prove some asymptotic results with respect to the intervention costs. Finally, we consider two further non-symmetric examples where a Nash equilibrium is found numerically. |
| Keywords: | stochastic differential game; impulse control; Nash equilibrium; quasi-variational inequality |
| JEL: | C1 |
| Date: | 2019–07–17 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:100003&r=all |
| By: | Francesco Cerigioni; Fabrizio Germano; Pedro Rey-Biel; Peio Zuazo-Garin |
| Abstract: | Identifying individual levels of rationality is crucial to modeling strategic interaction and understanding behavior in games. Nevertheless, there is no consensus on how to best identify levels of higher order rationality, and the identification of an empirical distribution remains highly elusive. In particular, the games used for the task can have a huge impact on the identified distribution. To tackle this fundamental problem, this paper introduces an axiomatic approach that singles out a simple class of games that minimizes the probability of misidentification errors. It then shows that the axioms are empirically meaningful in a within subject experiment that compares the distribution of orders of rationality across different games, including standard games from the literature. The games singled out by the axioms exhibit the highest correlation both with the distribution of the most frequent rationality level a subject has been classified with and with an independent measure of cognitive ability. Finally, there is no evidence in our sample of within subject consistency of identified rationality levels across games. |
| Keywords: | rationality, higher-order rationality, revealed rationality, levels of thinking |
| JEL: | C70 C72 C91 D01 D80 |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:1120&r=all |
| By: | Bugra Caskurlu; Ozgun Ekici; Fatih Erdem Kizilkaya |
| Abstract: | In a strategic form game a strategy profile is an equilibrium if no viable coalition of agents (or players) benefits (in the Pareto sense) from jointly changing their strategies. Weaker or stronger equilibrium notions can be defined by considering various restrictions on coalition formation. In a Nash equilibrium, for instance, the assumption is that viable coalitions are singletons, and in a super strong equilibrium, every coalition is viable. Restrictions on coalition formation can be justified by communication limitations, coordination problems or institutional constraints. In this paper, inspired by social structures in various real-life scenarios, we introduce certain restrictions on coalition formation, and on their basis we introduce a number of equilibrium notions. As an application we study our equilibrium notions in resource selection games (RSGs), and we present a complete set of existence and non-existence results for general RSGs and their important special cases. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.04648&r=all |
| By: | Idione Meneghel; Rabee Tourky |
| Abstract: | Abstract. In a recent paper Reny (2011) generalized the results of Athey (2001) and McAdams (2003) on the existence of monotone strategy equilibrium in Bayesian games. Though the generalization is subtle, Reny introduces far-reaching new techniques applying the fixed point theorem of Eilenberg and Montgomery (1946, Theorem 5). This is done by showing that with atomless type spaces the set of monotone functions is an absolute retract and when the values of the best response correspondence are non-empty sub-semilattices of monotone functions, they too are absolute retracts. In this paper we provide an extensive generalization of Reny (2011), McAdams (2003), and Athey (2001). We study the problem of existence of Bayesian equilibrium in pure strategies for a given partially ordered compact subset of strategies. The ordering need not be a semilattice and these strategies need not be monotone. The main innovation is the interplay between the homotopy structures of the order complexes that are the subject of the celebrated work of Quillen (1978), and the hulling of partially ordered sets, an innovation that extends the properties of Reny’s semilattices to the non-lattice setting. We then describe some auctions that illustrate how this framework can be applied to generalize the existing results and extend the class of models for which we can establish existence of equilibrium. As with Reny (2011) our proof utilizes the fixed point theorem in Eilenberg and Montgomery (1946). |
| Keywords: | Bayesian games, monotone strategies, pure-strategy equilibrium,auctions |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:acb:cbeeco:2019-669&r=all |
| By: | Aguirregabiria, Victor; Marcoux, Mathieu |
| Abstract: | Imposing equilibrium restrictions provides substantial gains in the estimation of dynamic discrete games. Estimation algorithms imposing these restrictions -- MPEC, NFXP, NPL, and variations -- have different merits and limitations. MPEC guarantees local convergence, but requires the computation of high-dimensional Jacobians. The NPL algorithm avoids the computation of these matrices, but -- in games -- may fail to converge to the consistent NPL estimator. We study the asymptotic properties of the NPL algorithm treating the iterative procedure as performed in finite samples. We find that there are always samples for which the algorithm fails to converge, and this introduces a selection bias. We also propose a spectral algorithm to compute the NPL estimator. This algorithm satisfies local convergence and avoids the computation of Jacobian matrices. We present simulation evidence illustrating our theoretical results and the good properties of the spectral algorithm. |
| Keywords: | convergence; Convergence selection bias; Dynamic discrete games; Nested pseudo-likelihood; Spectral algorithms |
| JEL: | C13 C61 C73 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:14007&r=all |
| By: | Sylvain Béal (Université de Bourgogne Franche-Comté, CRESE); Issofa Moyouwou (Department of Mathematics, University of Yaounde I - Cameroon); Eric Rémila (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France); Philippe Solal (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France) |
| Abstract: | A situation in which a finite set of agents can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. In the literature, various models of games with restricted cooperation can be found, in which only certain subsets of the agent set are allowed to form. In this article, we consider such sets of feasible coalitions that are closed under intersection, i.e., for any two feasible coalitions, their intersection is also feasible. Such set systems, called intersection closed systems, are a generalization of the convex geometries. We use the concept of closure operator for intersection closed systems and we define the restricted TU-game taking into account the limited possibilities of cooperation determined by the intersection closed system. Next, we study the properties of this restricted TU-game. Finally, we introduce and axiomatically characterize a family of allocation rules for games TU-games on intersection closed systems, which contains a natural extension of the Shapley value. |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2019-06&r=all |
| By: | Ginzburg, Boris |
| Abstract: | A continuum of agents are choosing whether to enter a competition. Entry is controlled by a firm that charges a price for it. The mass of agents is uncertain. I analyse how the distribution of the mass of agents determines the equilibrium price and the intensity of entry. A shift of the distribution towards more mass initially induces a reduction of price, and later – a reduction in entry. |
| Keywords: | contests, entry, university admission tests |
| JEL: | C72 D82 |
| Date: | 2019–10–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:96367&r=all |
| By: | Merkel, Anna; Vanberg, Christoph |
| Abstract: | We conduct 3-person bargaining experiments in which the surplus being divided is produced by completing a prior task. Using a Baron-Ferejohn framework, we investigate how differences in contributions to production affect bargaining under different decision rules. Under unanimity rule, all proposals and agreements constitute convex combinations of the equal and proportional splits. Contrary to our predictions, this pattern largely persists under majority rule. In sharp contrast to prior experiments in which an exogenous surplus is divided, few subjects attempt to build minimum winning coalitions when the surplus is jointly produced. |
| Keywords: | multilateral bargaining; claims; fairness; majority rule; experiments |
| Date: | 2019–10–11 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0670&r=all |
| By: | Kamei, Kenju; Putterman, Louis; Tyran, Jean-Robert |
| Abstract: | Effective states provide public goods by taxing their citizens and imposing penalties for non-compliance. However, accountable government requires that enough citizens are civically engaged. We study the voluntary cooperative underpinnings of the accountable state by conducting a two-level public goods experiment in which civic engagement can build a sanction scheme to solve the first-order public goods dilemma. We find that civic engagement can be sustained at high levels when costs are low relative to the benefits of public good provision. This cost-to-benefit differential yields what we call a "leverage effect" because it transforms modest willingness to cooperate into the larger social dividend from the power of taxation. In addition, we find that local social interaction among subgroups of participants also boosts cooperation. |
| Keywords: | Civic engagement; Cooperation; Experiment; Public goods provision |
| JEL: | C92 D02 D72 H41 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13985&r=all |
| By: | Jorge M. Streb |
| Abstract: | Signals are voluntary actions a sender may use to reveal its type. When this simple insight is formalized, a bewildering plethora of perfect Bayesian equilibria arise. In particular, separating equilibria are possible when no type has an incentive to separate and pooling equilibria are possible when all types do. This motivates a refinement for signaling games. A deviation from an equilibrium is credible if and only if it forms part of an alternative equilibrium where payoffs (weakly) increase. The self-selection condition then puts zero probability, when possible, on sender types for which a deviation from equilibrium is not credible. Las señales son acciones voluntarias del emisor para revelar su tipo. Cuando esto se formaliza, surge una plétora de equilibrios bayesianos perfectos. Son posibles equilibrios con diferenciación a pesar de que nadie tiene un incentivo para diferenciarse y equilibrios con mimetización a pesar de que todos sí lo tienen. Esto motiva un refinamiento para juegos de señales. Un desvío de un equilibrio es creíble si y solo si forma parte de un equilibrio alternativo donde los pagos aumentan (en sentido débil). La condición de autoselección pone probabilidad cero a los tipos para los cuáles un desvío no es creíble. |
| Keywords: | perfect Bayesian equilibrium, refinement, signals, credible deviations, self-selection condition |
| JEL: | D8 C7 |
| Date: | 2018–12 |
| URL: | http://d.repec.org/n?u=RePEc:cem:doctra:674&r=all |
| By: | Vladimir Pavlov (The Wharton School, University of Pennsylvania, 3730 Walnut St, Philadelphia, PA 19104 USA); Ron Berman (The Wharton School, University of Pennsylvania, 3730 Walnut St, Philadelphia, PA 19104 USA) |
| Abstract: | Should a peer-to-peer platform set prices for the products on the platform, or should it let sellers set their own prices while providing price recommendations? Centralized prices allow a platform to use demand information it observes, while price recommendations allow for competition in which sellers set prices based on their private information. On sharing economy platforms, for example, we observe a myriad of such pricing regimes. We investigate the implications of each pricing regime for the profits of platforms, buyers and sellers. When a platform recommends prices, it effectively plays the role of a sender in a multi-receiver cheap-talk game. platforms are not always better off by centralizing pricing. When the variance of aggregate demand is large, price recommendations can be sustained in equilibrium and are often more profitable for the platform. Otherwise, a price recommendation is not credible. High (low) quality sellers have a stronger (weaker) preference for centralized pricing than the platform. Buyers, in contrast, receive lower surplus when the platform provides price recommendations, and prefer centralized pricing or competition without price recommendations. The results provide tools for platform designers and policy makers to assess the impact of different pricing regimes in markets with platforms. Although price recommendations might seem to encourage lower prices among sellers through increased competition, this is not always the case. |
| Keywords: | two-sided markets; peer-to-peer platforms; sharing economy; price recommendations; cheap talk |
| JEL: | D21 L13 L16 L22 M31 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:net:wpaper:19-10&r=all |
| By: | Xiao Chen; Jin Hyuk Choi; Kasper Larsen; Duane J. Seppi |
| Abstract: | We solve in closed-form a Nash equilibrium model in which a finite number of exponential investors trade continuously with price-impact over a finite time horizon. By comparing our continuous-time Nash equilibrium model to the otherwise identical competitive Radner equilibrium model, we show that our Nash equilibrium model with price-impact can simultaneously help resolve the interest rate puzzle, the equity premium puzzle, and the stock volatility puzzle. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.02466&r=all |