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on Game Theory |
| By: | Werner Gueth (Max Planck Institute of Economics); Maria Vittoria Levati (Department of Economics (University of Verona)); Ivan Soraperra (Department of Economics (University of Verona)) |
| Abstract: | We provide experimental evidence on behavior in a public goods game featuring a so-called point of no return, meaning that if the group’s total contribution falls below this point all payoffs are reduced. Participants receive either common or private signals about the point of no return, and experience either high or low reductions in payoffs if insufficient contributions are made. Our data reveal that, as expected, contributions are higher if the cost of not reaching the threshold is high than if it is low. High signal values discourage contributions and endanger the likelihood of success when signals are common, but not when signals are private. In addition, successful coordination of contributions is less frequent in a control treatment featuring a standard provision point mechanism than in the experimental treatment where the payoff reduction factor is high, although the theoretical predictions of the two games are similar. |
| Keywords: | Public goods; Provision point mechanism; Experiments; Signal |
| JEL: | H41 C92 C72 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:ver:wpaper:09/2015&r=gth |
| By: | Fabrizio Germano; Peio Zuazo-Garin |
| Abstract: | We study an interactive framework that explicitly allows for non-rational behavior. We do not place any restrictions on how players can deviate from rational behavior. Instead we assume that there exists a lower bound p E [0,1] such that all players play and are believed to play rationally with a probability p or more. This, together with the assumption of a common prior, leads to what we call the set of p-rational outcomes, which we define and characterize for arbitrary p E [0,1]. We then show that this set varies continuously in p and converges to the set of correlated equilibria as p approaches 1, thus establishing robustness of the correlated equilibrium concept to relaxing rationality and common knowledge of rationality. The p-rational outcomes are easy to compute, also for games of incomplete information, and they can be applied to observed frequencies of play to compute a measure p that bounds from below the probability with which any given player is choosing actions consistent with payoff maximization and common knowledge of payoff maximization. |
| Keywords: | strategic interaction, correlated equilibrium, robustness to bounded rationality, approximate knowledge, incomplete information, measure of rationality, experiments. |
| JEL: | C72 D82 D83 |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1468&r=gth |
| By: | Fabrizio Germano; Peio Zuazo-Garin |
| Abstract: | We study an interactive framework that explicitly allows for non-rational behavior. We do not place any restrictions on how players can deviate from rational behavior. Instead we assume that there exists a lower bound p 2 [0; 1] such that all players play and are believed to play rationally with a probability p or more. This, together with the assumption of a common prior, leads to what we call the set of p-rational outcomes, which we define and characterize for arbitrary p 2 [0; 1]. We then show that this set varies continuously in p and converges to the set of correlated equilibria as p approaches 1, thus establishing robustness of the correlated equilibrium concept to relaxing rationality and common knowledge of rationality. The p-rational outcomes are easy to compute, also for games of incomplete information, and they can be applied to observed frequencies of play to compute a measure p that bounds from below the probability with which any given player is choosing actions consistent with payoff maximization and common knowledge of payoff maximization. |
| Keywords: | strategic interaction, correlated equilibrium, robustness to bounded rationality, approximate knowledge, incomplete information, measure of rationality, experiments |
| JEL: | C72 D82 D83 |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:812&r=gth |
| By: | Alexander Nesterov (Wissenschaftszentrum für Sozialforschung Berlin) |
| Abstract: | This paper considers the problem of allocating N indivisible objects among N agents according to their preferences when transfers are not allowed, and studies the tradeoff between fairness and efficiency in the class of strategy-proof mechanisms. The main finding is that for strategy-proof mechanisms the following efficiency and fairness criteria are mutually incompatible: (1) Ex-post efficiency and envy-freeness, (2) ordinal efficiency and weak envy-freeness and (3) ordinal efficiency and equal division lower bound. Result (1) is the first impossibility result for this setting that uses ex-post efficiency; results (2) and (3) are more relevant for practical implementation than similar results in the literature. In addition, for N = 3 the paper strengthens the characterization result by Bogomolnaia and Moulin (2001): the random serial dictatorship mechanism is the unique strategy-proof, ex-post efficient mechanism that eliminates strict envy between agents with the same preferences. Creation Date: 2014-11 |
| Keywords: | random assignment, random serial dictatorship, strategy-proofness, ex-post efficiency, weak envy-freeness, equal division lower bound |
| JEL: | C78 D71 D78 |
| URL: | http://d.repec.org/n?u=RePEc:bdp:wpaper:2014006&r=gth |
| By: | Atabati, Omid; Farzad, Babak |
| Abstract: | We present a network formation model based on a particularly interesting class of networks in social settings, where individuals' positions are determined according to a topic-based or hierarchical taxonomy. In this game-theoretic model, players are located in the leaves of a complete b-ary tree as the seed network with the objective of minimizing their collective distances to others in the network. In the grid-based model of Even-Dar and Kearns [3], they demonstrate the existence of small diameter networks with the threshold of a = 2 where the cost of a new link depends on the distance between the two endpoints to the power of a. We show the appearance of small diameter equilibrium networks with the threshold of a = 1/4 in the hierarchical or tree-based networks. Moreover, the general set of equilibrium networks in our model are guaranteed to exist and they are pairwise Nash stable with transfers [2]. |
| Keywords: | Network formation; Hierarchical networks; Linking game |
| JEL: | C79 D85 |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:62551&r=gth |
| By: | Volker Böhm (Bielefeld University) |
| Abstract: | The so-called El Farol problem describes a prototypical situation of interacting agents making binary choices to participate in a non-cooperative environment or to stay by themselves and choosing an outside option. In a much cited paper Arthur (1994) argues that persistent on-converging sequences of rates of participation with permanent forecasting errors occur due to the non-existence of a prediction model for agents to forecast the attendance appropriately to induce stable rational expectations solutions. From this he concludes the need for agents to use boundedly rational rules. This note shows that in a large class of such models the failure of agents to find rational prediction rules which stabilize is not due to a non-existence of perfect rules, but rather to the failure of agents to identify the correct class of predictors from which the perfect ones can be chosen. What appears as a need to search for boundedly rational predictors originates from the non existence of stable confirming self-referential orbits induced by predictors selected from the wrong class. Specifically, it is shown that, within a specified class of the model and due to a structural non-convexity (or discontinuity), symmetric Nash equilibria of the associated static game may fail to exist generically depending on the utility level of the outside option. If they exist, they may induce the least desired outcome while, generically, asymmetric equilibria are uniquely determined by a positive maximal rate of attendance. The sequential setting turns the static game into a dynamic economic law of the Cobweb type for which there always exist nontrivial ??perfect predictors implementing ??perfect steady states as stable outcomes. If zero participation is a Nash equilibrium of the game there exists a unique perfect predictor implementing the trivial equilibrium as a stable steady state. In general, Nash equilibria of the one-shot game are among the ??perfect foresight steady states of the dynamic model. If agents randomize over indifferent decisions the induced random Cobweb law together with recursive predictors becomes an iterated function system (IFS). There exist unbiased predictors with associated stable stationary solutions for appropriate randomizations supporting nonzero asymmetric equilibria which are not mixed Nash equilibria of the one-shot game. However, the least desired outcome remains as the unique stable stationary outcome for ? = 0 if it is a Nash equilibrium of the static game. |
| Keywords: | El Farol, participation games, repeated play, forecasting, rational expectations, Cobweb models |
| JEL: | C7 C73 D83 D84 |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:536&r=gth |
| By: | Mukherjee, Conan (Department of Economics, Lund University) |
| Abstract: | This paper establishes reserve price as an ethical necessity contrary to its popular interpretation as an instrument of revenue maximization. It provides an axiomatic justification to reserve pricing at Vickrey auction in single as well as multiple objects settings. In particular, it provides a topological interpretation of a reserve price as the infimum of the set of non-negative real numbers satisfying the following property: if all agents bid the same number from this set, then at least one object is allocated. Further, it shows how existence of this reserve price as well as the associated efficiency properties, are implications of ethical and strategic axioms. In particular, for the single object case, it is shown that any anonymous strategy-proof mechanism that satisfies non-bossiness (in decision) must have an allocation rule same as that of a Vickrey auction with reserve price (VARP). Further, two axiomatizations are provided for the class of VARP mechanisms in the single object context. In the multiple objects context, two new complications arise. One, any one agent getting the object no longer implies that all other agents do not get the object and two, at each profile of reports, all objects need not be allocated. To account for these complications, we introduce an ethical axiom called minimal impartiality (which requires that either all objects or no object be allocated at any profile where all agents report the same value) and a technical regularity condition. Under these restrictions, the single object results are shown to hold in the multiple objects case, too. Finally, we generalize the maxmed mechanisms of Sprumont [JET, 2013] to the multiple objects setting and provide an axiomatization. |
| Keywords: | Anonymous; non-bossy; strategy-proof mechanism; maxmed mechanisms |
| JEL: | C72 C78 D63 D71 |
| Date: | 2015–03–11 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2015_007&r=gth |
| By: | Fabrizio Germano; Peio Zuazo-Garin |
| Abstract: | Economic predictions are highly sensitive to model and informational specifications. Weinstein and Yildiz (2007) show that, in static games with incomplete information, only very weak predictions, namely, the interim correlated rationalizable (ICR) actions, are robust to higher-order belief misspecifications. This paper extends their robustness analysis to allow for higher-order uncertainty about rationality. We introduce interim correlated p-rationalizability (ICRp) as a solution concept for games with incomplete information. We first confirm the robustness of the ICR predictions to small departures from common belief in rationality by showing the continuity of ICRp actions at p = 1, where they coincide with ICR. At the same time, we show that Weinstein and Yildiz's (2007) deeper results on the structure of rationalizability, most notably, their discontinuity and generic local uniqueness properties, fail as soon as any arbitrarily small amount of higher-order uncertainty about rationality is introduced. Thus, we find that common belief in rationality is a necessary condition for Weinstein and Yildiz's (2007) discontinuity property to hold. Among other things, this reveals the diminishing strategic impact of higher-order belief constraints. |
| Keywords: | Robustness, rationalizability, uncertain rationality, incomplete information, belief hierarchies. |
| JEL: | C72 D82 D83 |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1470&r=gth |
| By: | Zhao, Guo |
| Abstract: | I propose a dynamic game model that is consistent with the paradigm of bounded rationality. Its main advantages over the traditional approach based on perfect rationality are that: (1) the strategy space is a chain-complete partially ordered set; (2) the response function is certain order-preserving map on strategy space; (3) the evolution of economic system can be described by the Dynamical System defined by the response function under iteration; (4) the existence of pure-strategy Nash equilibria can be guaranteed by fixed point theorems for ordered structures, rather than topological structures. This preference-response framework liberates economics from the utility concept, and constitutes a marriage of normal-form and extensive-form games. |
| Keywords: | Dynamic Games,Bounded Rationality,Dynamical System, fixed point theorems,chain-complete partially ordered set,Coase theorem,impossibility theorem, Keynesian beauty contest,Bertrand Paradox, backward induction paradox |
| JEL: | C7 D5 D7 |
| Date: | 2015–03–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:62688&r=gth |
| By: | Alessandro Bonatti; Johannes Horner (Cowles Foundation, Yale University) |
| Abstract: | We analyse strategic experimentation in which information arrives through fully revealing, publicly observable “breakdowns.” With hidden actions, there exists a unique equilibrium that involves randomization over stopping times. This randomization induces belief disagreement on the equilibrium path. When actions are observable, the equilibrium is pure, and welfare improves. We analyse the role of policy interventions such as subsidies for experimentation and risk-sharing agreements. We show that the optimal risk-sharing agreement restores the first-best outcome, independent of the monitoring structure. |
| Keywords: | Experimentation, Free-riding, Mixed strategies, Monitoring, Delay |
| JEL: | C73 D83 O33 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1991&r=gth |
| By: | Cagala, Tobias; Glogowsky, Ulrich; Grimm, Veronika; Rincke, Johannes |
| Abstract: | Public goods provision often involves groups of contributors repeatedly interacting with administrators who can extract rents from the pool of contributions. We suggest a novel identification approach that exploits the sequential ordering of decisions in a panel vector autoregressive model to study social interactions in the laboratory. Despite rent extraction, contributors and administrators establish a stable interaction with cooperation matching the level from a comparable Public Goods Game. In the short run, temporary changes in behavior trigger substantial behavioral multiplier effects. We demonstrate that cooperation breeds trustworthiness and vice versa and that one-time disruptions are particularly damaging in settings with a lack of cooperative attitudes and trust. |
| Keywords: | Cooperation,trustworthiness,rent extraction,methods for laboratory experiments,panel vector autoregressive model |
| JEL: | C32 C91 C92 H41 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc14:107597&r=gth |
| By: | Philipp D. Dimakopoulos (Humboldt-Universitaet zu Berlin, Department of Economics); Christian-Philipp Heller (Humboldt-Universitaet zu Berlin, Department of Economics) |
| Abstract: | We study the allocation of German lawyers to different regional courts for their compulsory legal traineeship. The number of applicants exceeds the number of available positions in a given time period in some regions, so that not all lawyers can be matched simultaneously. As a consequence some lawyers have to wait before they obtain a position. First, we analyse the currently used Berlin mechanism and demonstrate that it is unfair and that it does not respect improvements. Second, we introduce a matching with contracts model, using waiting time as the contractual term, for which we suggest an appropriate choice function for the courts that respects the capacity constraints of each court for each period. Despite the failure of the unilateral substitutes condition, under a weak assumption on lawyers’ preferences, a lawyer-optimal stable allocation exists. Using existing results, we can show that the resulting mechanism is strategy-proof, fair and respects improvements. Third, we extend our proposed mechanism to allow for a more flexible allocation of positions over time. Creation Date: 2014-11 |
| Keywords: | Many-to-One Matching, Matching with Contracts, Stability, Slot-Specific Priorities, Waiting Time, Legal Education |
| JEL: | D82 C78 H75 I28 |
| URL: | http://d.repec.org/n?u=RePEc:bdp:wpaper:2014005&r=gth |
| By: | Raphael Soubeyran (Laboratoire Montpelliérain d'Economie Théorique et Appliquée, INRA); Mabel Tidball (Laboratoire Montpelliérain d'Economie Théorique et Appliquée, INRA); Agnes Tomini (AMSE. Aix-Marseille School of Economics, Centre National de la Recherche Scientifique); Katrin Erdlenbruch (UMR G-EAU, Institut National de Recherche en Sciences et Technologies pour l'Environnement et l'Agriculture) |
| Abstract: | In this paper, we focus on resource conservation in a model of decentralized management of groundwater and rainwater. We show that a conservation policy may have opposite effects on the level of the resource, depending on the outcome of the decentralized management. More precisely, we consider identical farmers who can use two water resources (groundwater and/or rainwater) and we study the symmetric and asymmetric feedback stationary Nash equilibria of the dynamic game. We show that a subsidy on the use of rainwater may increase the level of the aquifer at the symmetric equilibrium, whereas it decreases the level of the aquifer at the asymmetric equilibrium. This suggests that the usual focus on (interior) symmetric equilibria in dynamic games may provide misleading policy implications. |
| Keywords: | asymmetric equilibrium, differential game, groundwater, rainwater, théorie des jeux, modèle dynamique, exploitation des ressourceseau pluvialeeau souterrainetaxe, gestion des ressources naturelles, économie de l'eau |
| JEL: | C72 Q25 Q15 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:inr:wpaper:279180&r=gth |
| By: | Richard P. McLean (Department of Economics, Rutgers University); Andrew Postlewaite (Department of Economics, University of Pennsylvania) |
| Abstract: | We showed in McLean and Postlewaite (2014) that when agents are informationally small, there exist small modifications to VCG mechanisms in interdependent value problems that restore incentive compatibility. This paper presents a two-stage mechanism that similarly restores incentive compatibility. The first stage essentially elicits that part of the agents’ private information that induces interdependence and reveals it to all agents, transforming the interdependent value problem into a private value problem. The second stage is a VCG mechanism for the now private value problem. Agents typically need to transmit substantially less information in the two stage mechanism than would be necessary for a single stage mechanism. Lastly, the firrst stage that elicits the part of the agents’ private information that induces interdependence can be used to transform certain other interdependent value problems into private value problems. |
| Keywords: | Auctions, Incentive Compatibility, Mechanism Design, Interdependent Values, Ex Post Incentive Compatibility, Informational Size |
| JEL: | C70 D44 D60 D82 |
| Date: | 2015–03–04 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:15-011&r=gth |
| By: | Baosen Zhang; Ramesh Johari; Ram Rajagopal |
| Abstract: | We investigate the impact of group formations on the efficiency of Cournot games where producers face uncertainties. In particular, we study a market model where producers must determine their output before an uncertainty production capacity is realized. In contrast to standard Cournot models, we show that the game is not efficient when there are many small producers. Instead, producers tend to act conservatively to hedge against their risks. We show that in the presence of uncertainty, the game becomes efficient when producers are allowed to take advantage of diversity to form groups of certain sizes. We characterize the trade-off between market power and uncertainty reduction as a function of group size. Namely, we show that when there are N producers present, competition between groups of size square root of N results in equilibria that are socially optimal. |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1503.02479&r=gth |
| By: | Amogh Deshpande; Saul D. Jacka |
| Abstract: | In this article we consider a game theoretic approach to the Risk-Sensitive Benchmarked Asset Management problem (RSBAM) of Davis and Lleo \cite{DL}. In particular, we consider a stochastic differential game between two players, namely, the investor who has a power utility while the second player represents the market which tries to minimize the expected payoff of the investor. The market does this by modulating a stochastic benchmark that the investor needs to outperform. We obtain an explicit expression for the optimal pair of strategies as for both the players. |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1503.01802&r=gth |
| By: | Hikaru Kondo; Shigehiro Serizawa |
| Abstract: | We search for impartiality in the allocation of objects when monetary transfers are not possible. Our main focus is anonymity. The standard definition requires that if agents' names are permuted, their assignments should be permuted in the same way. Since no rule satisfies this definition in this model, we introduce weaker variants, ganonymity on distinct preferences,h gpairwise-anonymity on distinct preferences,h gpairwise-anonymity on distinct profiles,h and gindependence of others' permutations.h We show that for more than two agents and two objects, no rule is pairwise-anonymous on distinct preferences and Pareto-efficient (Theorem 1), no rule is pairwise-anonymous on distinct preferences and independent of others' permutations (Theorem 2), and no rule is pairwise-anonymous on distinct profiles and strategy-proof (Theorem 3). These results suggest that introducing randomization to object allocation problems is almost inevitable for achieving impartiality. |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:0927&r=gth |
| By: | Martin Dufwenberg; Maroš Servátka (University of Canterbury); Radovan Vadovic |
| Abstract: | We develop, and experimentally test, models of informal agreements. Agents are assumed to be honest but suffer costs of overcoming temptations. We extend two classical bargaining solutions -- split-the-difference and deal-me-out -- to this informal agreement setting. For each solution there are two natural ways to do this, leaving us with 2×2 models to explore. In the experiment, a temptations-constrained version of deal-me-out emerges as the clear winner. |
| Keywords: | agreement, bargaining, behavioral economics, deal, experiment, honesty, lost wallet game, negotiation, temptation |
| JEL: | C70 C91 |
| Date: | 2015–02–15 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:15/04&r=gth |
| By: | Caterina Calsamiglia; Maia Güell |
| Abstract: | The Boston mechanism is a school allocation procedure that is widely used around the world. To resolve overdemands, priority is often given to families who live in the neighborhood school. We note that such priorities define some schools as being safer. We exploit an unexpected change in the definition of neighborhood in Barcelona to show that when allowing school choice under the BM with priorities: (1) the resulting allocation is not very different from a neighborhood-based assignment, and (2) important inequalities emerge beyond parents' naivete found in the literature. |
| Keywords: | school choice, Boston mechanism, priorities |
| JEL: | C78 D63 I24 |
| Date: | 2014–07 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:810&r=gth |
| By: | Aldasoro, Iñaki; Delli Gatti, Domenico; Faia, Ester |
| Abstract: | We present a network model of the interbank market in which optimizing risk averse banks lend to each other and invest in non-liquid assets. Market clearing takes place through a tâtonnement process which yields the equilibrium price, while traded quantities are determined by means of a matching algorithm. We compare three alternative matching algorithms: maximum entropy, closest matching and random matching. Contagion occurs through liquidity hoarding, interbank interlinkages and fire sale externalities. The resulting network configurations exhibits a core-periphery structure, dis-assortative behavior and low clustering coefficient. We measure systemic importance by means of network centrality and input-output metrics and the contribution of systemic risk by means of Shapley values. Within this framework we analyze the effects of prudential policies on the stability/efficiency trade-off. Liquidity requirements unequivocally decrease systemic risk but at the cost of lower efficiency (measured by aggregate investment in non-liquid assets); equity requirements tend to reduce risk (hence increase stability) without reducing significantly overall investment. |
| Keywords: | banking networks,centrality metrics,systemic risk |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:safewp:87&r=gth |
| By: | Caterina Calsamiglia; Chao Fu; Maia Güell |
| Abstract: | An important debate centers on what procedure should be used to allocate students across public schools. We contribute to this debate by developing and estimating a model of school choices by households under one of the most popular procedures known as the Boston mechanism (BM). We recover the joint distribution of household preferences and sophistication types using administrative data from Barcelona. Our counterfactual policy analyses show that a change from BM to the Gale-Shapley student deferred acceptance mechanism would create more losers than winners, while a change from BM to the top trading cycles mechanism has the opposite effect. |
| Keywords: | school choice, Boston mechanism, Gale-Shapley mechanism, Top Trading Cycles mechanism, priorities |
| JEL: | C78 I24 D63 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:811&r=gth |
| By: | Nicolas Querou (Laboratoire Montpelliérain d'Economie Théorique et Appliquée, INRA; Centre National de la Recherche Scientifique); Mabel Tidball (Laboratoire Montpelliérain d'Economie Théorique et Appliquée, INRA) |
| Abstract: | We consider a model of non-renewable resource extraction where players do not know their opponents’ utility functions and form conjectures on the behavior of others. Two forms of beliefs are introduced, one based on the state of the resource, the other on this state and on the others’ strategy (their consumption). We focus on consistent equilibria, where beliefs must be consistent with observed past plays. Closed form expressions of the optimal policies are derived. Comparisons are made with the full information benchmark case. With strategy and state based beliefs, the agents may behave more (respectively, less) aggressively than in the non-cooperative benchmark depending on the initial consumption level. When initial consumption is low, the optimal consumption path lies below that of the cooperative benchmark. We conclude the analysis by discussing the impact of public policies on the agents’ choice of consumption patterns, and the robustness of the results for the case of renewable resources. |
| Keywords: | conjectural variations, dynamic game, dynamic resource management, non probabilistic beliefs, théorie des jeuxgestion des ressources naturelles, ressource non renouvelable, modélisation économique |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:inr:wpaper:174806&r=gth |