
on Microeconomics 
Issue of 2012‒05‒02
eighteen papers chosen by JingYuan Chiou IMT Lucca Institute for Advanced Studies 
By:  Klaus Kultti; Hannu Salonen; Hannu Vartiainen 
Abstract:  In this paper we study the number of pure strategy Nash equilibria in large finite nplayer games. A distinguishing feature of our study is that we allow general  potentially multivalued  best reply correspondences. Given the number K of pure strategies to each player, we assign to each player a distribution over the number of his pure best replies against each strategy profile of his opponents. If the means of these distributions have a limit (mu)i for each player i as the number K of pure strategies goes to infinity, then the limit number of pure equilibria is Poisson distributed with a mean equal to the product of the limit means (mu)i. In the special case when all best reply mappings are equally likely, the probability of at least one pure Nash equilibrium approaches one and the expected number of pure Nash equilibria goes to infinity. 
Keywords:  random games, pure Nash equilibria, n players 
JEL:  C62 C72 
Date:  2011–12 
URL:  http://d.repec.org/n?u=RePEc:tkk:dpaper:dp71&r=mic 
By:  Marion Oury (THEMA, Universite de CergyPontoise) 
Abstract:  This paper examines manyplayer manyaction global games with multidimensional state parameters. It establishes that the notion of noiseindependent selection introduced by Frankel, Morris and Pauzner (Journal of Economic Theory 108 (2003) 1 44) for onedimensional global games is robust when the setting is extended to the one proposed by Carlsson and Van Damme (Econometrica, 61, 9891018). More precisely, our main result states that if an action prole of some complete information game is noiseindependently selected in some onedimensional global game, then it is also noiseindependently selected in all multidimensional global games. 
Keywords:  equilibrium selection, global games, strategic complementarities, robustness. 
JEL:  C72 D82 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:ema:worpap:201228&r=mic 
By:  A.W. Beggs 
Abstract:  This paper studies uniqueness of equilibrium in symmetric 2 x 2 bayesian games. It shows that if signals are highly but not perfectly dependent then players play their riskdominant actions for all but a vanishing set of signal realizations. In contrast to the global games literature, noise is not assumed to be additive. Dependence is modeled using the theory of copulas. 
Keywords:  Bayesian games, Global games, Uniqueness, Copulas, Risk dominance 
JEL:  C72 D82 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:oxf:wpaper:603&r=mic 
By:  Thomas W.L. Norman 
Abstract:  If players learn to play an infinitely repeated game using Bayesian learning, it is known that their strategies eventually approximate Nash equilibria of the repeated game under an absolutecontinuity assumption on their prior beliefs. We suppose here that Bayesian learners do not start with such a “grain of truth”, but with arbitrarily low probability they revise beliefs that are performing badly. We show that this process converges in probability to a Nash equilibrium of the repeated game. 
Keywords:  Repeated games, Nash equilibrium, Rational learning, Bayesian learning, Absolute continuity 
JEL:  C73 D83 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:oxf:wpaper:602&r=mic 
By:  Hannu Salonen 
Abstract:  Pure strategy Markov perfect equilibria (MPE) in dynamic cake sharing problems are analyzed. Each player chooses under perfect information how much to eat from the current cake and how much to leave to the next period. The left over cake grows according to a given growth function. With linear utilities and strictly concave increasing growth function the only symmetric equilibrium with continuous strategies is the trivial equilibrium in which a player eats the whole cake whenever it is his turn to move. This is quite different than in the corresponding single person decision problem (or at a social optimum) where the cake grows from small initial values towards the steady state. A nontrivial equilibrium with a positive steady state exist in the game. In such an equilibrium strategies cannot be continuous. When utilities are concave and the growth function is linear, a nontrivial MPE with a positive steady state may not exist. 
Keywords:  common pool resources, dynamic cake sharing, Markov perfect equilibrium 
JEL:  C72 C73 D92 
Date:  2012–03 
URL:  http://d.repec.org/n?u=RePEc:tkk:dpaper:dp72&r=mic 
By:  Julian C. Jamison 
Abstract:  Intuitively, we expect that players who are allowed to engage in costless communication before playing a game would be foolish to agree on an inefficient equilibrium. At the same time, however, such preplay communication has been suggested as a rationale for expecting Nash equilibrium in general. This paper presents a plausible formal model of cheap talk that distinguishes and resolves these possibilities. Players are assumed to have an unlimited opportunity to send messages before playing an arbitrary game. Using an extension of fictitious play beliefs, minimal assumptions are made concerning which messages about future actions are credible and hence contribute to final beliefs. In this environment it is shown that meaningful communication among players leads to a Nash equilibrium (NE) of the action game. Within the set of NE, efficiency then turns out to be a consequence of imposing optimality on the cheap talk portion of the extended game. This finding contrasts with previous "babbling" results. 
Keywords:  Game theory ; Stochastic analysis 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:fip:fedbwp:123&r=mic 
By:  Stéphane Gonzalez (Centre d'Economie de la Sorbonne  Paris School of Economics); Michel Grabisch (Centre d'Economie de la Sorbonne  Paris School of Economics) 
Abstract:  In cooperative games, the core is one of the most popular solution concept since it ensures coalitional rationality. For nonbalanced games however, the core is empty, and other solution concepts have to be found. We propose the use of general solutions, that is, to distribute the total worth of the game among groups rather than among individuals. In particular, the kadditive core proposed by Grabisch and Miranda is a general solution preserving coalitional rationality which distributes among coalitions of size at most k, and is never ampty for k ? 2. The extended core of Bejan and Gomez can also be viewed as a general solution, since it implies to give an amount to the grand coalition. The kadditive core being an unbounded set and therefore difficult to use in practice, we propose a subset of it called the minimal bargaining set. The idea is to select elements of the kadditive core minimizing the total amount given to coalitions of size greater than 1. Thus the minimum bargaining set naturally reduces to the core for balanced games. We study this set, giving properties and axiomatizations, as well as its relation to the extended core of Bejan and Gomez. We introduce also the notion of unstable coalition, and show how to find them using the minimum bargaining set. Lastly, we give a method of computing the minimum bargaining set. 
Keywords:  Cooperative game, core, balancedness, general solution. 
JEL:  C71 
Date:  2012–04 
URL:  http://d.repec.org/n?u=RePEc:mse:cesdoc:12022&r=mic 
By:  Hernández, Penélope (ERICES. Departamento de Análisis Económico. Facultad de Economía.); SilvaReus, José A. (Instituto Interuniversitario de Desarrollo Social y Paz) 
Abstract:  This note provides a way to translate an nperson strategic game to a characteristic cooperative game assuming that the set of players of the cooperative game is the set of pure actions of the strategic game. The Core is characterized through coalitions generated with only one action for each player and the total coalition. We obtain the worth of the total coalition to guarantee the nonemptyness condition. In particular, for a twoplayer game, this value is equal to the maximal sum of the diagonals. 
Keywords:  Cooperative games; Core 
JEL:  C71 C72 
Date:  2012–04–24 
URL:  http://d.repec.org/n?u=RePEc:ris:qmetal:2012_009&r=mic 
By:  Juan Carlos Carbajal (School of Economics, The University of Queensland); Andrew McLennan (School of Economics, The University of Queensland); Rabee Tourky (School of Economics, The University of Queensland) 
Abstract:  In a setting where agents have quasilinear utilities over social alternatives and a transferable commodity, we consider three properties that a social choice function may possess: truthful implementation (in dominant strategies); monotonicity in differences; lexicographic affine maximization. We introduce the notion of a flexible domain of preferences that allows elevation of pairs and study which of these conditions implies which others when the domain is flexible. We provide a generalization of the theorem of Roberts (1979) in restricted valuation domains. Flexibility holds (and the theorem is not vacuous) if the domain of valuation profiles is restricted to the space of continuous functions defined on a topological space, or the space of piecewise linear functions defined on an affine space, or the space of smooth functions defined on a compact differentiable man ifold. Our results can be applied in both public and private goods allocation settings, with finite or infinite alternative sets. 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:qld:uq2004:459&r=mic 
By:  Juan Carlos Carbajal (School of Economics, The University of Queensland); Jeffrey C. Ely 
Abstract:  We study mechanism design problems in quasilinear environments where the en velope theorem and revenue equivalence principle fail due to nonconvex and non differentiable valuations. Despite these obstacles, we obtain a characterization of in centive compatibility based on the familiar Mirrlees representation of the indirect util ity and a monotonicity condition on the allocation rule. These conditions pin down the range of possible payoffs as a function solely of the allocation rule, thus providing a revenue inequality. We illustrate the usefulness of our approach in three economic applications where standard techniques do not apply: we derive the optimal selling mechanism in a buyerseller situation where the buyer has lossaverse preferences; we find a zero payment (hence budgetbalanced) efficient mechanism in a public goods lo cation model; and we consider a principalâ€“agent model with ex post noncontractible actions available to the agent. 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:qld:uq2004:458&r=mic 
By:  Paula Jaramillo; Çagtay Kayi; Flip Klijn 
Abstract:  We study a particular restitution problem where there is an indivisible good (land or property) over which two agents have rights: the dispossessed agent and the owner. A third party, possibly the government, seeks to resolve the situation by assigning rights to one and compensate the other. There is also a maximum amount of money available for the compensation. We characterize a family of asymmetrically fair rules that are immune to strategic behavior, guarantee minimal welfare levels for the agents, and satisfy the budget constraint. 
Date:  2012–03–13 
URL:  http://d.repec.org/n?u=RePEc:col:000089:009425&r=mic 
By:  Dirk Bergemann (Cowles Foundation, Yale University); Ji Shen (Dept. of Finance, London School of Economics); Yun Xu (Dept. of Electrical Engineering, Yale University); Edmund M. Yeh (Dept. of Computer Science and Electrical Engineering, Northeastern University) 
Abstract:  We analyze a nonlinear pricing model with limited information. Each buyer can purchase a large variety, d, of goods. His preference for each good is represented by a scalar and his preference over d goods is represented by a ddimensional vector. The type space of each buyer is given by a compact subset of R_d^+ with a continuum of possible types. By contrast, the seller is limited to offer a finite number M of ddimensional choices. We provide necessary conditions that the optimal finite menu of the social welfare maximizing problem has to satisfy. We establish an underlying connection to the theory of quantization and provide an estimate of the welfare loss resulting from the usage of the ddimensional Mclass menu. We show that the welfare loss converges to zero at a rate proportional to d/M^{2/d}. We show that in higher dimensions, a significant reduction in the welfare loss arises from an optimal partition of the ddimensional type space that takes advantage of the correlation among the d parameters. 
Keywords:  Mechanism design, Multidimensional private information, Limited information, Nonlinear pricing, Quantization, Information theory 
JEL:  C72 C73 D43 D83 
Date:  2012–04 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:1859&r=mic 
By:  John K.H. Quah 
Abstract:  Consider a finite data set of price vectors and consumption bundles; under what conditions will there be a weakly separable utlity function that rationalizes the data? This paper shows that rationalization in this sense is possible if and only if there exists a preference order on some finite set of consumption bundles that is consistent with the observations and that is weakly separable. Since there can only be a finite number of preference orders on this set, the problem of rationalization with a weakly separable utility function is solvable. 
Keywords:  Afriat's theorem, Concave utility function, Budget set, Generalized axiom of revealed preference, Preorder 
JEL:  C14 C60 C61 D11 D12 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:oxf:wpaper:601&r=mic 
By:  Hannu Salonen 
Abstract:  We study information aggregation problems where to a set of measures a single measure of the same dimension is associated. The collection of measures could represent the beliefs of agents about the state of the world, and the aggregate would then represent the beliefs of the population. Individual measures could also represent the connectedness of agents in a social network, and the aggregate would reflect the importance of each individual. We characterize the aggregation rule that resembles the Nash welfare function. In the special case of probability aggregation problems, this rule is the only one that satisfies Bayesian updating and some wellknown axioms discussed in the literature. 
Keywords:  belief aggregation, belief updating, Nash welfare function 
JEL:  C71 D63 D74 
Date:  2012–03 
URL:  http://d.repec.org/n?u=RePEc:tkk:dpaper:dp73&r=mic 
By:  Katarzyna Werner; Horst Zank 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:man:sespap:1210&r=mic 
By:  Gill, David; Prowse, Victoria 
Abstract:  In this paper we investigate how cognitive ability influences behavior, success and the evolution of play towards Nash equilibrium in repeated strategic interactions. We study behavior in a pbeauty contest experiment and find striking differences according to cognitive ability: more cognitively able subjects choose numbers closer to equilibrium, converge more frequently to equilibrium play and earn more even as behavior approaches the equilibrium prediction. To understand better how subjects with different cognitive abilities learn differently, we estimate a structural model of learning based on levelk reasoning. We find a systematic positive relationship between cognitive ability and levels; furthermore, the average level of more cognitively able subjects responds positively to the cognitive ability of their opponents, while the average level of less cognitively able subjects does not respond at all. Our results suggest that, in strategic environments, higher cognitive ability translates into better analytic reasoning and a better ‘theory of mind’ 
Keywords:  Cognitive ability; Bounded rationality; Learning; Convergence; Levelk; Nonequilibrium behavior; Beauty contest; Repeated games; Structural modeling; Theory of mind; Intelligence; Raven test 
JEL:  D83 C73 C91 
Date:  2012–04–23 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:38317&r=mic 
By:  Peter Duersch; Joerg Oechssler; Burkhard Schipper (Department of Economics, University of California Davis) 
Abstract:  We show that for many classes of symmetric twoplayer games, the simple decision rule ``imitateifbetter'' can hardly be beaten by any strategy. We provide necessary and sufficient conditions for imitation to be unbeatable in the sense that there is no strategy that can exploit imitation as a money pump. In particular, imitation is subject to a money pump if and only if the relative payoff function of the game is of the rockscissorspaper variety. We also show that a sufficient condition for imitation not being subject to a money pump is that the relative payoff game is a generalized ordinal potential game or a quasiconcave game. Our results apply to many interesting examples of symmetric games including 2 x 2 games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games. 
Keywords:  Imitatethebest, learning, symmetric games, relative payoffs, zerosum games, rockpaperscissors, finite population ESS, generalized ordinal potential games, quasiconcave games 
JEL:  C72 C73 D43 
Date:  2012–04–17 
URL:  http://d.repec.org/n?u=RePEc:cda:wpaper:125&r=mic 
By:  Ronald Wendner (KarlFranzens University Graz) 
Abstract:  This paper analyzes the effects of nonatmospheric consumption externalities on optimal commodity taxation and on the social cost and optimal levels of public good provision. A negative consumption externality, by lowering the social cost of public good provision, may require the secondbest level of public good provision to exceed the firstbest level. If those households who are most important for building up the consumption reference level respond the least to commodity taxation, heterogeneity may imply an equityefficiency tradeoff. This tradeoff is present only if the consumption externality is of the nonatmospheric type. 
Keywords:  Consumption externality, Optimal commodity taxation, Pigou, Public good provision, Ramsey rule 
JEL:  D62 H21 H41 
Date:  2011–11 
URL:  http://d.repec.org/n?u=RePEc:grz:wpaper:201201&r=mic 