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on Microeconomics |
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Issue of 2012‒05‒02
eighteen papers chosen by Jing-Yuan 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 n-player 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 Cergy-Pontoise) |
| Abstract: | This paper examines many-player many-action global games with multidimensional state parameters. It establishes that the notion of noise-independent 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, 989-1018). More precisely, our main result states that if an action prole of some complete information game is noise-independently selected in some one-dimensional global game, then it is also noise-independently 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:2012-28&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 risk-dominant 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 absolute-continuity 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 non-trivial 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:12-3&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 non-balanced 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 k-additive 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 k-additive 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 k-additive 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 (ERI-CES. Departamento de Análisis Económico. Facultad de Economía.); Silva-Reus, José A. (Instituto Interuniversitario de Desarrollo Social y Paz) |
| Abstract: | This note provides a way to translate an n-person 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 non-emptyness condition. In particular, for a two-player 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 quasi-linear 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 quasi-linear environments where the en- velope theorem and revenue equivalence principle fail due to non-convex 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 buyer-seller situation where the buyer has loss-averse preferences; we find a zero payment (hence budget-balanced) efficient mechanism in a public goods lo- cation model; and we consider a principal–agent model with ex post non-contractible 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 d-dimensional 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 d-dimensional 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 d-dimensional M-class 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 d-dimensional type space that takes advantage of the correlation among the d parameters. |
| Keywords: | Mechanism design, Multi-dimensional 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 well-known 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 p-beauty 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 level-k 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; Level-k; 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 two-player games, the simple decision rule ``imitate-if-better'' 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 rock-scissors-paper 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: | Imitate-the-best, learning, symmetric games, relative payoffs, zero-sum games, rock-paper-scissors, 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:12-5&r=mic |
| By: | Ronald Wendner (Karl-Franzens University Graz) |
| Abstract: | This paper analyzes the effects of non-atmospheric 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 second-best level of public good provision to exceed the first-best 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 equity-efficiency tradeoff. This tradeoff is present only if the consumption externality is of the non-atmospheric 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:2012-01&r=mic |