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on Microeconomics |
| By: | Luciano De Castro |
| Abstract: | Despite their importance, games with incomplete information and dependent types are poorly understood; only special cases have been considered and a general approach is not yet available. In this paper, we propose a new condition (named richness) for correlation of types in (asymmetric) Bayesian games. Richness is related to the idea that “beliefs do not determine preferences” and that types should be modeled with two explicit parts: one for payoffs and another for beliefs. With this condition, we are able to provide the first pure strategy equilibrium existence result for a general model of multi-unit auctions with correlated types. We then focus on a special case of richness, called “grid distributions,” and establish necessary and sufficient conditions for the existence of a symmetric monotonic pure strategy equilibrium in first-price auctions with general levels of correlation. We also provide a polynomial-time algorithm to verify this existence and suggest, using simulations, that the revenue superiority of English auctions may not hold for positively correlated types in general. JEL Classification Numbers: C62, C72, D44, D82 |
| Date: | 2012–01–12 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1556&r=mic |
| By: | Thomas Epper; Helga Fehr-Duda |
| Abstract: | Almost all important decisions in people’s lives entail risky and delayed consequences. Regardless of whether we make choices involving health, wealth, love or education, almost every choice involves costs and benefits that are uncertain and materialize over time. Because risk and delay often arise simultaneously, theories of decision making should be capable of explaining how behavior under risk and over time interacts. There is, in fact, a growing body of evidence indicating important interactions between behaviorally revealed risk tolerance and patience. Risk taking behavior is delay dependent, and time discounting is risk dependent. Here we show that the inherent uncertainty of future events conjointly with people’s proneness to weight probabilities nonlinearly generates a unifying framework for explaining time-dependent risk taking, risk-dependent time discounting, preferences for late resolution of uncertainty, and several other puzzling interaction effects between risk and time. |
| Keywords: | Risk taking, time discounting, probability weighting, decreasing impatience, increasing risk tolerance, preference for late resolution of uncertainty, preference for one-shot resolution of uncertainty |
| JEL: | D01 D81 D91 |
| Date: | 2012–11 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:096&r=mic |
| By: | John Duffy (University of Pittsburgh); Huan Xie (Concordia University) |
| Abstract: | We study how group size affects cooperation in an infinitely repeated n-player Prisoner's Dilemma (PD) game. In each repetition of the game, groups of size n less than or equal to M are randomly and anonymously matched from a fixed population of size M to play the n-player PD stage game. We provide conditions for which the contagious strategy (Kandori, 1992) sustains a social norm of cooperation among all M players. Our main finding is that if agents are sufficiently patient, a social norm of society-wide cooperation becomes easier to sustain under the contagious strategy as n converges to M. |
| Keywords: | Cooperation, Social Norms, Group Size, Repeated Games, Random Matching, Prisoner's Dilemma |
| JEL: | C72 C73 C78 Z13 |
| Date: | 2012–09–12 |
| URL: | http://d.repec.org/n?u=RePEc:crd:wpaper:12010&r=mic |
| By: | Forges, Françoise; Iehlé, Vincent |
| Abstract: | According to a minimalist version of Afriat’s theorem, a consumer behaves as a utility maximizer if and only if a feasibility matrix associated with his choices is cyclically consistent. An ”essential experiment” consists of observed consumption bundles (x1,xn) and a feasibility matrix α. Starting with a standard experiment, in which the economist has specific budget sets in mind, we show that the necessary and sufficient condition for the existence of a utility function rationalizing the experiment, namely, the cyclical consistency of the associated feasibility matrix, is equivalent to the existence, for any budget sets compatible with the deduced essential experiment, of a utility function rationalizing them (and typically depending on them). In other words, the conclusion of the standard rationalizability test, in which the economist takes budget sets for granted, does not depend on the full specification of the underlying budget sets but only on the essential data that these budget sets generate. Starting with an essential experiment (x1,...,xn;α), we show that the cyclical consistency of α, together with a further consistency condition involving both (x1,...,xn) and α, guarantees that the essential experiment is rationalizable almost robustly, in the sense that there exists a single utility function which rationalizes at once almost all budget sets which are compatible with (x1,...,xn;α). The conditions are also trivially necessary. |
| Keywords: | revealed preference; rational choice; cyclical consistency; budget sets; Afriat’s theorem; |
| JEL: | D11 C81 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ner:dauphi:urn:hdl:123456789/9256&r=mic |
| By: | Ramón Jesús Flores Díaz; Elisenda Molina; Juan Tejada |
| Abstract: | We propose a new type of values for cooperative TU-games, which we call pyramidal values. Assuming that the grand coalition is sequentially formed, and all orderings are equally likely, we define a pyramidal value to be any expected payoff in which the entrant player receives a salary and the right to get part of the benefits derived from subsequent incorporations to the just formed coalition, whereas the remaining benefit is distributed among the incumbent players. To be specific, we consider some parametric families of pyramidal values: the egalitarian pyramidal family, which coincides with the a-consensus value family introduced by Ju et al. in (2007), the proportional pyramidal family, and the weighted pyramidal family, which in turn includes the other two families as special cases. We also analyze the properties of these families, as well as their relationships with other previously defined values. |
| Keywords: | Game theory, TU games, Pyramidal values, Consensus values |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws122418&r=mic |
| By: | Yang, Yi-You |
| Abstract: | This paper studies the effect of free disposal on the existence of Walrasian equilibrium for exchange economies with indivisible objects. It is shown that allowing an agent to enjoy free disposal has the same effect for generating an equilibrium (or eliminating existing equilibria) as allowing every agent to enjoy free disposal. A new equilibrium existence theorem is given to show how this observation can enhance the existence results by Kelso and Crawford (1982) and Sun and Yang (2006). |
| Keywords: | Indivisibility; equilibrium; free disposal; monotonic cover |
| JEL: | D5 D51 |
| Date: | 2012–11–13 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:42585&r=mic |
| By: | Jayant V. Ganguli; Aviad Heifetz |
| Abstract: | We prove that a universal preference type space exists under much more general conditions than those postulated by Epstein and Wang (1996). To wit, it is enough that preferences can be encoded by a countable collection of continuous functionals, while the preferences themselves need not necessarily be continuous or regular, like, e.g., in the case of lexicographic preferences. The proof relies on a far-reaching generalization of a method developed by Heifetz and Samet (1998). |
| Date: | 2012–11–13 |
| URL: | http://d.repec.org/n?u=RePEc:esx:essedp:722&r=mic |
| By: | Mongin, Philippe; Pivato, Marcus |
| Abstract: | We introduce a two-stage ranking of multidimensional alternatives, including uncertain prospects as particular case, when these objects can be given a suitable matrix form. The first stage defines a ranking of rows and a ranking of columns, and the second stage ranks matrices by applying natural monotonicity conditions to these auxiliary rankings. Owing to the Debreu-Gorman theory of additive separability, this framework is sufficient to generate very precise numerical representations. We apply them to three main types of multidimensional objects: streams of commodity baskets through time, monetary input-output matrices, and most extensively, uncertain prospects either in a social or an individual context of decision. Among other applications, the new approach delivers the strongest existing form of Harsanyi's (1955) Aggregation Theorem and casts light on the classic comparison between the ex ante and ex post Pareto principle. It also provides a novel derivation of subjective probability from preferences, in the style of Anscombe and Aumann (1963). |
| Keywords: | additively separable; multiattribute decisions; utilitarian; social welfare; social aggregation; ex ante Pareto; input-output matrix; subjective expected utility |
| JEL: | D81 D57 D60 |
| Date: | 2012–11–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:42515&r=mic |