Mas-Colell Bargaining Set of Large Games

We study the equivalence between the MB-set and the core in the general context of games with a measurable space of players. In the first part of the paper, we study the problem without imposing any restriction on the class of games we consider. In the second part, we apply our findings to specific classes of games for which we provide new equivalence results. These include non-continuous convex games, exact non-atomic market games and non-atomic non-exact games. We also introduce, and characterize, a new class of games, which we call thin games. For these, we show not only that the MB-set is equal to the core, but also that it is the unique stable set in the sense of von Neumann and Morgenstern. Finally, we study the relation between thin games, market games and convex games.Mas-Colell Bargaining Set, maximal excess game, core-equivalence, thin games, market games, convex games.

School Attendance, Child Labor and Cash Transfers. An Impact Evaluation of PANES

In this paper we analyze the impact an emergency social assistance program, PANES, on school attendance and child labour. The program was carried out in Uruguay from April 2005 to December 2007. Specifically, we analyze the effects of the cash transfer component of the plan (Ingreso Ciudadano), and explore potential explanatory channels such as labour market outcomes, income and awareness of conditionalities. This research is based on a panel of successful and unsuccessful applicants to PANES. The first wave uses the administrative records of the program and the second wave is a follow-up survey that was gathered two months after the program ended and was specifically designed to carry out the impact evaluation of the program. In order to check the robustness of our results, we provide evidence based on two different identification strategies: a regression discontinuity approach using data from the second wave of the panel, and a difference-in-difference approach that exploits the longitudinal nature of the collected data. Our results indicate that the program did not affect school attendance or child labour, whether children are considered as one group or are disaggregated by age or sex. We also do not find any impact on household income, which suggests that income substitution does not explain the lack of results in terms of schooling. It therefore appears that either the size of the transfer was not generous enough to promote school attendance or that the determinants of child school attendance are more complex and require complementary interventions. Our results are particularly relevant for understanding of the role of cash transfers in middle-income countries where attendance rates at primary school are already high, and where the main challenge is to keep students in school at the secondary level. The data also allows us to explore the role of conditionalities. Only a small share of households was aware of the school enrolment condition (20%). Conditionalities were announced and are present in other social security programs in Uruguay, but were ultimately not monitored in this case. We did not find the conditionality to have any robust impact (as perceived by the household) on children’s school enrolment.Cash transfer program; Impact evaluation; School attendance, Child labour, Uruguay

A Characterization of Exact Non-atomic Market Games

Continuous exact non-atomic games are naturally associated to certain operators between Banach spaces. It thus makes sense to study games by means of the corresponding operators. We characterize non-atomic exact market games in terms of the properties of the associated operators. We also prove a separation theorem for weak compact sets of countably additive measures, which is of independent interest

Toward a rational-choice foundation of non-additive theories

A classical argument of de Finetti holds that Rationality implies Subjective Expected Utility (SEU). In contrast, the Knightian distinction between Risk and Ambiguity suggests that a rational decision maker would obey the SEU paradigm when the information available is in some sense good, and would depart from it when the information available is not good. Unlike de Finetti's, however, this view does not rely on a formal argument. In this paper, we study the set of all information structures that might be availabe to a decision maker, and show that they are of two types: those compatible with SEU theory and those for which SEU theory must fail. We also show that the former correspond to "good" information, while the latter correspond to information that is not good. Thus, our results provide a formalization of the distinction between Risk and Ambiguity. As a consequence of our main theorem (Theorem 2, Section 8), behavior not-conforming to SEU theory is bound to emerge in the presence of Ambiguity. We give two examples of situations of Ambiguity. One concerns the uncertainty on the class of measure zero events, the other is a variation on Ellberg's three-color urn experiment. We also briefly link our results to two other strands of literature: the study of ambiguous events and the problem of unforeseen contingencies. We conclude the paper by re-considering de Finetti's argument in light of our findings

Ambiguity, measurability and multiple priors

The paper provides a notion of measurability which is suited for a class of Multiple Prior Models. Those characterized by nonatomic countably additive priors. Preferences generating such representations have been recently axiomatized in [12]. A notable feature of our definition of measurability is that an event is measurable if and only if it is unambiguous in the sense of Ghirardato, Maccheroni and Marinacci [8]. In addition, the paper contains a thorough description of the basic properties of the family of measurable/unambiguous sets, of the measure defined on those and of the dependence of the class of measurable sets on the set of priors. The latter is obtained by means of an application of Lyapunov's convexity theorem

Ambiguous events

We focus on a class of Multiple Prior Models. Those characterized by nonatomic countably additive priors. Preferences generating such representations have been recently axiomatized in [17]. We argue that this is the proper setting for comparing the notions of unambiguous event given by Epstein and Zhang in [7] and by Ghirardato, Maccheroni and Marinacci in [10]. The two definitions are known to be nonequivalent. Our main result is that an event T is unambiguous in the sense of Epstein and Zhang if and only if either (i) it is unambiguous in the sense of [10]; or (ii) conditional on T, the decision maker is an expected utility maximizer. We also provide an easy operational criterion for establishing whether or not an event is unambiguous in the sense of Epstein and Zhang

Analogy in Decision-Making

In the context of decision making under uncertainty, we formalize the concept of analogy: an analogy between two decision problems is a mapping that transforms one problem into the other while preserving the problem's structure. We identify the basic structure of a decision problem, and provide a representation of the mappings that pre- serve this structure. We then consider decision makers who use multiple analogies. Our main results are a representation theorem for "aggregators" of analogies satisfying certain minimal requirements, and the identification of preferences emerging from analogical reasoning. We show that a large variety of multiple-prior preferences can be thought of as emerging from analogical reasoning

On the uniqueness of convex-ranged probabilities

We provide an alternative proof of a theorem of Marinacci [2] regarding the equality of two convex-ranged measures. Specifically, we show that, if P and Q are two nonatomic, countably additive probabilities on a measurable space (S, Σ), the condition [∃A∗ ∈ Σ with 0 P(B)=⇒ Q(A) ≥ Q(B)]. Moreover, either one is equivalent to P = Q