Salvatore Modica

Awareness and partitional information structures

This is the first of two papers where we present a formal model of unawareness. We contrast unawareness with certainty and uncertainty. A subject is certain of something when he knows that thing; he is uncertain when he does not know it, but he knows he does not: he is consciously uncertain. On the other hand, he isunaware of something when he does not know it, and he does not know he does not know, and so on ad infinitum: he does not perceive, does not have in mind, the object of knowledge. The opposite of unawareness is awareness, which includes certainty and uncertainty.This paper has three main purposes. First, we formalize the concept of awareness, and introduce a symmetry axiom which states that a subject can be aware of something, ϕ say, if and only if he is aware of its negation not-ϕ; in other words, that ϕ and not-ϕ are perceived together, or neither is. We then derive the basic properties of awareness.The second purpose is to prove a different axiomatic characterization, based on the concept of awareness of the system which underlies the model of information with partitional structures (known asS5).The third purpose of this paper is to show that without a substantial weakening of the rules of inferences normally assumed in modal logic a satisfactory model of unawareness, which includes the symmetry axiom, is impossible. This alternative approach is developed in a second paper by the same authors.

A note on comparative downside risk aversion

We provide comparative global conditions for downside risk aversion, which are similar to the ones studied by Ross for risk aversion. We define a coefficient of downside risk aversion, and study its local properties.

Credit Market Failures and Policy

In a simple model of the credit market, based on Stiglitz-Weiss (1981), equilibria are computed and optimal policies to correct market failures are characterized. Some widely applied policies, notably interest-rate subsidies and investment subsidies, are compared to theoretical optimum, and an alternative optimal policy is described which we argue is more robust to model misspecification. An insight on the trade-off between credit policy and infrastructural investment is also offered. A discussion of some aspects of regional policy in Italys Mezzogiorno is finally presented as an application of the analysis.

A neo 2 Bayesian foundation of the maxmin value for two-person zero-sum games

A joint derivation of utility and value for two-person zero-sum games is obtained using a decision theoretic approach. Acts map states to consequences. The latter are lotteries over prizes, and the set of states is a product of two finite sets (m rows andn columns). Preferences over acts are complete, transitive, continuous, monotonie and certainty-independent (Gilboa and Schmeidler (1989)), and satisfy a new axiom which we introduce. These axioms are shown to characterize preferences such that (i) the induced preferences on consequences are represented by a von Neumann-Morgenstern utility function, and (ii) each act is ranked according to the maxmin value of the correspondingm × n utility matrix (viewed as a two-person zero-sum game). An alternative statement of the result deals simultaneously with all finite two-person zero-sum games in the framework of conditional acts and preferences.

GRADING ACROSS SCHOOLS

Abstract This paper reports some facts about grading standards across a varied sample of 16 countries participating in the 2003 OCSE-PISA Survey. Our main finding is that in all countries except Ireland and the USA there is conspicuous heterogeneity in standards across schools (Table 3, Figures 1 & 2). In most of the countries where heterogeneity is present a grading-on-a-curve practice emerges, with grading standards increasing with average competence of the schools students (Table 4, Figures 3 & 4). Where this phenomenon is more pronounced, it may be related to existence of a tracking (as opposed to comprehensive) school system (Table 5, Figure 5).

Dynamics in stochastic evolutionary models

We characterize transitions between stochastically stable states and relative ergodic probabilities in the theory of the evolution of conventions. We give an application to the fall of hegemonies in the evolutionary theory of institutions and conflict and illustrate the theory with the fall of the Qing Dynasty and rise of Communism in China. (This abstract was borrowed from another version of this item.)

Conflict, Evolution, Hegemony, and the Power of the State

In a model of evolution driven by conflict between societies more powerful states have an advantage. When the influence of outsiders is small we show that this results in a tendency to hegemony. In a simple example in which institutions differ in their “exclusiveness” we find that these hegemonies will be inefficiently “extractive” in the sense of having inefficiently high taxes, high compensation for state officials, and low welfare.

Government Size, the Role of Commitments

We explore the hypothesis that long-term commitments affect the dynamics of government expenditure. With the aid of a simple median-voter model we interpret the pattern of increasing-then-constant tax rates observed in OECD countries in the second half of the last century: persistence of public expenditure and a lower bound on new interventions will push government size upward, and preferences of the electorate put a halt to this growth at some point. In this view, the fiscal policy variable is seen to consist of only a part of the total expenditure, the rest being predetermined by its past level.

Evolving to the Impatience Trap: The Example of the Farmer-Sheriff Game

The literature on the evolution of impatience, focusing on one-person decision problems, finds that evolutionary forces favor the more patient individuals. This paper shows that in the context of a game, this is not necessarily the case. In particular, it offers a two-population example where evolutionary forces favor impatience in one group while favoring patience in the other. Moreover, not only evolution but also efficiency may prefer impatient individuals. In our example, it is efficient for one population to evolve impatience and for the other to develop patience. Yet, evolutionary forces move the wrong populations.

Collusion constrained equilibrium

We study collusion within groups in non-cooperative games. The primitives are the preferences of the players, their assignment to non-overlapping groups and the goals of the groups. Our notion of collusion is that a group coordinates the play of its members among different incentive compatible plans to best achieve its goals. Unfortunately, equilibria that meet this requirement need not exist. We instead introduce the weaker notion of collusion constrained equilibrium. This allows groups to put positive probability on alternatives that are suboptimal for the group in certain razors edge cases where the set of incentive compatible plans changes discontinuously. These collusion constrained equilibria exist and are a subset of the correlated equilibria of the underlying game. We examine four perturbations of the underlying game. In each case we show that equilibria in which groups choose the best alternative exist and that limits of these equilibria lead to collusion constrained equilibria. We also show that for a sufficiently broad class of perturbations every collusion constrained equilibrium arises as such a limit. We give an application to a voter participation game showing how collusion constraints may be socially costly.