The minority game: An economics perspective

This paper gives a critical account of the minority game literature. The minority game is a simple congestion game: players need to choose between two options, and those who have selected the option chosen by the minority win. The learning model proposed in this literature seems to differ markedly from the learning models commonly used in economics. We relate the learning model from the minority game literature to standard game-theoretic learning models, and show that in fact it shares many features with these models. However, the predictions of the learning model differ considerably from the predictions of most other learning models. We discuss the main predictions of the learning model proposed in the minority game literature, and compare these to experimental findings on congestion games.Comment: 30 pages, 4 figure

Congestion, equilibrium and learning: The minority game

The minority game is a simple congestion game in which the players' main goal is to choose among two options the one that is adopted by the smallest number of players. We characterize the set of Nash equilibria and the limiting behavior of several well-known learning processes in the minority game with an arbitrary odd number of players. Interestingly, different learning processes provide considerably different predictions

Finite depth of reasoning and equilibrium play in games with incomplete information

The standard framework for analyzing games with incomplete information models players as if they have an infinite depth of reasoning, which is not always consistent with experimental evidence. This paper generalizes the type spaces of Harsanyi (1967-1968) so that players can have a finite depth of reasoning. We do this restricting the set of events that a player of a finite depth can reason about. This approach allows us to extend the Bayesian-Nash equilibrium concept to environments with players with a finite depth of reasoning. We demonstrate that the standard approach of modeling beliefs with Harsanyi type spaces fails to capture the equilibrium behavior of players with a finite depth, at least in some games. Consequently, the standard approach cannot be used to describe the equilibrium behavior of players with a finite depth in general

Sectoral TFP developments in the OECD

This note describes the sectoral total factor productivity (TFP) developments in the OECD between 1970-1990. Based on the ISDB data of the OECD, we confirm the stylised fact that TFP growth is relatively high in agriculture and relatively low in services. Within manufacturing, the TFP growth in chemicals and in capital goods is high whereas it is low in food processing, paper and publishing and metals. The TFP growth in services sectors like construction, financial services and other (government) services seems to be zero or even negative, while it is relatively high in transport and communication. These sectoral pictures are not universal. Differences between countries are rather large. Also, the TFP growth per year appears to be non constant over time. We use the results from this study in our dynamic CGE model WorldScan to model differences in productivity growth between the sectors. In particular, we employ this mechanism in the European long term scenarios.

Non-C02 greenhouse gases; all gases count

Under the Kyoto Protocol, a group of countries commit themselves to reduce the emissions of greenhouse gases to some 5% below the 1990 level. Countries can decide to spread their reduction commitment over several gases to lower compliance costs. Employing a multi-gas strategy can offer considerable efficiency gains because of the widely diverging marginal abatement cost for the different emission sources. In this Discussion Paper, the analysis of climate policy for the most important greenhouse gas, carbon dioxide, is extended with two other important greenhouse gases, methane and nitrous oxide. The multi-region and multi-sector Applied General Equilibrium model WorldScan has been used as an instrument for addressing this issue. The approach presented is consistent with the bottom-up information on reduction possibilities for those non-CO2 greenhouse gases while it allows for general equilibrium effects and intergas interactions. Including non-CO2 greenhouse gases into the analysis has important sectoral impacts while the regional effects are limited. A considerable part of the burden on gas, coal and oil products will be shifted to the agricultural sectors. Reductions of non-CO2 gases could be especially important for countries like China and India.

A logic for reasoning about ambiguity

Standard models of multi-agent modal logic do not capture the fact that information is often \emph{ambiguous}, and may be interpreted in different ways by different agents. We propose a framework that can model this, and consider different semantics that capture different assumptions about the agents' beliefs regarding whether or not there is ambiguity. We examine the expressive power of logics of ambiguity compared to logics that cannot model ambiguity, with respect to the different semantics that we propose.Comment: Some of the material in this paper appeared in preliminary form in "Ambiguous langage and differences of belief" (see arXiv:1203.0699

Learning to be prepared

Behavioral economics provides several motivations for the common observation that agents appear somewhat unwilling to deviate from recent choices: salience, inertia, the formation of habits, the use of rules of thumb, or the locking in on certain modes of behavior due to learning by doing. This paper provides discrete-time adjustment processes for strategic games in which players display precisely such a bias towards recent choices. In addition, players choose best replies to beliefs supported by observed play in the recent past, in line with much of the literature on learning. These processes eventually settle down in the minimal prep sets of Voorneveld (2004, 2005).adjustment; learning; minimal prep sets; behavioral bias; salience

Robust multiplicity with a grain of naiveté

In an important paper, Weinstein and Yildiz (2007) show that if players have an infinite depth of reasoning and this is commonly believed, types generically have a unique rationalizable action in games that satisfy a richness condition. We show that this result does not extend to environments where players may have a finite depth of reasoning, or think it is possible that the other player has a finite depth of reasoning, or think that the other player may think that is possible, and so on, even if this so-called grain of naiveté is arbitrarily small. More precisely, we show that even if there is almost common belief in the event that players have an infinite depth of reasoning, there are types with multiple rationalizable actions, and the same is true for nearby types. Our results demonstrate that both uniqueness and multiplicity are robust phenomena when we relax the assumption that it is common belief that players have an infinite depth, if only slightly

Challenging Conformity: A Case for Diversity

Why do diverse groups outperform homogeneous groups in some settings, but not in others? We show that while diverse groups experience more frictions than homogeneous ones, they are also less conformist. Homogeneous groups minimize the risk of miscoordination, but they may get stuck in an inefficient equilibrium. Diverse groups may fail to coordinate, but if they do, they tend to attain efficiency. This fundamental tradeoff determines how the optimal level of diversity varies with social and economic factors. When it is vitally important to avoid miscoordination, homogeneous groups are optimal. However, when it is critical to implement new and efficient practices, diverse groups perform better