Finite order automorphisms and real forms of affine Kac-Moody algebras in the smooth and algebraic category

Automorphisms of finite order and real forms of "smooth" affine Kac-Moody algebras are studied, i.e. of 2-dimensional extensions of the algebra of smooth loops in a simple Lie algebra. It is shown that they can be parametrized by certain invariants and that in particular the classification of involutions essentially follows from Cartan's classifications in finite dimensions. We also prove that our approach works equally well in the usual algebraic setting and leads to the same results there

Reputation and Credit Market Formation: How Relational Incentives and Legal Contract Enforcement Interact

The evidence suggests that relational contracting and legal rules play an important role in credit markets but on the basis of the prevailing field data it is difficult to pin down their causal impact. Here we show experimentally that relational incentives are a powerful causal determinant for the existence and performance of credit markets. In fact, in the absence of legal enforcement and reputation formation opportunities the credit market breaks down almost completely while if reputation formation is possible a stable credit market emerges even in the absence of legal enforcement of debt repayment. Introducing legal enforcement of repayments causes a further significant increase in credit market trading but has only a surprisingly small impact on overall efficiency. The reason is that legal enforcement of debt repayments weakens relational incentives and exacerbates another moral hazard problem in credit markets – the choice of inefficient high-risk projects.credit markets, relationship lending, reputation formation, legal enforcement

Contracts as Reference Points: Experimental Evidence

In a recent paper, Hart and Moore (2008) introduce new behavioral assumptions that can explain long term contracts and important aspects of the employment relation. However, so far there exists no direct evidence that supports these assumptions and, in particular, Hart and Moore's notion that contracts provide reference points. In this paper, we examine experimentally the behavioral forces stipulated in their theory. The evidence confirms the model's prediction that there is a tradeoff between rigidity and flexibility in a trading environment with incomplete contracts and ex ante uncertainty about the state of nature. Flexible contracts – which would dominate rigid contracts under standard assumptions –cause a significant amount of shading on ex post performance while under rigid contracts much less shading occurs. Thus, although rigid contracts rule out trading in some states of the world, parties frequently implement them. While our results are broadly consistent with established behavioral concepts, they cannot easily be explained by existing theories. The experiment appears to reveal a new behavioral force: ex ante competition legitimizes the terms of a contract, and aggrievement and shading occur mainly about outcomes within the contract.contracts, reference points, experiment

How Do Informal Agreements and Renegotiation Shape Contractual Reference Points?

Previous experimental work provides encouraging support for some of the central assumptions underlying Hart and Moore (2008)’s theory of contractual reference points. However, existing studies ignore realistic aspects of trading relationships such as informal agreements and ex post renegotiation. We investigate the relevance of these features experimentally. Our evidence indicates that the central behavioral mechanism underlying the concept of contractual reference points is robust to the presence of informal agreements and ex post renegotiation. However, our data also reveal new behavioral features that suggest refinements of the theory. In particular, we find that the availability of informal agreements and ex post renegotiation changes how trading parties evaluate ex post outcomes. Interestingly, the availability of these additional options affects ex post evaluations even in situations in which the parties do not use them.contracts, reference points, fairness, renegotiation, informal agreement

Big Experimenter Is Watching You! Anonymity and Prosocial Behavior in the Laboratory

Social preference research has received considerable attention in recent years. Researchers have demonstrated that the presence of people with social preferences has important implications in many economic domains. However, it is important to be aware of the fact that the empirical basis of this literature relies to a large extent on experiments that do not provide anonymity between experimenter and subject. It has been argued that this lack of experimenter-subject anonymity may create selfish incentives to engage in seemingly other-regarding behavior. If this were the case these experiments would overestimate the importance of social preferences. Previous studies provide mixed results and methodological differences within and across studies make it difficult to isolate the impact of experimenter-subject anonymity on prosocial behavior. In this paper we use a novel procedure that allows us to examine the impact of the exact same ceteris-paribus variation in anonymity on behavior in three of the most commonly used games in the social preference literature. Our data does not support the hypothesis that introducing experimenter-subject anonymity affects observed prosocial behavior. We do not observe significant effects of experimenter-subject anonymity on prosocial behavior in any of our games.scrutiny, prosocial behavior, anonymity, laboratory experiments

A Behavioral Account of the Labor Market: The Role of Fairness Concerns

In this paper, we argue that important labor market phenomena can be better understood if one takes (i) the inherent incompleteness and relational nature of most employment contracts and (ii) the existence of reference-dependent fairness concerns among a substantial share of the population into account. Theory shows and experiments confirm, that even if fairness concerns were only to exert weak effects in one-shot interactions, repeated interactions greatly magnify the relevance of such concerns on economic outcomes. We also review evidence from laboratory and field experiments examining the role of wages and fairness on effort, derive predictions from our approach for entry-level wages and incumbent workers' wages, confront these predictions with the evidence, and show that reference-dependent fairness concerns may have important consequences for the effects of economic policies such as minimum wage laws.fairness, contracts, wages, effort, experiments

Big experimenter is watching you! Anonymity and prosocial behavior in the laboratory

Social preference research has received considerable attention in recent years. Researchers have demonstrated that the presence of people with other-regarding preferences can have important implications in many economic dimensions. However, it is important to be aware of the fact that the empirical basis of this literature relies to a large extent on experiments that do not provide anonymity between experimenter and subject. It has been argued that this lack of experimenter-subject anonymity may create selsh incentives to engage in seemingly other-regarding behavior. If this were the case these experiments would overestimate the importance of social preferences. Previous studies provide mixed results and methodological dierences within and across studies make it difcult to isolate the impact of experimenter-subject anonymity on prosocial behavior. In this paper we use a novel procedure that allows us to examine the impact of the exact same ceteris-paribus variation in anonymity on behavior in three of the most commonly used games in the social preference literature. Our data reveals that introducing experimenter-subject anonymity has only minor, insignicant, eects on prosocial behavior.Scrutiny, anonymity, laboratory experiments, prosocial behavior

Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions

For trigonometric and modified trigonometric integrators applied to oscillatory Hamiltonian differential equations with one or several constant high frequencies, near-conservation of the total and oscillatory energies are shown over time scales that cover arbitrary negative powers of the step size. This requires non-resonance conditions between the step size and the frequencies, but in contrast to previous results the results do not require any non-resonance conditions among the frequencies. The proof uses modulated Fourier expansions with appropriately modified frequencies.Comment: 26 page