In this paper we suggest a model of sequential auctions with endogenous participation where each bidder conjectures about the number of participants at each round. Then, after learning his value, each bidder decides whether or not to participate in the auction. In the calculation of his expected value, each bidder uses his conjectures about the number of participants for each possible subgroup. In equilibrium, the conjectured probability is compatible with the probability of staying in the auction. In our (...) model, players face participation costs, bidders may buy as many objects as they wish and they are allowed to drop out at any round. Bidders can drop out at any time, but they cannot come back to the auction. In particular we can determine the number of participants and expected prices in equilibrium. We show that for any bidding strategy, there exists such a probability of staying in the auction. For the case of stochastically independent objects, we show that in equilibrium every bidder who decides to continue submits a bid that is equal to his value at each round. When objects are stochastically identical, we are able to show that expected prices are decreasing. (shrink)

The article presents an Internet experiment where subjects sequentially bid for basic gifts and binary-lotteries on these gifts in incentive compatible Vickrey auctions. Subjects exhibit uniformly pessimistic prize-weighting in spite of precautions to reduce suspicion and prohibit collusion. The bids for lotteries are close to the minimal payable value, even when the probability of obtaining a better prize is larger than 50%. Prize-weighting becomes even more conservative as the distance in value of payable prizes increases. The twofold aversive affect (...) appears for three distinct groups of students; we demonstrate, however, that the same subjects overweight small win-probabilities in standard binary-choice. (shrink)

The economics of search is a prominent component of economic theory, and it has a richness and elegance that underpins a host of practical applications. In this book Brian and John McCall present a comprehensive overview of the economic theory of search, from the classical model of job search formulated 40 years ago to the recent developments in equilibrium models of search. The book gives decision-theoretic foundations to seemingly slippery issues in labour market theory, estimation theory and economic dynamics in (...) general, and surveys the entire field of the economics of search, including its history, theory, and econometric applications. Theoretical models of the economics of search are covered as well as estimation methods used in search theory and topics covered include job search, turnover, unemployment, liquidity, house selling, real options and auctions. The mathematical methods used in search theory such as dynamic programming are reviewed as well as structural estimation methods and econometric methods for duration models. The authors also explore the classic sequential search model and its extensions in addition to recent advances in equilibrium search theory. (shrink)

Games and Decision Making, Second Edition, is a unique blend of decision theory and game theory. From classical optimization to modern game theory, authors Charalambos D. Aliprantis and Subir K. Chakrabarti show the importance of mathematical knowledge in understanding and analyzing issues in decision making. Through an imaginative selection of topics, Aliprantis and Chakrabarti treat decision and game theory as part of one body of knowledge. They move from problems involving the individual decision-maker to progressively more complex problems such as (...) sequential rationality, auctions, and bargaining. By building each chapter on material presented earlier, the authors offer a self-contained and comprehensive treatment of these topics. Successfully class-tested in an advanced undergraduate course at the Krannert School of Management and in a graduate course in economics at Indiana University, Games and Decision Making, Second Edition, is an essential text for advanced undergraduates and graduate students of decision theory and game theory. The book is accessible to students who have a good basic understanding of elementary calculus and probability theory. (shrink)

Internet fraud is an issue that increasingly concerns regulators, consumers, firms, and business ethics researchers. In this article, we examine one common form of internet fraud, the practice of shill bidding (when a seller in an auction enters a bid on his or her own item). The significant incidence of shill bidding on eBay (in spite of the fact that it is illegal just as it is in live auctions) exemplifies the current ineffectiveness of regulatory means as well as (...) the lack of effective societal mechanisms to prevent online fraud. Further, the proliferation of shill bidding along with other types of internet fraud may have broader implications. If unethical behavior such as shill bidding becomes too widespread on the internet, regulators and other societal forces may deem it necessary to institute controls that will impact the entire online marketplace as well as the future development and regulation of business activities on the internet. Our results indicate that shill bidding is perpetrated on eBay significantly more often than 0.1% rate of fraud estimated by the firm. This suggests that regulators, users, and others stakeholders may become concerned enough to act. The impact of those responses on the internet of the future may affect a broad array of users beyond the unethical sellers on eBay. (shrink)

This article explores the possibilities offered by Collins’ model of interaction rituals to an understanding of the emotional dynamics of art auctions. It argues that whilst it explains how the art object becomes the focus of attention, and thus the repository of solidarity and emotional energy, it also obliterates some of the institutional aspects of the auction market that can influence such outcomes. It discusses the need to include an examination of the specific practices of auction houses operating in (...) an international market in their capacity to target specific audiences for their sales. (shrink)

We study a first-price auction preceded by a negotiation stage with complete information, during which bidders may form a bidding ring. We prove that in the absence of externalities, the grand cartel forms in equilibrium, allowing ring members to gain the auctioned object for a minimal price. However, identity-dependent externalities may lead to the formation of small rings, as often observed in practice. Potential ring members may condition their participation on high transfer payments as a compensation for their expected externalities (...) if the ring forms. The cartel may therefore profitably exclude these bidders, although risking tougher competition in the auction. We also analyze ring efficiency in the presence of externalities, showing that a ring may prefer sending an inefficient member to the auction, if the efficient member exerts threatening externalities on bidders outside the ring, which in turn leads to a higher winning price. (shrink)

We study a dynamic auction mechanism in the context of private provision of a discrete public good under incomplete information. The bidders have private valuations, and the cost of the public good is common knowledge. No bidder is willing to provide the good on her own. We show that a natural application of open ascending auctions in such environments fails dramatically: The probability of provision is zero in any equilibrium. The mechanism effectively auctions off the ‘right’ to be (...) the last one to contribute, but intuition suggests that neither player wishes to be the last one to contribute. Since the player who contributes first has the advantage of being able to free ride on the contributions of the other players, no player wants to ‘win’ the auction. (shrink)

In this paper, we study the auction to allocate an indivisible good when each potential buyer has a private and independent valuation for the item and suffers a negative externality if a competitor acquires it. In that case, the outside option of each buyer is mechanism-dependent, which implies that participation is endogenous. As several works in the literature have shown, the optimal auction entails strong threats to induce full entry and maximal expected revenue. This results from the full commitment assumption, (...) which ensures that threats are credible. We show that absent credible threats, the entry process does not lead to full participation: the equilibrium entails screening of agents in the entry stage and a trade-off between reserve prices and entry fees. Besides, we discuss the conditions under which the impossibility to use threats does not prevent the seller from ensuring a minimal screening and reaching a high expected revenue. (shrink)

The effect of recent experience on current behavior has been studied extensively in simple laboratory tasks. We explore the nature of sequential effects in the more naturalistic setting of automobile driving. Driving is a safety-critical task in which delayed response times may have severe consequences. Using a realistic driving simulator, we find significant sequential effects in pedal-press response times that depend on the history of recent stimuli and responses. Response times are slowed up to 100 ms in particular (...) cases, a delay that has dangerous practical consequences. Further, we observe a significant number of history-related pedal misapplications, which have recently been noted as a cause for concern in the automotive safety community. By anticipating these consequences of sequential context, driver assistance systems could mitigate the effects of performance degradations and thus critically improve driver safety. (shrink)

We show that linear logic can serve as an expressive framework in which to model a rich variety of combinatorial auction mechanisms. Due to its resource-sensitive nature, linear logic can easily represent bids in combinatorial auctions in which goods may be sold in multiple units, and we show how it naturally generalises several bidding languages familiar from the literature. Moreover, the winner determination problem, i.e., the problem of computing an allocation of goods to bidders producing a certain amount of (...) revenue for the auctioneer, can be modelled as the problem of finding a proof for a particular linear logic sequent. (shrink)

According to T. M. Scanlon’s anti-aggregation principle, it is wrong to save a larger number of people from minor harms rather than a smaller number from much more serious harms. This principle is a central part of many influential and anti-utilitarian ethical theories. According to the sequential-dominance principle, one does something wrong if one knowingly performs a sequence of acts whose outcome would be worse for everyone than the outcome of an alternative sequence of acts. The intuitive appeal of (...) the sequential-dominance principle should be obvious; everyone is knowingly made worse off if it is violated. In this paper, I present a number of cases where one is forced to violate either the anti-aggregation principle or the sequential-dominance principle. I show that these principles conflict regardless of whether one accepts a counterfactual or a temporal, worsening view of harm. Moreover, I show that this result holds regardless of how much worse a harm has to be in order to count as a much more serious harm. (shrink)

The constructions of sequential calculi are based on the idea of application to the deduction process not only single logical constants but complexes of them as well. Surely, making use of this idea is not obligatory in paraconsistent logic. Nevertheless, using it in this field gives us a convenient tool for seeking proofs in formulation of many paraconsistent logics. Each of sequential propositional logics discussed in this paper is obtained as a result of a transformation of a starting (...) calculus GCL – one of sequential formalizations of classical propositional logic. Let α be a standard propositional language with a vocabulary {p1, p2, p3, . . . , −,∨, &, ⊃,¬,), we shall denote any formulas of α and by the letters Γ,∆, Σ, Θ finite sets of α-formulas. (shrink)

In the first author's thesis [10], a sequential language, LRT, for real number computation is investigated. That thesis includes a proof that all polynomials are programmable, but that work comes short of giving a complete characterization of the expressive power of the language even for first-order functions. The technical problem is that LRT is non-deterministic. So a natural characterization of its expressive power should be in terms of relations rather than in terms of functions. In [2], Brattka examines a (...) formalization of recursive relations in the style of Kleene's recursive functions on the natural numbers. This paper is an expanded version of [13] which establishes the expressive power of LRTp, a variant of LRT, in terms of Brattka's recursive relations. Because Brattka already did the work of establishing the precise connection between his recursive relations and Type 2 Theory of Effectivity, we thus obtain a complete characterization of first-order definability in LRTp. (shrink)

We deal with situations incongruent with our automatic response tendencies much better right after having done so on a previous trial than after having reacted to a congruent trial. The nature of the mechanisms responsible for these sequential congruency effects is currently a hot topic of debate. According to the conflict monitoring model these effects depend on the adjustment of control triggered by the detection of conflict on the preceding situation. We tested whether these conflict monitoring processes can operate (...) implicitly in an implicit learning procedure, modulating the expression of knowledge of which participants are not aware. We reanalyze recently published data, and present an experiment with a probabilistic sequence learning procedure, both showing consistent effects of implicit sequence learning. Despite being implicit, the expression of learning was reduced or completely eliminated right after trials incongruent with the learned sequence, thus showing that sequential congruency effects can be obtained even when the source of congruency itself remains implicit. (shrink)

The practical importance of auction theory is widely recognized. Indeed, economists have been recognized for their contribution to the design of several auction-like mechanisms, such as the U. S. Federal Communications Commission spectrum auctions, the 3G auctions in Europe and beyond, and the auction markets for electricity markets around the world. This book provides a step-by-step, self-contained treatment of the theory of auctions. The aim is to provide an introductory textbook that will allow students and readers with (...) a calculus background to work through all the basic results. Coverage includes: the basic independent-private-model; the effects of introducing correlation in valuations on equilibrium behaviour and the seller's expected revenue; mechanism design; and the theory of multi-object auctions. The paperback edition of the text includes a new chapter which acts as a guide to current developments in auction theory. (shrink)

Do hard budget constraints work in favour or against truth telling in double auctions? McAfee constructed a simple double auction mechanism, which is strategyproof and minimally inefficient, but may resort to dual prices, where the difference between prices is channelled as a surplus to the market maker, preventing MDA from achieving a balanced budget. We construct a variant of MDA in which no-loss constraints play a major positive role. Our variant of MDA is also strategyproof, as efficient as MDA (...) but improves on it by achieving a balanced budget via always having a uniform price. (shrink)

It is shown that in any model of constructive mathematics in which a certain omniscience principle is false, for strongly extensional functions on an interval the distinction between sequentially continuous and regulated disappears. It follows, without the use of Markov's Principle, that any recursive function of bounded variation on a bounded closed interval is recursively sequentially continuous.

The global allocation of vaccines during the COVID-19 pandemic is widely perceived as unfair. Priority was given to countries that paid the most with little or no concern for who needed the vaccines the most. No satisfactory institutions have been established to allocate vaccines in a future pandemic. In this paper, we join reformers in proposing a new scheme for vaccine distribution: a global auction for vaccines where profits are distributed fairly to participating countries. Our proposal improves upon previous suggestions (...) morally by taking countries’ differing valuations of money and vaccines seriously. Since an auction is in the interest of both vaccine manufacturers and high-income countries, it is also politically feasible. A global redistributive auction for vaccines thus promises to be a robust and morally desirable way to allocate vaccines. -/- . (shrink)

We present a theory of sequential information processing in persuasion. It extends assumptions of the heuristic-systematic model, in particular the idea that information encountered early in a persuasion situation may affect the processing of subsequent information. SIP also builds on the abstraction from content-related dichotomies in accord with the parametric unimodel of social judgment. SIP features one constitutional axiom and three main postulates: Persuasion is the sequential processing of information that is relevant to judgment formation. Inferences drawn from (...) initial information may bias the processing of subsequent information if they are either activated rules or valence expectations that are relevant to the subsequent information. Inferences drawn from initial information are resistant to change. Thus, the interpretation of subsequent information is assimilated to inferences drawn from the initial information. Or, if assimilation is impossible, contrast effects occur. The overall effect of a persuasion attempt corresponds to the recipient’s judgment at the moment the processing of information is terminated. We illustrate how our predictions for assimilation and contrast effects may be tested by presenting results from an experiment in which we presented exactly the same arguments but varied the processing sequence. We discuss theoretical and applied implications of sequence effects for persuasion phenomena, as well as challenges for further research developing and testing the theory. (shrink)

We respond to recent comments on our proposal to improve justice in ventilator triage, in which we used as an example New Jersey’s publicly available and legally binding Directive Number 2020-03. We agree with Bernard Lo and Doug White that equity implications of triage frameworks should be continually reassessed, which is why we offered six concrete options for improvement, and called for monitoring the consequences of adopted triage models. We disagree with their assessment that we mis-characterised their Model Guidance, as (...) included in the NJ Directive, in ways that undermine our conclusions. They suggest we erroneously described their model as a two-criterion allocation framework; that recognising other operant criterion reveals it ‘likely mitigate[s] rather than exacerbate[s] racial disparities during triage’, and allege that concerns about inequitable outcomes are ‘without evidence’. We highlight two major studies robustly demonstrating why concerns about disparate outcomes are justified. We also show that White and Lo seek to retrospectively—and counterfactually—correct the version of the Model Guideline included in the NJ Directive. However, as our facsimile reproductions show, neither the alleged four-criteria form, nor other key changes, such as dropping the Sequential Organ Failure Assessment score, are found in the Directive. These points matter because our conclusions hence stand, because the public version of the Model Guidance had not been updated to reduce the risk of inequitable outcomes until June 2021 and NJ’s Directive still does not reflect these revisions, and, hence, represents a less equitable version, as acknowledged by its authors. We comment on broader policy implications and call for ways of ensuring accurate, transparent and timely updates for users of high-stakes guidelines. (shrink)

The main result of this paper is a weak constructive version of the uniform continuity theorem for pointwise continuous, real-valued functions on a convex subset of a normed linear space. Recursive examples are given to show that the hypotheses of this theorem are necessary. The remainder of the paper discusses conditions which ensure that a sequentially continuous function is continuous. MSC: 03F60, 26E40, 46S30.

This paper develops a deontic logic based on dynamic logic for reasoning about permission and prohibition of sequential actions. Our approach is characterized by two main features. First, permission and prohibition of sequential actions are not necessarily reduced to permission and prohibition of the actions’ constituent parts. Second, we incorporate the idea that actions may be permitted or prohibited conditional on another action being performed first. The logic interprets actions in terms of sequences of states, and the deontic (...) component of the logic is introduced by relating sequences of states to their legal and illegal future continuations. We consider various different logics obtained by imposing natural constraints on models, and formulate complete axiom systems for several of these logics. (shrink)

This article uses transcriptions from video recordings of airline pilots at work, on actual flights, to consider some locations and the interactional significance of a feature of routine talk in the airline cockpit: and-prefaced turns. As pilots’ work is formally organized for them as many discrete and ordered tasks, and-prefacing is a local means for maintaining an ongoing sense of their conduct of a flight as a whole. By and-prefacing their talk, pilots present some new talk or task as connected (...) and relevantly next in a larger macro-sequence of work for their flight. And-prefacing is evidence of pilots’ orientation to a sense of sequence that can extend well beyond pairs of turns at talk and/or non-talk activities, or even a series of such paired sequences. It allows pilots to make salient the sequentiality of their work where the officially prescribed wordings they must use can leave this implicit. (shrink)

Independence is the condition that, if X is preferred to Y, then a lottery between X and Z is preferred to a lottery between Y and Z given the same probability of Z. Is it rationally required that one’s preferences conform to Independence? The main objection to this requirement is that it would rule out the alleged rationality of Allais and Ellsberg Preferences. In this paper, I put forward a sequential dominance argument with fairly weak assumptions for a variant (...) of Independence (called Independence for Constant Prospects), which shows that Allais and Ellsberg Preferences are irrational. Hence this influential objection (that is, the alleged rationality of Allais and Ellsberg Preferences) can be rebutted. I also put forward a number of sequential dominance arguments that various versions of Independence are requirements of rationality. One of these arguments is based on very minimal assumptions, but the arguments for the versions of Independence which are strong enough to serve in the standard axiomatization of Expected Utility Theory need notably stronger assumptions. (shrink)

Previous studies of Hebrew nu investigate this discourse marker in casual conversation. The current study explores nu on Israeli political phone-in radio programs and broadens our knowledge both about the functions and grammaticization processes of discourse markers and about some particularities of Israeli political talk radio. The comparison to casual talk reveals both qualitative and quantitative differences. In casual talk, the main function of nu is a sequential one – urging further development of an ongoing topic. In the radiophonic (...) data, the most common role of nu is as a keying token, functioning in the affective realm. Furthermore, the talk-radio data show a wider variety of keys constructed by nu – which range from joking to sheer contempt – clustering closer towards the latter, in contrast to the case of casual talk, manifesting mostly the joking key. Structurally, whereas sequential functions are generally accomplished by stand-alone nu, affective tokens are accompanied by same-speaker talk. The analysis sheds new light on how a sequential token might come to function in the affective realm. (shrink)

It will be shown that the Peres–Mermin square admits value-definite noncontextual hidden-variable models if the observables associated with the operators can be measured only sequentially but not simultaneously. Namely, sequential measurements allow for noncontextual models in which hidden states update between consecutive measurements. Two recent experiments realizing the Peres–Mermin square by sequential measurements will also be analyzed along with other hidden-variable models accounting for these experiments.

It is widely assumed that language in some form or other originated by piggybacking on pre-existing learning mechanism not dedicated to language. Using evolutionary connectionist simulations, we explore the implications of such assumptions by determining the effect of constraints derived from an earlier evolved mechanism for sequential learning on the interaction between biological and linguistic adaptation across generations of language learners. Artificial neural networks were initially allowed to evolve “biologically” to improve their sequential learning abilities, after which language (...) was introduced into the population. We compared the relative contribution of biological and linguistic adaptation by allowing both networks and language to change over time. The simulation results support two main conclusions: First, over generations, a consistent head-ordering emerged due to linguistic adaptation. This is consistent with previous studies suggesting that some apparently arbitrary aspects of linguistic structure may arise from cognitive constraints on sequential learning. Second, when networks were selected to maintain a good level of performance on the sequential learning task, language learnability is significantly improved by linguistic adaptation but not by biological adaptation. Indeed, the pressure toward maintaining a high level of sequential learning performance prevented biological assimilation of linguistic-specific knowledge from occurring. (shrink)

Prediction‐based processes appear to play an important role in language. Few studies, however, have sought to test the relationship within individuals between prediction learning and natural language processing. This paper builds upon existing statistical learning work using a novel paradigm for studying the on‐line learning of predictive dependencies. Within this paradigm, a new “prediction task” is introduced that provides a sensitive index of individual differences for developing probabilistic sequential expectations. Across three interrelated experiments, the prediction task and results thereof (...) are used to bridge knowledge of the empirical relation between statistical learning and language within the context of nonadjacency processing. We first chart the trajectory for learning nonadjacencies, documenting individual differences in prediction learning. Subsequent simple recurrent network simulations then closely capture human performance patterns in the new paradigm. Finally, individual differences in prediction performances are shown to strongly correlate with participants’ sentence processing of complex, long‐distance dependencies in natural language. (shrink)

Causal Decision Theory reckons the choice-worthiness of an option to be completely independent of its evidential bearing on its non-effects. But after one has made a choice this bearing is relevant to future decisions. Therefore it is possible to construct problems of sequential choice in which Causal Decision Theory makes a guaranteed loss. So Causal Decision Theory is wrong. The source of the problem is the idea that agents have a special perspective on their own contemplated actions, from which (...) evidential connections that observers can see are either irrelevant or invisible. (shrink)

Text classification involves deciding whether or not a document is about a given topic. It is an important problem in machine learning, because automated text classifiers have enormous potential for application in information retrieval systems. It is also an interesting problem for cognitive science, because it involves real world human decision making with complicated stimuli. This paper develops two models of human text document classification based on random walk and accumulator sequential sampling processes. The models are evaluated using data (...) from an experiment where participants classify text documents presented one word at a time under task instructions that emphasize either speed or accuracy, and rate their confidence in their decisions. Fitting the random walk and accumulator models to these data shows that the accumulator provides a better account of the decisions made, and a “balance of evidence” measure provides the best account of confidence. Both models are also evaluated in the applied information retrieval context, by comparing their performance to established machine learning techniques on the standard Reuters‐21578 corpus. It is found that they are almost as accurate as the benchmarks, and make decisions much more quickly because they only need to examine a small proportion of the words in the document. In addition, the ability of the accumulator model to produce useful confidence measures is shown to have application in prioritizing the results of classification decisions. (shrink)

Gossip, in its most general sense, means talking about absent third parties with regards to their strengths and weaknesses in an evaluative or informative tone. It is a common phenomenon and has been investigated from different perspectives of research such as human sciences, behavioural psychology, anthropology and so forth. Although it is a prevalent research topic amongst researchers of various disciplines, the sequential organisation of gossip talk still keeps its authenticity in terms of real-life talk-in-action research. This study aims (...) to provide a micro-analysis of the sequential organisation of gossip talk adopting an emic perspective. The data set consists of a collection of 90 hours of audio data collected from a retirement home in Turkey. The data are analysed using Conversation Analysis. The results of the micro-analysis of authentic gossip talk points to a systematicity in gossip talk sequences in terms of initiation, response and closing. (shrink)

Working within Bishop-style constructive mathematics, we derive a number of results relating the nonconstructive LPO and sequential compactness property on the one hand, and the intuitionistically reasonable anti-Specker property on the other.

In computer-mediated communication, users cannot ensure that responsive postings are placed in a directly adjacent position. Yet, paired actions are discernible in which a first pair part makes a second pair part conditionally relevant. While previous studies of short messaging service communication show that users usually send clusters of FPPs and that SPPs are ordered in the same chronology, little is known about sequential practices of dealing with multiple FPPs in text-based WhatsApp communication. This article shows that in German (...) WhatsApp dialogues, users apply a chronological as well as a reversed ordering of SPPs. It is argued that this result can only be partly attributed to the affordances of the mobile messenger. Rather, users arrange SPPs in order to foreground particular topics in extended, chat-like dialogues. (shrink)

Two key research issues in the field of causal learning are how people acquire causal knowledge when observing data that are presented sequentially, and the level of abstraction at which learning takes place. Does sequential causal learning solely involve the acquisition of specific cause-effect links, or do learners also acquire knowledge about abstract causal constraints? Recent empirical studies have revealed that experience with one set of causal cues can dramatically alter subsequent learning and performance with entirely different cues, suggesting (...) that learning involves abstract transfer, and such transfer effects involve sequential presentation of distinct sets of causal cues. It has been demonstrated that pre-training can modulate classic causal learning phenomena such as forward and backward blocking. To account for these effects, we propose a Bayesian theory of sequential causal learning. The theory assumes that humans are able to consider and use several alternative causal generative models, each instantiating a different causal integration rule. Model selection is used to decide which integration rule to use in a given learning environment in order to infer causal knowledge from sequential data. Detailed computer simulations demonstrate that humans rely on the abstract characteristics of outcome variables to select a causal integration rule, which in turn alters causal learning in a variety of blocking and overshadowing paradigms. When the nature of the outcome variable is ambiguous, humans select the model that yields the best fit with the recent environment, and then apply it to subsequent learning tasks. Based on sequential patterns of cue-outcome co-occurrence, the theory can account for a range of phenomena in sequential causal learning, including various blocking effects, primacy effects in some experimental conditions, and apparently abstract transfer of causal knowledge. (shrink)

We show that a given data ow language l has the property that for any program P and any demand for outputs D (which can be satis ed) there exists a least partial computation of P which satis es D, i all the operators of l are stable. This minimal computation is the demand-driven evaluation of P. We also argue that in order to actually implement this mode of evaluation, the operators of l should be further restricted to be e (...) ectively sequential ones. (shrink)