In the standard money pump, an agent with cyclical preferences can avoid exploitation if he shows foresight and solves his sequential decision problem using backward induction (BI). This way out is foreclosed in a modified money pump, which has been presented in Rabinowicz (2000). There, BI will lead the agent to behave in a self-defeating way. The present paper describes another sequential decision problem of this kind, the Centipede for an Intransitive Preferrer, which in some respects is even more (...) striking than the modified pump. In the new problem, the BI reasoning that implies self-defeating behavior does not rest on the controversial robustness assumption concerning beliefs in one's future rationality. This strengthens the claim that foresight cannot save the intransitive preferrer from a self-defeating course of action. (shrink)

One of the most fundamental features of the body plan of arthropods is its segmental design. There is considerable variation in segment number among arthropod groups (about 20‐fold); yet, paradoxically, the vast majority of arthropod species have a fixed number of segments, thus providing no variation in this character for natural selection to act upon. However, the 1000‐species‐strong centipede order Geophilomorpha provides an exception to the general rule of intraspecific invariance in segment number. Members of this group, and especially (...) our favourite animal Strigamia maritima, may thus help us to understand the evolution of segment number in arthropods. Evolution must act by modifying the formation of segments during embryogenesis. So, how this developmental process operates, in a variable‐segment‐number species, is of considerable interest. Strigamia maritima turns out to be a tractable system both at the ecological level of investigating differences in mean segment number between populations and at the molecular level of studying the expression patterns of developmental genes. Here we report the current state of play in our work on this fascinating animal, including our recent finding of a double‐segment periodicity in the expression of two Strigamia segmentation genes, and its possible implications for our understanding of arthropod segmentation mechanisms in general. BioEssays 27:653–660, 2005. © 2005 Wiley Periodicals, Inc. (shrink)

The standard backward-induction reasoning in a game like the centipede assumes that the players maintain a common belief in rationality throughout the game. But that is a dubious assumption. Suppose the first player X didn't terminate the game in the first round; what would the second player Y think then? Since the backwards-induction argument says X should terminate the game, and it is supposed to be a sound argument, Y might be entitled to doubt X's rationality. Alternatively, Y might (...) doubt that X believes Y is rational, or that X believes Y believes X is rational, or Y might have some higher-order doubt. X’s deviant first move might cause a breakdown in common belief in rationality, therefore. Once that goes, the entire argument fails. The argument also assumes that the players act rationally at each stage of the game, even if this stage could not be reached by rational play. But it is also dubious to assume that past irrationality never exerts a corrupting influence on present play. However, the backwards-induction argument can be reconstructed for the centipede game on a more secure basis.1 It may be implausible to assume a common belief in rationality throughout the game, however the game might go, but the argument requires less than this. The standard idealisations in game theory certainly allow us to assume a common belief in rationality at the beginning of the game. They also allow us to assume this common belief persists so long as no one makes an irrational move. That is enough for the argument to go through. (shrink)

In the standard money pump, an agent with cyclical preferences can avoid exploitation if he shows foresight and solves his sequential decision problem using backward induction. This way out is foreclosed in a modified money pump, which has been presented in Rabinowicz. There, BI will lead the agent to behave in a self-defeating way. The present paper describes another sequential decision problem of this kind, the Centipede for an Intransitive Preferrer, which in some respects is even more striking than (...) the modified pump. In the new problem, the BI reasoning that implies self-defeating behavior does not rest on the controversial robustness assumption concerning beliefs in one's future rationality. This strengthens the claim that foresight cannot save the intransitive preferrer from a self-defeating course of action. (shrink)

According to the standard objection to backward induction in games, its application depends on highly questionable assumptions about the players' expectations as regards future counterfactual game developments. It seems that, in order to make predictions needed for backward reasoning, the players must expect each player to act rationally at each node that in principle could be reached in the game, and also to expect that this confidence in the future rationality of the players would be kept by each player come (...) what may: even at the game-nodes that could only be reached by irrational play. Both expectations seem to be rather unreasonable: a player's initial disposition to rational behaviour may be weakened by a long stretch of irrational play on his part and, even more importantly, his initial confidence in the other players' future rationality may be undermined by an irrational play on their part. For different formulations of this objection see Binmore, Reny and, Bicchieri, Pettit and Sugden. and Aumann and.). (shrink)

Two philosophical questions arise about rationality in centipede games that are logically prior to attempts to apply the formal tools of game theory to this topic. First, given that the players have common knowledge of mutual rationality and common knowledge that they are each motivated solely to maximize their own profits, is there a backwards-induction argument that employs only familiar non-technical concepts about rationality, leads to the conclusion that the first player is rationally obligated to end the game at (...) the first step, is deductively valid, employs premises all of which are prima facie highly plausible, and is prima facie sound and )? Second, if there is such an argument, then is it actually sound, or is it instead defective somehow despite being prima facie sound? Addressing these two questions is our project. We present a backwards-induction argument that is prima facie sound; we argue that it is an instance of the notorious sorites paradox, and hence that the concepts of rational obligatoriness and rational permissibility are vague; and we briefly address the potential consequences of all this for the foundations of game theory and decision theory. (shrink)

Normative game theory unsatisfactorily explains rational behavior. Real people do not behave as predicted, and what is prescribed as rational behavior is normally unattainable in real-life. The problem is that current normative analysis does not account for people's cognitive limitations – their bounded rationality. However, this paper develops an account of bounded rationality that explains the rationality of more realistic behavior. I focus on the Centipede Game, in which boundedly rational players explore and test others' immediate behavior, until they (...) can apply limited backward induction. The result is that the game has a solution in the form of a subjective Nash equilibrium, which boundedly rational players can possibly realize. (shrink)

This study analyses behaviour in non-zero-sum finite multi-stage games, particularly the Centipede Game. The classical Nash Equilibrium fails to explain empirical behaviour and intuitive logic and has therefore been challenged. This paper introduces the ‘Pure Collective Equilibrium’, or PCE, which describes the equilibrium reached when agents assess their utility not by their own payoffs but by the mean collective payoff of the team, as outlined by some team-reasoning hypotheses. Classical behaviour and purely collective team reasoning then both represent special (...) cases—the first in which agents and their counterparts are on the Nash Equilibrium path, and the second in which agents and their counterparts are purely collective team reasoners. It is argued that agents intentionally and consistently deviate from classical rationality in the Centipede Game, even in the absence of philanthropic altruists or error-plagued populations. (shrink)

The partial cooperation displayed by subjects in the Centipede Game deviates radically from the predictions of traditional game theory. Even standard, infinite population, evolutionary settings have failed to provide an explanation for this behavior. However, recent work in finite population evolutionary models has shown that such settings can produce radically different results from the standard models. This paper examines the evolution of partial cooperation in finite populations. The results reveal a new possible explanation that is not open to the (...) standard models and gives us reason to be cautious when employing these otherwise helpful idealizations. *Received January 2007; revised November 2007. †To contact the author, please write to: Department of Logic and Philosophy of Science, University of California, 3151 Social Science Plaza A, Irvine, CA 92697-5100; e-mail: [email protected]. (shrink)

Tom Six’s The Human Centipede (First Sequence) (2009) and The Human Centipede II (Full Sequence) (2011) are based on a disturbing premise: people are abducted and stitched together mouth-to-anus. The consequent combinations of faeces and bloodshed, torture and degradation have been roundly vilified by the critical press. Additionally, the sequel was officially banned or heavily censored in numerous countries. This article argues that these reactive forms of suppression fail to engage with the films themselves, or the concepts (such (...) as disgust and offense) on which those judgements are made. Six’s films are far more sophisticated than has been accounted for. These films wear their generic lineage on their grimy sleeves, contextualising conventional motifs such as the mad scientist archetype against contemporary cultural anxieties regarding the body, sex and violence. Furthermore, Six’s constructed persona exposes the interplay between commercial success, grotesquery and censoriousness as a cyclic system that can be abused. Thus, the series epitomises how repulsion can be strategically utilised. Six anticipates his detractors’ offense, and disarms them of their ability to critique his films without adding to their notoriety. The Human Centipede films demonstrate how controversy can be tactically generated to create meaning. (shrink)

Rational choice theory enjoys unprecedented popularity and influence in the behavioral and social sciences, but it generates intractable problems when applied to socially interactive decisions. In individual decisions, instrumental rationality is defined in terms of expected utility maximization. This becomes problematic in interactive decisions, when individuals have only partial control over the outcomes, because expected utility maximization is undefined in the absence of assumptions about how the other participants will behave. Game theory therefore incorporates not only rationality but also common (...) knowledge assumptions, enabling players to anticipate their co-players' strategies. Under these assumptions, disparate anomalies emerge. Instrumental rationality, conventionally interpreted, fails to explain intuitively obvious features of human interaction, yields predictions starkly at variance with experimental findings, and breaks down completely in certain cases. In particular, focal point selection in pure coordination games is inexplicable, though it is easily achieved in practice; the intuitively compelling payoff-dominance principle lacks rational justification; rationality in social dilemmas is self-defeating; a key solution concept for cooperative coalition games is frequently inapplicable; and rational choice in certain sequential games generates contradictions. In experiments, human players behave more cooperatively and receive higher payoffs than strict rationality would permit. Orthodox conceptions of rationality are evidently internally deficient and inadequate for explaining human interaction. Psychological game theory, based on nonstandard assumptions, is required to solve these problems, and some suggestions along these lines have already been put forward. Key Words: backward induction; Centipede game; common knowledge; cooperation; epistemic reasoning; game theory; payoff dominance; pure coordination game; rational choice theory; social dilemma. (shrink)

is used to give a formalization of Artemov’s knowledge based reasoning approach to game theory, (KBR), [ 4 , 5 ]. Epistemic states of players are represented explicitly and reasoned about formally. We give a detailed analysis of the Centipede game using both proof theoretic and semantic machinery. This helps make the case that PDL + E can be a useful basis for the logical investigation of game theory.

A centipede can walk until it thinks about howit does so. Thereafter it stumbles, over thesheer impossibility of the information andcoordination required. Life in the economy islittle different. Those engaged in productionand exchange discover, pragmatically, ways tomake them work. Those observing the processsee, realistically, the immense improbabilitythat it should do so. That most economies workin practice, but must pass such toughteleological tests to succeed in theory,highlights a difference between players' andspectators' outlook which may help to explainwhy the game has (...) repeatedly been thrown wideopen just when conclusive results seemed withinreach.Section 1 of this paper identifies the fourforms of realism which economists have tendedto adopt. Section 2 considers the pragmatism ofeconomic agents, when observed in action bypsychologists and management scholars notoverly steeped in economic theory. Theconcluding section reviews the ways in whicheconomists have tried to blur the distinction,by reclassifying agents as realistic or theirown views as pragmatic, and suggests that amore pragmatic economics might bridge thedivide. (shrink)

The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term. Under 'things in the broadest possible sense' I include such radically different items as not only 'cabbages and kings', but numbers and duties, possibilities and finger snaps, aesthetic experience and death. To achieve success in philosophy would be, to use a contemporary turn of phrase, to 'know one's way around' with respect (...) to all these things, not in that unreflective way in which the centipede of the story knew its way around before it faced the question, 'how do I walk?', but in that reflective way which means that no intellectual holds are barred. (shrink)

A puzzling finding from research on strategic decision making concerns the effect that predictions have on future actions. Simply stating a prediction about an opponent changes the total probability (pooled over predictions) of a player taking a future action as compared to not stating any prediction. These interference effects are difficult to explain using traditional economic models, and instead these results suggest turning to a quantum cognition approach to strategic decision making.

Topics in Cognitive Science, Volume 14, Issue 3, Page 492-507, July 2022.

How anything acts depends upon what it is, both as a kind of thing and as a distinct individual of that kind: “agere sequitur esse” — action follows being. This is as true of signs as it is of lions or centipedes: therefore, in order to determine the range or extent of semiosis we need above all to determine the kind of being at stake under the name “sign”. Since Poinsot, in a thesis that the work of Peirce centuries later (...) confirmed, the proper being of signs as signs lies in a relation, a relationship irreducibly unifying three distinct terms: a foreground term representing another than itself — the representamen or sign vehicle; the other represented — the significate or object signified; and the third term to or for whom the other-representation is made — the interpretant, which need not be a person and, indeed, need not even be mental. The action of signs then is the way signs influence the world, including the world of experience and knowledge, but extending even to the physical world of nature beyond the living. It is a question of what is the causality proper to signs in consequence of the being proper to them as signs, an indirect causality, just as relations are indirectly dependent upon the interactions of individuals making up the plurality of the universe; and a causality that models what could or might be in contrast to what is here and now. To associate this causality with final causality is correct insofar as signs are employed in shaping the interactions of individual things; but to equate this causality with “teleology” is a fundamental error into which the contemporary development of semiotics has been inclined to fall, largely through some published passages of Peirce from an essay within which he corrects this error but in passages so far left unpublished. By bringing these passages to light, in which Peirce points exactly in the direction earlier indicated by Poinsot, this essay attempts a kind of survey of the contemporary semiotic development in which the full vista of semiosis is laid out, and shown to be co-extensive with the boundaries of the universe itself, wherever they might fall. Precisely the indirect extrinsically specificative formal causality that signs exercise is what enables the “influence of the future” according to which semiosis changes the relevance of past to present in the interactions of Secondness. Understanding of this point also manifests the error of reducing the universe to signs, the error sometimes called “pansemiosis”. (shrink)

I discuss how simulating another agent can be useful in some game-theoretical situations, particularly iterated games such as the centipede game.

The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a necessary and a su cient for them to play the backward induction solution in centipede games. To obtain this (...) result, we do not need to assume that rationality is commonly known (as is done in [Aumann (1995)]) or commonly hypothesized by the players (as done in [Samet (1996)]). The proposed model is compared with the account of hypothetical knowledge presented by Samet in [Samet (1996)] and with other possible strategies for extending information structures with conditional propositions. (shrink)

How anything acts depends upon what it is, both as a kind of thing and as a distinct individual of that kind: “agere sequitur esse” — action follows being. This is as true of signs as it is of lions or centipedes: therefore, in order to determine the range or extent of semiosis we need above all to determine the kind of being at stake under the name “sign”. Since Poinsot, in a thesis that the work of Peirce centuries later (...) confirmed, the proper being of signs as signs lies in a relation, a relationship irreducibly unifying three distinct terms: a foreground term representing another than itself — the representamen or sign vehicle; the other represented — the significate or object signified; and the third term to or for whom the other-representation is made — the interpretant, which need not be a person and, indeed, need not even be mental. The action of signs then is the way signs influence the world, including the world of experience and knowledge, but extending even to the physical world of nature beyond the living. It is a question of what is the causality proper to signs in consequence of the being proper to them as signs, an indirect causality, just as relations are indirectly dependent upon the interactions of individuals making up the plurality of the universe; and a causality that models what could or might be in contrast to what is here and now. To associate this causality with final causality is correct insofar as signs are employed in shaping the interactions of individual things; but to equate this causality with “teleology” is a fundamental error into which the contemporary development of semiotics has been inclined to fall, largely through some published passages of Peirce from an essay within which he corrects this error but in passages so far left unpublished. By bringing these passages to light, in which Peirce points exactly in the direction earlier indicated by Poinsot, this essay attempts a kind of survey of the contemporary semiotic development in which the full vista of semiosis is laid out, and shown to be co-extensive with the boundaries of the universe itself, wherever they might fall. Precisely the indirect extrinsically specificative formal causality that signs exercise is what enables the “influence of the future” according to which semiosis changes the relevance of past to present in the interactions of Secondness. Understanding of this point (the causality proper to signs) also manifests the error of reducing the universe to signs, the error sometimes called “pansemiosis”. (shrink)

The time of the literary work of art is a schematized aspect of the represented objectivities of the literary work. Roman Ingarden’s analysis of the time of the literary work extends upon Husserl’s phenomenology of time consciousness but nevertheless remains consistent with it, insofar as within a literary work as well as actuality, an objective time or literary objective time is constituted from an experience of temporal objects. The time of the literary work of art is experienced through its represented (...) objectivities and depends on an already existent concept of objective time. The time of the literary work, however, gains an indeterminacy, as the author of the literary work is able to manipulate our experience of time within the literary work by predicting how the reader will concretize its events, characters, and objects with respect to time. I use Alain Robbe-Grillet’s representation of the centipede in La Jalousie as an example of the possible manipulations of time, explicable through Ingarden’s analysis of time in the literary work of art. (shrink)

Backward induction was one of the earliest methods developed for solving finite sequential games with perfect information. It proved to be especially useful in the context of Tom Schelling’s ideas of credible versus incredible threats. BI can be also extended to solve complex games that include an infinite number of actions or an infinite number of periods. However, some more complex empirical or experimental predictions remain dramatically at odds with theoretical predictions obtained by BI. The primary example of such a (...) troublesome game is Centipede. The problems appear in other long games with sufficiently complex structure. BI also shares the problems of subgame perfect equilibrium and fails to eliminate certain unreasonable Nash equilibria. (shrink)

Transformation of the sparrow and the butterfly -- Meeting the gods of poverty in a dream -- The greatest joys of the cicada and its cast-off shell -- The owl's understanding -- The centipede questions the snake -- The toad's way of the gods -- The mysterious technique of the cat -- Afterword by William Scott Wilson.

What are the benefits of liberating museum objects from their colonial frames of reference to reincorporate them into Indigenous ways of knowing? As curators working together with Torres Strait Islanders to interpret museum objects, the authors focus on collected items relating to centipedes acquired during the experimental era of scientific investigation by a zoologist and an ethnographer in eastern Zenadth Kes, the Torres Strait waters between northern Australia and Papua New Guinea. In the scientific sphere, the centipede Scolopendra existed (...) for a time as an insect before “becoming” a myriapod. In Zenadth Kes it has always existed as isi. (shrink)

At the very end of the 19th century, Gabriele Tarde wrote that all society was a product of imitation and innovation. This view regarding the development of society has, to a large extent, fallen out of favour, and especially so in those areas where the rational actor model looms large. I argue that this is unfortunate, as models of imitative learning, in some cases, agree better with what people actually do than more sophisticated models of learning. In this paper, I (...) contrast the behaviour of imitative learning with two more sophisticated learning rules (one based on Bayesian updating, the other based on the Nash-Brown-von Neumann dynamics) in the context of social deliberation problems. I show for two social deliberation problems, the Centipede game and a simple Lewis sender-receiver game, that imitative learning provides better agreement with what people actually do, thus partially vindicating Tarde. (shrink)

The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a necessary and a sufficient for them to play the backward induction solution in centipede games. To obtain this result, (...) we do not need to assume that rationality is commonly known (as is done in [Aumann (1995)]) or commonly hypothesized by the players (as done in [Samet (1996)]). The proposed model is compared with the account of hypothetical knowledge presented by Samet in [Samet (1996)] and with other possible strategies for extending information structures with conditional propositions. (shrink)

The effect of upper bounds on message delivery times in a computer network upon the dynamics of knowledge gain is investigated. Recent work has identified centipedes and brooms—causal structures that combine message chains with time bound information—as necessary conditions for knowledge gain and common knowledge gain, respectively. This paper shows that, under the full-information protocol, these structures are both necessary and sufficient for such epistemic gain. We then apply this analysis to gain insights into the relation between “everyone knows” and (...) common knowledge. We prove a tight threshold on the depth k, beyond which Ek G (everyone in G knows nested to depth k) collapses into CG (common knowledge), when this knowledge concerns the occurrence of a spontaneous event. The threshold depends on the size of the group G of agents, as well as the time that has elapsed since the event of interest occurred. The existence of such a threshold is not guaranteed for all protocols, which is demonstrated here by presenting a counterexample in which no such threshold exists. (shrink)

With the 2015 publication of Pope Francis's encyclical Laudato Si', many people of faith have found themselves challenged to seek new ways of addressing serious ecological questions -- issues essential to the flourishing of all creatures and not just human beings. This volume brings together fifteen select scholars to consider pressing contemporary environmental concerns through the lens of Catholic theology. Drawing from the early church fathers and other authoritative voices in the Christian tradition, the contributors to On Earth as It (...) Is in Heaven show how ancient, creedal Christianity offers significant insights into our current ecological dilemmas and speaks powerfully about what it means for us today to care well for God's good creation. CONTRIBUTORS and TOPICS Robert Louis Wilken on honoring centipedes and toads -- and all of God's created works Christopher J. Thompson on not reducing creatures to "resources" solely to be "used" Steven A. Long on understanding the created order as a participation in the divine, eternal law Marie George on human stewardship of creation as both kingship and kinship Matthew Levering on "be fruitful and multiply, and fill the earth" -- a good idea? Dawn M. Nothwehr, OSF, on sustainability from a Franciscan perspective John A. Cuddeback on land use and household stewardship Faith Pawl on animal flourishing and suffering Paul M. Blowers on evolutionary theory and the promise of restoration for all creation Christopher A. Franks on Job, poverty, gratitude, and "a gentle life" Jonathan J. Sanford on how Aristotle and Maritain illuminate our obligation to care for creation Paige E. Hochschild on contemplating rather than dominating nature, building on Augustine and George Grant Chris Killheffer on how monastic sources help us rethink gluttony and its remedies David Vincent Meconi, SJ, on the wonderful, awe-filled interrelationship between creatures and their Creator Esther Mary Nickel, RSM, on the liturgy as the space in which all creation is consecrated before the cross of Christ. (shrink)

Exposing and illustrating how an ongoing engagement with nihilistic alienation may contribute to, rather than detract from, the value of life, Cinematic Nihilism both challenges and builds upon past scholarship that has scrutinised nihilism in the media, but which has generally over-emphasisedits negative and destructive aspects. Through case studies of popular films, including Prometheus, The Dark Knight Rises, Dawn of the Dead and The Human Centipede, and with chapters on Scotland's cinematic portrayal as both a site of "nihilistic sacrifice" (...) and as "nowhere in particular", this bookpresents a necessary corrective, re-emphasising the constructive potential of cinematic nihilism and casting it as a phenomenon that need not be overcome. (shrink)