The concept of an infinite game played on a finite graph is perhaps novel in the context of an rather extensive recent literature in which infinite games are generally played on an infinite game tree. We claim two advantages for our model, which is admittedly more restrictive. First, our games have a more apparent resemblance to ordinary parlor games in spite of their infinite duration. Second, by distinguishing those nodes of the graph that determine the winning and losing (...) of the game , we are able to offer a complexity analysis that is useful in computer science applications. (shrink)

A general game player automatically learns to play arbitrary new games solely by being told their rules. For this purpose games are specified in the general Game Description Language (GDL), a variant of Datalog with function symbols that uses a few game-specific keywords. A recent extension of basic GDL allows the description of nondeterministic games with any number of players who may have incomplete, asymmetric information. In this paper, we analyse the epistemic structure and expressiveness (...) of this language in terms of modal epistemic logic and prove two main results: (1) The operational semantics of GDL entails that the situation at any stage of a game can be characterised by a multi-agent epistemic (i.e., S5-) model; (2) GDL is sufficiently expressive to model any situation that can be described by a (finite) multi-agent epistemic model. (shrink)

Forty years have passed since video-games were first made widely available to the public and subsequently playing games has become a favorite past-time for many. Players continuously engage with dynamic visual displays with success contingent on the time-pressured deployment, and flexible allocation, of attention as well as precise bimanual movements. Evidence to date suggests that both brief and extensive exposure to video-game play can result in a broad range of enhancements to various cognitive faculties that generalize beyond the (...) original context. Despite promise, video-game research is host to a number of methodological issues that require addressing before progress can be made in this area. Here an effort is made to consolidate the past 30 years of literature examining the effects of video-game play on cognitive faculties and, more recently, neural systems. Future work is required to identify the mechanism that allows the act of video-game play to generate such a broad range of generalized enhancements. (shrink)

There are well-known problems for formalist accounts of game-play with regards to cheating. Such accounts seem to be committed to cheaters being unable to win–or even play–the game, yet it seems that there are instances of cheaters winning games. In this paper, I expand the discussion of such problems by introducing cases of pre-game cheating, and see how a formalist–specifically a Suitsian–account can accommodate such problems. Specifically, I look at two (fictional) examples where the alleged game-players (...) cheat prior to a game-instance in such as a way as to cast doubt on whether the alleged game-players are truly playing the game. To escape the worries brought about by these examples of pre-game cheating, I will appeal to the concept of nested games. This concept will give us the needed tools to explain how the alleged players are cheating and how the alleged players are players. On the whole, this discussion should help illuminate some important issues with regards to cheating and rules on a Suitsian account of game-play, and help give support for formalist accounts more generally. (shrink)

Hunting is typically valued for its instrumentality for food procurement, wildlife management, conservation, heurism, and atavism. More importantly, some hunting is valued intrinsically. A particular form of hunting is a game and game playing, categorically, is often valued intrinsically. This view can be further supported with an application of a concept of caring and an accompanying argument that hunting generally, and fair-chase hunting in particular, is cared about deeply by millions of its practitioners. There are normative grounds (...) for a shift in the way that hunting is valued. While hunting as game playing is valued and cared about deeply by millions of fair-chase practitioners, which is far more important than any of its various instrumentalities, the position that such hunting is morally villainous can be sustained. (shrink)

Seventy-three children between 6 and 7 years of age were presented with a problem having ambiguous subgoal ordering. Performance in this task showed reliable fingerprints: a non-monotonic dependence of performance as a function of the distance between the beginning and the end-states of the problem, very high levels of performance when the first move was correct, and states in which accuracy of the first move was significantly below chance. These features are consistent with a non-Markov planning agent, with an inherently (...) inertial decision process, and that uses heuristics and partial problem knowledge to plan its actions. We applied a statistical framework to fit and test the quality of a proposed planning model. Our framework allows us to parse out independent contributions to problem-solving based on the construction of the value function and on general mechanisms of the search process in the tree of solutions. We show that the latter are correlated with children's performance on an independent measure of planning, while the former is highly domain specific. (shrink)

During the COVID-19 pandemic, several countries implemented social distancing measures to contain virus transmission. However, these vital safety measures have the potential to impair mental health or wellbeing, for instance, from increased perceived loneliness. Playing social video games may offer a way to continue to socialize while adhering to social distancing measures. To examine this issue further, the present online survey investigated social gaming during the pandemic and its association to perceived loneliness within a German-speaking sample. Results indicated a (...) small positive correlation between general gaming frequency and perceived loneliness. Detailed analysis revealed a negative association between perceived loneliness and increased social forms of video gaming. Specifically, gamers with a higher social motive for gaming perceived less loneliness, but gamers with a dominant escape motive demonstrated a positive link to perceived loneliness. The use of social gaming in times of social distancing seems to play a small but significant factor in perceived loneliness compared to other demographical data. The findings are discussed with respect to methodological limitations, effect sizes, and sample characteristics. The results enrich the current knowledge on video gaming and its link to social wellbeing and provide a more nuanced picture than simplistic investigations of screen time. (shrink)

Many people have a strong intuition that there is something morally objectionable about playing violent video games, particularly with increases in the number of people who are playing them and the games' alleged contribution to some highly publicized crimes. In this paper,I use the framework of utilitarian, deontological, and virtue ethical theories to analyze the possibility that there might be some philosophical foundation for these intuitions. I raise the broader question of whether or not participating in authentic simulations (...) of immoral acts in generalis wrong. I argue that neither the utilitarian, nor the Kantian has substantial objections to violent game playing, although they offer some important insights into playing games in general and what it is morally to be a ``good sport.'' The Aristotelian, however, has a plausible and intuitive way to protest participation in authentic simulations of violent acts in terms of character: engaging in simulated immoral actserodes one's character and makes it more difficult for one to live a fulfilled eudaimonic life. (shrink)

This article engages with the fabrication of experiences in first-person shooter video games. On one hand, it explores the forms of affective and cognitive engagement this novel type of immersive imagery demands of the player. On the other hand, the article speculates on how video games images resonate and coincide with other key practices and imaginations defining the political reality of life today. What matters most in the politics of life today is a particular locus of mediation – the brain. (...) The ways we imagine ourselves are today characterized by a figure of the ‘cerebral subject’. The article presents an attempt to chart video games imagery in relation to this key contemporary image of who we are, and to consider how the rhythms of the console screen might be seen as emblematic of a more general anthropology of subjectivity today. (shrink)

Since the seminal paper of Nash (Proc Natl Acad Sci USA 36:48–49, 1950) game theoretic literature has focused mostly on equilibrium and not on maximin (minimax) strategies. In a recent paper of Pruzhansky (Int J Game Theory 40:351–365, 2011) it was shown that under fairy general conditions maximin strategies in completely mixed games can guarantee the same expected payoff as completely mixed Nash equilibrium strategies. Based on this finding, the current paper argues that maximin strategies have important (...) properties. For instance, maximin strategies may refine Nash equilibria in subjective mixed strategies. Further, Bayesian rationality of the players may favor maximin strategies more often than Nash equilibrium strategies. The paper concludes with several suggestions for further experimental research that may shed more light on whether maximin behavior can explain reality better than Nash equilibrium. (shrink)

Strategic games require reasoning about other people’s and one’s own beliefs or intentions. Although they have clear commonalities with psychological tests of theory of mind, they are not clearly related to theory of mind tests for children between 9 and 10 years of age “Flobbe et al. J Logic Language Inform 17(4):417–442 (2008)”. We studied children’s (5–12 years of age) individual differences in how they played a strategic game by analyzing the strategies that they applied in a zero, first, (...) and second-order reasoning task. For the zero-order task, we found two subgroups with different accuracy levels. For the first-order task, subgroups of children applied different suboptimal strategies or an optimal strategy. For the second-order task only suboptimal strategies were present. Strategy use for all tasks was related to age. The 5- and 6-year old children were additionally tested on theory of mind understanding and executive functioning. Strategy-use in these children was related to working memory, but not to theory of mind after correction for age, verbal ability and general IQ. (shrink)

As a contribution to the challenge of building game-playing AI systems, we develop and analyse a formal language for representing and reasoning about strategies. Our logical language builds on the existing general Game Description Language and extends it by a standard modality for linear time along with two dual connectives to express preferences when combining strategies. The semantics of the language is provided by a standard state-transition model. As such, problems that require reasoning about games can (...) be solved by the standard methods for reasoning about actions and change. We also endow the language with a specific semantics by which strategy formulas are understood as move recommendations for a player. To illustrate how our formalism supports automated reasoning about strategies, we demonstrate two example methods of implementation: first, we formalise the semantic interpretation of our language in conjunction with game rules and strategy rules in the Situation Calculus; second, we show how the reasoning problem can be solved with Answer Set Programming. (shrink)

A charming black-figured olpe in the Ashmolean Museum, Oxford shows two warriors playing a game. Between them stands the goddess Athena, an alert figure looking sharply to the left while holding her shield to the right. She holds it rather tactlessly, for the shield entirely obscures the head of the right-hand warrior. Although Cassandra, clinging desperately to the statue of Athena, sometimes has her head obscured in a similar manner behind the goddess's shield, it seems more likely that (...) the painter here has simply misjudged the space available than that he has conflated two iconographical types.The Oxford olpe, though imperfectly planned and executed, is clearly an example of the subject which is best known through the beautiful amphora in the Vatican painted by Exekias. Exekias represented two warriors playing a game at least twice, and is generally believed to have been the first to paint this theme on a vase. (shrink)

The very title of the paper indicates my dissent from the view now prevalent in Heraclitean scholarship that Heraclitus put forward the theory of cosmological stability. Since my interpretative argument presupposes Heraclitus’ belief in cosmogony and general conflagration, it seems advisable to address this issue first.

Strategic games require reasoning about other people’s and one’s own beliefs or intentions. Although they have clear commonalities with psychological tests of theory of mind, they are not clearly related to theory of mind tests for children between 9 and 10 years of age “Flobbe et al. J Logic Language Inform 17:417–442 ”. We studied children’s individual differences in how they played a strategic game by analyzing the strategies that they applied in a zero, first, and second-order reasoning task. (...) For the zero-order task, we found two subgroups with different accuracy levels. For the first-order task, subgroups of children applied different suboptimal strategies or an optimal strategy. For the second-order task only suboptimal strategies were present. Strategy use for all tasks was related to age. The 5- and 6-year old children were additionally tested on theory of mind understanding and executive functioning. Strategy-use in these children was related to working memory, but not to theory of mind after correction for age, verbal ability and general IQ. (shrink)

We consider Effort Games, a game-theoretic model of cooperation in open environments, which is a variant of the principal-agent problem from economic theory. In our multiagent domain, a common project depends on various tasks; carrying out certain subsets of the tasks completes the project successfully, while carrying out other subsets does not. The probability of carrying out a task is higher when the agent in charge of it exerts effort, at a certain cost for that agent. A central authority, (...) called the principal, attempts to incentivize agents to exert effort, but can only reward agents based on the success of the entire project.We model this domain as a normal form game, where the payoffs for each strategy profile are defined based on the different probabilities of carrying out each task and on the boolean function that defines which task subsets complete the project, and which do not. We view this boolean function as a simple coalitional game, and call this game the underlying coalitional game. We suggest the Price of Myopia as a measure of the influence the model of rationality has on the minimal payments the principal has to make in order to motivate the agents in such a domain to exert effort.We consider the computational complexity of testing whether exerting effort is a dominant strategy for an agent, and of finding a reward strategy for this domain, using either a dominant strategy equilibrium or using iterated elimination of dominated strategies. We show these problems are generally #P-hard, and that they are at least as computationally hard as calculating the Banzhaf power index in the underlying coalitional game. We also show that in a certain restricted domain, where the underlying coalitional game is a weighted voting game with certain properties, it is possible to solve all of the above problems in polynomial time. We give bounds on PoM in weighted voting effort games, and provide simulation results regarding PoM in another restricted class of effort games, namely effort games played over Series-Parallel Graphs. (shrink)

In the wake of the Corrupted Blood incident, which afflicted the massively multiplayer online computer role-playing game World of Warcraft in 2005, it has been suggested that both, the incident itself and massively multiplayer online computer role-playing games in general, can be utilised to inform and assist real-world epidemic and public health research. In this paper, I engage critically with these claims.

Universal Game Theory - The theory that all of life is a game played by consciousness’es, (Living Beings). The board is a dream like structure of the universe. The progression is through an active process of intent witnessing, and passive meditation. Which releases the tension in the nerves of the body and leads to selfless actions, moral goodness, and eventually the finish, Enlightenment. Just like a wounded creature only cares about it’s own self. Man in tensionthrough self-centered thought (...) only thinks about his own predicaments. Even if he is thinking about others it is only through his own objectionable view from his false-created center. The enemy or deterrents in the game is the conditioning created by society for ambition, greed, control and general brain washing to give theindividual a false sense of identity, the ego. This is achieved by Religion; tradition, culture, education, reasoning, linear thought, and the creation of time. Leaving him/her in constant anxiety about millions of future contingencies. Through witnessing one realizes the whole futility of one dimensional thought which only leads to more and more thought. Simple or constructed elaborately, thought being time, a human construction. The final step of the Universal Game Theory is understanding the whole process of thought and the eventual revelation of Enlightenment, Bliss, ecstasy. Which the person then understands that he/she is the creator of the life/dream with which they are in. That point being a sexual ecstasy similar to what happens in death to men. i.e. Human males release semenwhen they die, having a sexual ecstasy at their last breath. (shrink)

We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like “rationality at a node” and “knowledge at a node.” We distinguish between the game theorist's and the players' own “theory of the game.” The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in (...) general the game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves. We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it. Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory. (shrink)

We generalize the intuitionistic Hyland–Ong games to a notion of polarized games allowing games with plays starting by proponent moves. The usual constructions on games are adjusted to fit this setting yielding game models for both Intuitionistic Linear Logic and Polarized Linear Logic. We prove a definability result for this polarized model and this gives complete game models for various classical systems: , λμ-calculus, … for both call-by-name and call-by-value evaluations.

Video-game play (particularly “action” video-games) holds exciting promise as an activity that may provide generalized enhancement to a wide range of perceptual and cognitive abilities (for review see Latham et al., 2013a). However, in this article we make the case that to assess accurately the effects of video-game play researchers must better characterize video-game experience and expertise. This requires a more precise and objective assessment of an individual's video-game history and skill level, and making finer distinctions (...) between video-games that fall under the umbrella of “action” games. Failure to consider these factors may partly be responsible for mixed findings (see Boot et al., 2011). (shrink)

For years, legal scholars and environmental activists have maintained that traditional tort proof requirements create insurmountable obstacles to recovery for most plaintiffs in chemical exposure cases, be they pharmaceutical suits or environmental toxic tort cases. Generally, tort law requires a plaintiff to show that the defendant owed a duty, that the defendant breached that duty, and that the breach of that duty caused the injury that is the subject of the suit. In some cases those requirements can be relaxed, as (...) for example, when an injury is of a type that does not occur except as a result of negligence. (shrink)

The design, implementation, and outcome of game-based learning for learners with disabilities have not been sufficiently examined systematically. Particularly, learner-based and contextual factors, as well as the essential roles played by various stakeholders, have not been addressed when game-based learning applications are used in special education. Therefore, a systematic literature review using the Activity Theory was conducted to analyse studies about game-based learning for learners with disabilities. Content analysis of 96 studies reported relevant information with respect to (...) each activity component— subject, technology, object, rules, community, division of labour and outcome. Furthermore, this study identified existing gaps from the reviewed studies, including occasional lack of parental engagement, difficulty of standardising performance measures due to the heterogeneity of learner profiles and contradictions. Finally, recommendations were made under each activity component. The study concluded that both general and domain-specific guidelines should be created for each disability category proposed in this review to assist practitioners who wish to use game-based learning with learners with disabilities. (shrink)

Many philosophical and public discussions of the ethical aspects of violent computer games typically centre on the relation between playing violent videogames and its supposed direct consequences on violent behaviour. But such an approach rests on a controversial empirical claim, is often one-sided in the range of moral theories used, and remains on a general level with its focus on content alone. In response to these problems, I pick up Matt McCormick’s thesis that potential harm from playing (...) computer games is best construed as harm to one’s character, and propose to redirect our attention to the question how violent computer games influence the moral character of players. Inspired by the work of Martha Nussbaum, I sketch a positive account of how computer games can stimulate an empathetic and cosmopolitan moral development. Moreover, rather than making a general argument applicable to a wide spectrum of media, my concern is with specific features of violent computer games that make them especially morally problematic in terms of empathy and cosmopolitanism, features that have to do with the connections between content and medium, and between virtuality and reality. I also discuss some remaining problems. In this way I hope contribute to a less polarised discussion about computer games that does justice to the complexity of their moral dimension, and to offer an account that is helpful to designers, parents, and other stakeholders. (shrink)

_An in-depth look at the philosophical issues behind HBO's _Game of Thrones_ television series and the books that inspired it_ George R.R. Martin's _New York Times_ bestselling epic fantasy book series, A Song of Ice and Fire, and the HBO television show adapted from it, have earned critical acclaim and inspired fanatic devotion. This book delves into the many philosophical questions that arise in this complex, character-driven series, including: Is it right for a "good" king to usurp the throne of (...) a "bad" one and murder his family? How far should you go to protect your family and its secrets? In a fantasy universe with medieval mores and ethics, can female characters reflect modern feminist ideals? Timed for the premiere of the second season of the HBO _Game of Thrones_ series Gives new perspectives on the characters, storylines, and themes of _Game of Thrones_ Draws on great philosophers from ancient Greece to modern America to explore intriguing topics such as the strange creatures of Westeros, the incestuous relationship of Jaime and Cersei Lannister, and what the kings of Westeros can show us about virtue and honor as they play their game of thrones Essential reading for fans, _Game of Thrones and Philosophy_ will enrich your experience of your favorite medieval fantasy series. (shrink)

BackgroundAddictive behavior of gambling, gaming and internet activity is partly a new research domain and has not been well investigated with regard to sexual minority populations. Although health disparities between sexual minorities and the general population are well documented, there is a lack of inclusion of sexual minorities in both research and clinic. Among lesbian, gay and bisexual populations certain features could be present that play a role for the development of addictive behaviors, such as social isolation and increased (...) risk of other psychiatric problems. The aim of this study was to investigate problem gambling, problem gaming and problematic internet behavior in a European context and if it is affected by sexual orientation status.MethodsAn online web-survey was distributed among web-panels in England, Poland, Switzerland, Italy, Spain, Denmark, and Sweden in 2017–2018.Result10 983 complete answers were collected. 7.1% of the participants had a sexual minority status. Regression models found that there was no difference in gambling, gaming and internet behavior among heterosexual and sexual minority men. Sexual minority women were associated with problematic gambling and gaming behavior, when also controlling for age and nationality. When also controlling for psychological distress, women defining as having another sexual minority status than lesbian and bisexual remained significant for having a problematic gaming behavior.ConclusionAn awareness of female sexual minority perspectives is relevant in facilities treating behavioral addiction as well as in future research in behavioral addiction. More research is needed in problematic gambling and gaming behavior in different sexual minority populations with regard to psychiatric comorbidity and living conditions. An inclusion of sexual minority groups defining as other than gay and bisexual is needed in future research. No significant differences were found between heterosexual and sexual minority men in adjusted analysis in this study. (shrink)

We have taken a look at the rules of games in order to acquire some knowledge concerning constitutive rules and, probably, institutional phenomena in general. In this paper we tried to elaborate a system account of constitutive rules. We claim that all accounts that put emphasis on the form of rules are vulnerable. It appears that constitutive rules are interconnected and always form a system that can be internally differentiated. Thanks to adopting certain qualitative criterion we were able to (...) distinguish central and peripheral constitutive rules. Moreover, that very account makes it possible to distinguish between different types of practices that are determined by types of systems of rules. Secondly, it appears there are three “layers” of games that should not be confused: deep conventions, constitutive rules that establish the game and determine games’ identities, and “rules of efficiency” that are some sort of recommendations as to how to play well. (shrink)

The aim of this paper is to show that the meaning and significance of legal evidence is being constituted throughout the course of a singular instance of legal proceedings. This is to be achieved by describing what legal agents _do_ while appealing to different propositions of fact and inferring from them throughout the course of legal proceedings. The authors claim that the process of applying the law is ultimately rooted in the inferential discursive practices of exchanging reasons on the part (...) of the participants of legal proceedings. Therefore, they set forth a model of legal proceedings that consists of an interplay between three types of reasons, which are exchanged by the participants of legal proceedings: i.e. legal reasons, epistemic reasons and stake reasons. To illustrate this interplay, the authors deploy a metaphor of law as a game, and provide a description of legal proceedings as a particular instance of playing a game of law. The conclusion is that the legal concept of evidence is (at least in part) constituted by the role that evidence plays in affecting which reasons for action the participants to legal proceedings choose to act on. The other final assumption of this paper is metatheoretical: authors want to show that when analyzing what legal evidence is, one should begin from the perspective of a singular instance of legal proceedings, rather than from the perspective of law in general. (shrink)

Despite the emergence of computer games as a dominant cultural industry, we know little or nothing about the ethics of computer games. Considerations of the morality of computer games seldom go beyond intermittent portrayals of them in the mass media as training devices for teenage serial killers. In this first scholarly exploration of the subject, Miguel Sicart addresses broader issues about the ethics of games, the ethics of playing the games, and the ethical responsibilities of game designers. He (...) argues that computer games are ethical objects, that computer game players are ethical agents, and that the ethics of computer games should be seen as a complex network of responsibilities and moral duties. Players should not be considered passive amoral creatures; they reflect, relate, and create with ethical minds. The games they play are ethical systems, with rules that create gameworlds with values at play. Drawing on concepts from philosophy and game studies, Sicart proposes a framework for analyzing the ethics of computer games as both designed objects and player experiences. After presenting his core theoretical arguments and offering a general theory for understanding computer game ethics, Sicart offers case studies examining single-player games, multiplayer games, and online gameworlds from an ethical perspective. He explores issues raised by unethical content in computer games and its possible effect on players and offers a synthesis of design theory and ethics that could be used as both analytical tool and inspiration in the creation of ethical gameplay. (shrink)

The order of stages in a multistage game is often interpreted by looking at earlier stages as involving more long term decisions. For the purpose of making this interpretation precise, the notion of a delay supergame of a bounded multistage game is introduced. A multistage game is bounded if the length of play has an upper bound. A delay supergame is played over many periods. Decisions on all stages are made simultaneously, but with different delays until they (...) become effective. The earlier the stage the longer the delay. A subgame perfect equilibrium of a bounded multistage game generates a subgame perfect equilibrium in every one of its delay supergames. This is the first main conclusion of the paper. A subgame perfect equilibrium set is a set of subgame perfect equilibria all of which yield the same payoffs, not only in the game as a whole, but also in each of its subgames. The second xmain conclusion concerns multistage games with a unique subgame perfect equilibrium set and their delay supergames which are bounded in the sense that the number of periods is finite. If a bounded multistage game has a unique subgame perfect equilibrium set, then the same is true for every one of its bounded delay supergames. Finally the descriptive relevance of multistage game models and their subgame perfect equilibria is discussed in the light of the results obtained. (shrink)

As described in Benjamin Hale’s Introduction to “Philosophy Looks at Chess”: -/- “Deb Vossen asks whether chess can rightly be considered a game in the first place. She concludes, much to the surprise of many readers, that chess is not a game. Her evocative claim turns on a distinction between a game and the idea of a game, which evolved out of Bernard Suits’s phenomenally underappreciated work The Grasshopper: Games, Life and Utopia. She advances this position (...) by way of a technical argument that employs Suits’s discussion of “prelusory” goals and “lusory” attitudes. The word “lusory” generally means sporty or playful; and in Suits’s sense, it means that when we engage in the play of chess, we must enter the lusory attitude. She uses the notion of a prelusory goal to argue that such goals exist in a game (in this case, a game of chess) but not at all in the idea of the game (in the idea of chess).”. (shrink)

Besides its intrinsic interest, the definition of ‘game’ is important for three reasons. Firstly, in Wittgenstein's Philosophical Investigations ‘game’ is the paradigm family resemblance concept. If he is wrong in thinking that ‘game’ cannot be defined, then the persuasive force of his argument against definition generally will be considerably weakened. This, in its turn, will have important consequences for our understanding of concepts and philosophical method. Secondly, Wittgenstein's later writings are full of analogies drawn from games—chess alone (...) is mentioned scores of times—and a proper understanding of ‘game’ can lead us to exercise more caution when considering the parallels between games and non-games. Thirdly, games and play are intriguingly and closely related to art and ritual, and an analysis of games can throw considerable light on both of the latter. (shrink)

Typical applications of Hintikka’s game-theoretical semantics give rise to semantic attributes—truth, falsity—expressible in the $\Sigma^{1}_{1}$-fragment of second-order logic. Actually a much more general notion of semantic attribute is motivated by strategic considerations. When identifying such a generalization, the notion of classical negation plays a crucial role. We study two languages, $L_{1}$ and $L_{2}$, in both of which two negation signs are available: $\rightharpoondown $ and $\sim$. The latter is the usual GTS negation which transposes the players’ roles, while (...) the former will be interpreted via the notion of mode. Logic $L_{1}$ extends independence-friendly logic; $\rightharpoondown $ behaves as classical negation in $L_{1}$. Logic $L_{2}$ extends $L_{1}$, and it is shown to capture the $\Sigma^{2}_{1}$-fragment of third-order logic. Consequently the classical negation remains inexpressible in $L_{2}$. (shrink)

Twenty-two experienced action video-game players (AVGPs) and 18 non-VGPs were tested on a pen-and-paper line bisection task that was untimed. Typically, right-handers bisect lines 2 % to the left of true centre, a bias thought to reflect the dominance of the right-hemisphere for visuospatial attention. Expertise may affect this bias, with expert musicians showing no bias in line bisection performance. Our results show that experienced-AVGPs also bisect lines with no bias with their right hand and a significantly reduced bias (...) with their left hand compared to non-AVGPs. Bisections by experienced-AVGPs were also more precise than those of non-AVGPs. These findings show the cognitive proficiencies of experienced-AVGPs can generalize beyond computer based tasks, which resemble their training environment. (shrink)

In this paper, I engage the debate on Suits’ theory of games by providing a Kantian view of Utopia. I argue that although the Kantian aspects of Suits’ approach are often overlooked in comparison to its Socratic-Platonic aspects, Kant’s ideas play a fundamental role in Suits’ proposal. In particular, Kant’s concept of ‘regulative idea’ is the basis of Suits’ Utopia. I regard Utopia as Suits’ regulative idea on game playing. In doing so, I take Utopia to play a (...) double role in Suits’ theory of games. First, it highlights the primary condition of possibility of game-playing, namely, the lusory attitude. Second, it provides a normative criterion that serves as a critical principle to evaluate instances of game playing and as a counterfactual assumption that makes game playing possible. I provide further support for my Kantian interpretation of Suits’ Utopia by bringing to light the anthropological assumptions upon which Utopia is built. In doing so, I argue that both Suits’ theory of games, in general, and his Utopia, in particular, lay out the conditions of possibility of game playing, not an analysis on the life most worth living. (shrink)

This paper reports laboratory data for games that are played only once. These games span the standard categories: static and dynamic games with complete and incomplete information. For each game, the treasure is a treatment in which behavior conforms nicely to predictions of the Nash equilibrium or relevant refinement. In each case, however, a change in the payoff structure produces a large inconsistency between theoretical predictions and observed behavior. These contradictions are generally consistent with simple intuition based on the (...) interaction of payoff asymmetries and noisy introspection about others’ decisions. (shrink)

AbstractCorruption is one of the most intractable problems that the world is faced with and its reported impact is widespread and pervasive. Since the mid-1990s, international efforts to combat this problem expanded significantly, driven by the involvement governments, international financial institutions and non-governmental organisations. The objective of this article is to use Michel Foucault’s work in a critical analysis of the international fight against corruption. This analysis is centred on Foucault’s concept of governmentality, as well as his notions of knowledge, (...) power and ethics. The primary focus is on the role played by the World Bank, the International Monetary Fund and Transparency International in the proliferation of international anti-corruption discourse and practices. Furthermore, South Africa will be used as a case study to unpack the historical and contextual factors that play a role in the legitimisation of corruption. As will be shown in this assessment, without adequately understanding the local factors that stimulate corruption and the other societal characteristics that serve to compound its pervasiveness, internationally driven anti-corruption initiatives have limited scope for success. Corruption will persist where there is a lack of resonance between international anti-corruption ideals and local norms, values and ideologies. (shrink)

Schmidt’s game and other similar intersection games have played an important role in recent years in applications to number theory, dynamics, and Diophantine approximation theory. These games are real games, that is, games in which the players make moves from a complete separable metric space. The determinacy of these games trivially follows from the axiom of determinacy for real games, $\mathsf {AD}_{\mathbb R}$, which is a much stronger axiom than that asserting all integer games are determined, $\mathsf {AD}$. One (...) of our main results is a general theorem which under the hypothesis $\mathsf {AD}$ implies the determinacy of intersection games which have a property allowing strategies to be simplified. In particular, we show that Schmidt’s $(\alpha,\beta,\rho )$ game on $\mathbb R$ is determined from $\mathsf {AD}$ alone, but on $\mathbb R^n$ for $n \geq 3$ we show that $\mathsf {AD}$ does not imply the determinacy of this game. We then give an application of simple strategies and prove that the winning player in Schmidt’s $(\alpha, \beta, \rho )$ game on $\mathbb {R}$ has a winning positional strategy, without appealing to the axiom of choice. We also prove several other results specifically related to the determinacy of Schmidt’s game. These results highlight the obstacles in obtaining the determinacy of Schmidt’s game from $\mathsf {AD}$. (shrink)

This paper introduces a new Ehrenfeucht-Fraïssé type game that is played on two classes of models rather than just two models. This game extends and generalizes the known Ajtai-Fagin game to the case when there are several alternating moves played in different models. The game allows Duplicator to delay her choices of the models till the very end of the game, making it easier for her to win. This adds on the toolkit of winning strategies (...) for Duplicator in Ehrenfeucht-Fraïssé type games and opens up new methods for tackling some open problems in descriptive complexity theory. As an application of the class game, it is shown that, if m is a power of a prime, then first order logic augmented with function quantifiers F1n of arity 1 and height n < m can not express that the size of the model is divisible by m. This, together with some new expressibility results for Henkin quantifiers H1n gives some new separation results on the class of finite models among various F1n on one hand and between F1n and H1n on the other. Since function quantifiers involve a bounded type of second order existential quantifiers, the class game solves an open problem raised by Fagin, which asks for some inexpressibility result using a winning strategy by Duplicator in a game that involves more than one coloring round. (shrink)

We present an infinite-game characterization of the well-founded semantics for function-free logic programs with negation. Our game is a simple generalization of the standard game for negation-less logic programs introduced by van Emden [M.H. van Emden, Quantitative deduction and its fixpoint theory, Journal of Logic Programming 3 37–53] in which two players, the Believer and the Doubter, compete by trying to prove a query. The standard game is equivalent to the minimum Herbrand model semantics of logic (...) programming in the sense that a query succeeds in the minimum model semantics iff the Believer has a winning strategy for the game which begins with the Doubter doubting this query. The game for programs with negation that we propose follows the same rules as the standard one, except that the players swap roles every time the play “passes through” negation. We start our investigation by establishing the determinacy of the new game by using some classical tools from the theory of infinite-games. Our determinacy result immediately provides a novel and purely game-theoretic characterization of the semantics of negation in logic programming. We proceed to establish the connections of the game semantics to the existing semantic approaches for logic programming with negation. For this purpose, we first define a refined version of the game that uses degrees of winning and losing for the two players. We then demonstrate that this refined game corresponds exactly to the infinite-valued minimum model semantics of negation [P. Rondogiannis,W.W. Wadge, Minimum model semantics for logic programs with negation-as-failure, ACM Transactions on Computational Logic 6 441–467]. This immediately implies that the unrefined game is equivalent to the well-founded semantics. (shrink)

In the Nash demand game n players announce utility demands, the demands are implemented if they are jointly feasible, and otherwise no one gets anything. If the utilities set is the simplex, the game is called “divide-the-dollar”. Brams and Taylor studied variants of divide-the-dollar, on which they imposed reasonableness conditions. I explore the implications of these conditions on general NDGs. In any reasonable NDG, the egalitarian demand profile cannot be obtained via iterated elimination of weakly dominated strategies. (...) Further, a reasonable NDG may fail to have a Nash equilibrium, even in mixed strategies. In the 2-person case, existence of pure strategy equilibrium is equivalent to the existence of a value, in the sense that each player can secure the egalitarian payoff level independent of his opponent’s play. This result does not extend to reasonable NDGs with more than two players. Interestingly, there are results for reasonable NDGs that hold for two and three players, but not for n≥4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 4$$\end{document} players. (shrink)

While talking about sports (and games) we use such expressions as ?random victory?, ?winning by accident?, ?skill against luck?, ?chance (fortune) favours the better player?, etc. Unfortunately, chance-related notions that occur in these expressions are not well defined?their meaning is vague and it is not clear whether they refer to one or many different phenomena. Because such phenomena play an important role in sport, from the viewpoint of the philosophy of sport it is necessary to give a systematic account of (...) this topic. Although the works of De Wachter, Simon, Dixon, Breivik and Loland contain many important insights, there is still a room for further research in this field. The author tries to establish a typology of phenomena that could generally be called ?chance-phenomena?, which however, should be precisely distinguished. As such the primary task is to present an analysis of several different kinds of chance in sports. In constructing this typology the author uses both the distinction between different kinds of games (performative vs. kinetic) as well as analysis of structure of a game (four constitutive elements: players, constitutive rules, material substrate of the game and the world of the game). The most important method used is phenomenological analysis, especially Ingarden-style analysis. These kinds of ?chance-phenomena? are: aleatoriness, chaos, irregularity, imprecision and arbitrariness. The paradigm cases of each kind of chance are discussed. The genesis and functions of the respective phenomena in sports and games are also shown, as well as their position in the structure of the game. Such analytic work should precede any solutions of the chance vs. skill problem, or other problems concerning chance in sport. As a test of usefulness of the provided distinctions, the author considers the veracity of the judgements expressed in such sentences as ?Fortune favours the better player? (shrink)

In classical logic and rhetoric the strategies of argumentation known as topoi played a crucial role. Yet, topoi refer there to different kinds of strategies that this study intends to explain synoptically. Main focus will be on passages from Aristotle and Cicero. Indeed, these sources contain examples and theoretical considerations, which provide the basis for a general investigation of the complex phenomenon of topoi in the ancient world. Four main types of topoi will be juxtaposed and discusses comparatively as (...) a way to inspire historical reconstructions of the system of topoi, as well as modern theory formation on argumentation where topoi still receive much attention. (shrink)

The work under consideration attempts to discover a definition of game such as may serve as a foundation for a philosophical theory of games. It incorporates material from papers earlier published in Philosophy of Science, Ethics and in Osterhoudt's Philosophy of Sport. The exposition consists in the defense of a proposed definition against an array of criticisms until, after considerable exploration, a revised definition is arrived at to which no further objection is made. The author assures unity of form (...) and content by presenting the material in the manner of a philosophical dialogue and then by embellishing the dialogue with genial language and charming examples. As a result, it is clear that the search for a definition of game is meant to be a case that falls under the eventual definiendum. Although this work not only counters the Wittgensteinian proscription against definitions but does so relative to just that example by which Wittgenstein intended to show that the search for definitions is futile, the author cautions in the Preface that it was not his objective to write an "anti-anti-definitional manifesto." Yet engaging as this study is, the definition in which it culminates will neither dissuade the Wittgensteinians nor fully convince those more sympathetic with its aims, for the treatment of such topics as make-believe games and "Bernean" games seems less than conclusive, and the definition's implications may be problematical for questions such as, e.g., whether love-making is to be construed as a game and whether activities governed by Robert's rules of order qualify as games. The last chapter's metaphysical excursus on games, work, and life departs from the earlier playfulness, and the author's contention that ultimately it is games that make life worthwhile gives this study a serious character that goes beyond that customarily associated with a search for a definition. This study has value both for the specialist working in the philosophical theory of games and for the teacher seeking a text that will expose students to careful philosophical reasoning, analytical and critical skills, and the methodologies of counter-example and mental experiment, and do so in an imaginative and appealing way.--J.K. (shrink)

This paper explores the role the Panhellenic centers played in facilitating the circulation of wisdom in ancient Greece. It argues that there are substantial thematic overlaps among practitioners of wisdom , who are typically understood as belonging to different categories . By focusing on the presence of σοφοί at the Panhellenic centers in general, and Delphi in particular, we can acquire a more accurate picture of the particular expertise they possessed, and of the range of meanings the Greeks attributed (...) to the word σοφία. This approach seeks to challenge the conventional categories of modern scholarship and to offer a broader and more inclusive interpretive framework in its stead. One such thematic overlap is the way in which many σοφοί are described as exerting an almost uncanny, yet highly conventional ability to attract listeners and enchant them with their verbal performances. There is plenty of material to support the view that σοφοό, through tapping into the repository of σοφία that Delphi constituted and by aligning themselves with its authority, were seen as themselves being a conduit for a similar type of charismatic speech. (shrink)

Recent debate by feminist scholars in philosophy of sport has been focused on the status of women’s sport as a protected category. Positions have varied significantly, from no need for a protected category anymore—to allow women’s sport to flourish and to give them a fair opportunity, given that men’s sport still dominates, just as it has in the past.It will be argued that: i) the concept of a ‘protected category’ is tied logically to the concept of fair play and has (...) been defined and enforced through the rules in sport and generally requires some kind of certification for inclusion. These specific rules will be analyzed in detail. Having separate women’s events means that logically it must be possible to exclude, and exclusion is not a popular stance as many have argued that the onus is on inclusion from a human rights perspective. Thus, sport policy makers are truly in an intractable position. On the one hand, no qualifying athlete should have to ‘dope down’ (or ‘dope up’) to compete in the Olympic Games. On the other hand, women athletes have argued that sex equality in competitive sport is a legitimate goal and that separating athletes in competition by biological sex traits is the only way to achieve this goal. It seems criminal to ask athletes to ‘dope down’ to be able to compete in the Olympic Games, however, although a new auxiliary rule creating new sub-classification of women athletes with testosterone higher than the stipulated cut off seems logical on the face of it, these cases are statistically rare. It is concluded that the community of women athletes should have the most significant voice, as historically, the criteria for the women’s sport-protected category have been predominantly determined by men. That is not to say that men’s voices, or voices outside of the women’s sports community of practitioners, cannot be heard, but they should not be the deciding factor. (shrink)

Biologists and philosophers of biology have argued that learning rules that do not lead organisms to play evolutionarily stable strategies (ESSes) in games will not be stable and thus not evolutionarily successful. This claim, however, stands at odds with the fact that learning generalization---a behavior that cannot lead to ESSes when modeled in games---is observed throughout the animal kingdom. In this paper, I use learning generalization to illustrate how previous analyses of the evolution of learning have gone wrong. It has (...) been widely argued that the function of learning generalization is to allow for swift learning about novel stimuli. I show that in evolutionary game theoretic models learning generalization, despite leading to suboptimal behavior, can indeed speed learning. I further observe that previous analyses of the evolution of learning ignored the short term success of learning rules. If one drops this assumption, I argue, it can be shown that learning generalization will be expected to evolve in these models. I also use this analysis to show how ESS methodology can be misleading, and to reject previous justifications about ESS play derived from analyses of learning. (shrink)