Externality games are studied in Grafe et al. (1998, Math. Methods Op. Res. 48, 71). We define a generalization of this class of games and show, using the methodology in Izquierdo and Rafels (1996, 2001, Working paper, Univ Barcelona; Games Econ. Behav. 36, 174), some properties of the new class of generalized externality games. They include, among others, the algebraic structure of the game, convexity, and their implications for the study of cooperative solutions. (...) Also the proportional rule is characterized for this class of games. (shrink)

Ethics in video gaming is broad topic that extends beyond the familiar instances of “moral panics”. This chapter will first divide ethical issues into internal and external moral questions. Roughly, this equates to a distinction between the ethics in games and the ethics of games. The ethical issues internal to video games arise due to both their status as fictions and their status as games. Many games afford players the opportunity to perform violent and vicious (...) acts; however, these are of course fictional actions and are often contextualized as part of the game’s competitive play. This raises the general question whether it can ever be morally wrong to perform some fictional action in a video game. To approach this question, this section will first consider how moral values are inherent within games. Players engage with the embedded moral values of games both at the level of their narratives and their rules. Games become objects for moral reflection, not only through the stories that they tell, but also through the ways in which players are invited to engage actively with those stories. Next, external ethical issues are those that focus on the nature of the gaming industry and gaming cultures. The gaming industry has notoriously struggled with representations of gender and race, both in their workforce and in the games that they produce. Turning to the ecological impacts, the gaming industry is a major source of e-waste through the production of gaming technologies. The hardware used in gaming has a lifecycle that begins with the exploitation of resource-rich developing countries that produce the precious materials used in computer screens and processing chips and ends with those same products being dumped in toxic landfills in other developing countries. Additionally, gaming is a major source of energy consumption, particularly as cloud gaming servers are required to run continuously. When considering the ethics of games, such social and ecological concerns must surely figure in one’s moral calculation. Finally, some moral issues straddle the line between the above distinction between internal and external due to the porous nature of virtual interactivity, particularly regarding multiplayer games. Various gaming cultures struggle with their own ethical issues—from the failure to promote sportsmanship in e-sports to the widespread harassment of players in online platforms. This final section will briefly consider problems with multiplayer games, harassment, and trolling. (shrink)

In this paper, I first introduce the main motivations for the internalism/externalism dichotomy in epistemology and explore different accounts of epistemic justification, mostly externalist, arising from Dretske’s relevant alternatives theory of knowledge, namely the reliabilism of Goldman and Nozick, the contextualism of Cohen and DeRose, which is governed by fallibilist standards, and Lewis’ version of contextualism, to which infallibilist standards apply. I then argue that Wittgenstein critically anticipates many of these strategies and tries to avoid such a dichotomy by assuming (...) a form of infallibilism which is neither internal nor external. After introducing the idea of a Wittgensteinian hinge epistemology and how it responds to the problem of epistemic justification and to the particular challenge posed by radical scepticism, I defend the view that infallibility is logically unavoidable when we realize that we are always trapped in one language-game or another, even if we constantly switch between language-games. (shrink)

Game theorists assume that rational defensibility is a necessary condition for moral, social, or political justification. By itself, this is a fairly uncontroversial claim; most moral or political philosophers would agree. And yet game theorists tend to be advocates of the free market. External critics of game theory usually claim this is because game theorists assume that individuals are atomistic and self-interested. Game theorists themselves deny this, however, for what strike us as good reasons. In principle, game theory has no (...) necessary ties to right-wing distribution schemes. Why, then, is game theory almost exclusively the province of conservative philosophers, political scientists, and economists? The problem, we believe, lies in the theory of rational choice standardly employed by game theory. Even if we accept, for the purposes of argument, game theory's account of the justification of moral dispositions — that a disposition is morally justified if and only if, in its absence, it would be game theoretically rational to acquire it — we need not be led to right-wing solutions. If we expand the kinds of choices facing individuals to include choices about what we will call ‘institutional roles,’ then we can explain the game theoretic rationality of the kinds of emotions and behavior exemplified by duty, loyalty, and love. (shrink)

Pedagogical description and reflection upon an activity focusing on the use of a questioning game to display epistemological uncertainty and the impact of a possible Cartesian evil demon on the game’s players’ ability to come to have knowledge.

Summary The presentation will proceed as follows: (§ 3:) For the truth of an affirmative present‐tensed proposition Boethius required that its terms have actual referents, he would not accept any uninstantiated essence as a verifier. He also denied that any proposition about corruptible beings can be strictly necessary. He thus had a problem explaining how a theorem of one of the natural sciences differs from an ordinary contingent proposition. His rejection of uninstantiated essences also (§ 4) raised the question how (...) words can stay significant independently of the existence of referents, and more generally, to which degree language mirrors external reality. After a sketch of his solution to the semantic problems, § 5 returns to the question about scientific propositions. It is claimed that the core of Boethius' solution is a substitution of causal relationships for ordinary things (existents or essences) as an answer to the question what scientific knowledge is knowledge of and what scientific propositions are about. Since (§ 6) to Boethius axiomatized geometry provided the model for all sciences, consistency of a science's set of theorems should be important for him. A preoccupation with consistency can be seen in the rules he lays down for the dialogical game of “obligation” that was used as an academic exercise. An analysis (§ 7) of his description of another such game, the dialectical disputation, shows that he operated with a notion of truth‐within‐a‐game (requiring only conformity with the rules) as as opposed to absolute truth. § 8 claims that Boethius operated with a similar notion of truth‐within‐a‐science as opposed to absolute truth, and that his reason for so doing was the inaccessibility to human minds of the totality of causes. Doing science, then, (§ 9) is much like participating in a scholastic disputational game, and there may be scientifically‐true theorems conflicting with absolute truth known through revelation. § 10 epilogizes about Boethius' views about the highest good. (shrink)

In strategic situations, agents base actions on knowledge and beliefs. This includes knowledge about others’ strategies and preferences over strategy profiles, but also about other external factors. Bernheim and Pearce in 1984 independently defined the game theoretic solution concept of rationalizability, which is built on the premise that rational agents will only take actions that are the best response to some situation that they consider possible. This accounts for other agents’ rationality as well, limiting the strategies to which a particular (...) agent must respond, enabling further elimination until the strategies stabilize. We seek to generalize rationalizability to account not only for actions, but knowledge of the world as well. This will enable us to examine the interplay between action based and knowledge based rationality. We give an account of what it means for an action to be rational relative to a particular state of affairs, and in turn relative to a state of knowledge. We present a class of games, Epistemic Messaging Games, with a communication stage that clarifies the epistemic state among the players prior to the players’ actions. We use a history based model, which frames individual knowledge in terms of local projections of a global history. With this framework, we give an account of rationalizability for subclasses of EMG. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Richard Shusterman T. S. ELIOT ON READING: PLEASURE, GAMES, AND WISDOM Eliot frequently speaks of poetry as essentially a game or amusement whose first and foremost function is to give pleasure. "The poet," says Eliot, "would like to be something of a popular entertainer... would like to convey die pleasures ofpoetry.... As things are, and as fundamentally they must always be, poetry is not a career but a (...) mug's game" (TUPTUC, p. 154). ' Surely much ofthe point and appeal ofthese remarks is their deflationary contrast to the overlofty claims made for poetry since romanticism, claims which continue to be heard in Arnold's ideas of poetry as criticism of life and surrogate of religion and which extend to modernism with Richards's claim that "poetry is capable of saving us." In mordant debunking of the poet's putative status as world legislator, prophet, and savior, Eliot says he would be pleased to secure for the poet "a part to play in society as worthy as that of the music hall comedian." But Eliot's idea of poetry as an amusement or game is much more than an ironic rhetorical ploy against romantic attitudes. It contains a positive and complex view of what poetry is and how it satisfies. Eliot wants to remind us of "that simple truth that literature is primarily literature, a means of refined and intellectual pleasure."2 However, he also realizes that this truth is really not all that simple to understand or elucidate properly; for it does not mean (though it might seem to suggest ) that literature is a mere means to obtain some external end of pleasure. Nor does it mean that in aiming essentially at pleasure, literature is confined to satisfying our sensual or emotional faculties, and is 2 Philosophy and Literature therefore not significandy connected with improving thought or communicating wisdom, for the pleasure is described as intellectual pleasure. Because of the likely misunderstandings that it is apt to provoke, Eliot's claim that literature is a refined game, that "poetry is a superior amusement," is not confidendy offered as an adequately "true definition, but because if you call it something else, you are likely to call it something still more false" (SW, p. ix). But what substance or value is there in Eliot's preferred view? The idea of poetry as a superior game or amusement is developed in many ways throughout the Eliot critical corpus. We cannot consider them all, but the first we should consider concerns the character of pleasure or enjoyment derived from poetry. If poetry is a refined game, and since games are activities, the pleasure (enjoyment) of poetry would be that ofan activity rather than that ofa pleasant sensation. Eliot's idea of poetic pleasure is thus fundamentally Aristotelian.3 Such pleasure is not a separate sensation or pleasant feeling external to and identifiable apart from the game played, but rather represents the attendant zest or satisfaction with which the game is played or the activity pursued. For Aristotle, "pleasure completes the activity" by the dual and reciprocal action of making it more rewarding and thus promoting it. Our pleasure intensifies our interest in the activity which makes us better pursue it, while displeasure conversely impedes it, as does submitting to the alien pleasures from other activities. If the pleasures of different activities can conflict and impede their respective activities, then these pleasures must be distinguishable and are so in terms of the activities to which they attend. Our enjoyment of an activity thus logically depends on the constitutive structure of that activity and is inseparable from it. We therefore distinguish the pleasures of different games by the different game-activities to which they are bound. One may enjoy tennis, cricket, and football and perhaps feel similar pleasurable sensations from each. But the enjoyment of each game is clearly distinguishable and understood not in terms of these sensations but in terms of the different activities which constitute the formal object or ground of that pleasure. Different games or, more generally, different activities are differendy enjoyable, and each has what Aristotle calls its own "proper pleasure." One could not get the pleasure of playing tennis from playing... (shrink)

An intelligent machine surpassing human intelligence across a wide set of skills has been proposed as a possible existential catastrophe. Among those concerned about existential risk related to artificial intelligence, it is common to assume that AI will not only be very intelligent, but also be a general agent. This article explores the characteristics of machine agency, and what it would mean for a machine to become a general agent. In particular, it does so by articulating some important differences between (...) belief and desire in the context of machine agency. One such difference is that while an agent can by itself acquire new beliefs through learning, desires need to be derived from preexisting desires or acquired with the help of an external influence. Such influence could be a human programmer or natural selection. We argue that to become a general agent, a machine needs productive desires, or desires that can direct behavior across multiple contexts. However, productive desires cannot sui generis be derived from non-productive desires. Thus, even though general agency in AI could in principle be created by human agents, general agency cannot be spontaneously produced by a non-general AI agent through an endogenous process. In conclusion, we argue that a common AI scenario, where general agency suddenly emerges in a non-general agent AI, such as DeepMind’s superintelligent board game AI AlphaZero, is not plausible. (shrink)

First-order logic is known to have a severely limited expressive power on finite structures. As a result, several different extensions have been investigated, including fragments of second-order logic, fixpoint logic, and the infinitary logic L∞ωω in which every formula has only a finite number of variables. In this paper, we study generalized quantifiers in the realm of finite structures and combine them with the infinitary logic L∞ωω to obtain the logics L∞ωω, where Q = {Qi: iε I} is a (...) family of generalized quantifiers on finite structures. Using the logics L∞ωω, we can express polynomial-time properties that are not definable in L∞ωω, such as “there is an even number of x” and “there exists at least n/2 x” , without going to second-order logic. We show that equivalence of finite structures relative to L∞ωω can be characterized in terms of certain pebble games that are a variant of the Ehrenfeucht—Fraïssé games. We combine this game-theoretic characterization with sophisticated combinatorial tools from Ramsey theory, such as van der Waerden's Theorem and Folkman's Theorem, in order to investigate the scope and limits of generalized quantifiers in finite model theory. We obtain sharp lower bounds for expressibility in the logics L∞ωω and discover an intrinsic difference between adding finitely many simple unary generalized quantifiers to L∞ωω adding infinitely many. In particular, we show that if Qis a finite sequence of simple unary generalized quantifiers, then the equicardinality, or Härtig, quantifier is not definable in L∞ωω. We also show that the query “does the equivalence relation E have an even number of equivalence classes” is not definable in the extension L∞ωω of L∞ωω by the Härtig quantifier I and any finite sequence Q of simple unary generalized quantifiers. (shrink)

Motivated by aspects of reasoning in theories of physics, Robin Giles defined a characterization of infinite valued Łukasiewicz logic in terms of a game that combines Lorenzen-style dialogue rules for logical connectives with a scheme for betting on results of dispersive experiments for evaluating atomic propositions. We analyze this game and provide conditions on payoff functions that allow us to extract many-valued truth functions from dialogue rules of a quite general form. Besides finite and infinite valued Łukasiewicz logics, also Meyer (...) and Slaney’s Abelian logic and Cancellative Hoop Logic turn out to be characterizable in this manner. (shrink)

This article discusses the set of Harsanyi payoff vectors of a cooperative TU-game, also known as the Selectope. We reconsider some results on Harsanyi payoff vectors within a more general framework. First, an intuitive approach is used, showing that the set of Harsanyi payoff vectors is the core of an associated convex game. Next, the set of individual rational Harsanyi payoff vectors, the Harsanyi imputations in short, is considered. Existence conditions are provided, and if non-empty, we provide a description as (...) the core of a well-defined convex game, and show that it is an externally stable set. (shrink)

We give a new characterization of the hyperarithmetic sets: a set X of integers is recursive in e α if and only if there is a Turing machine which computes X and "halts" in less than or equal to the ordinal number ω α of steps. This result represents a generalization of the well-known "limit lemma" due to J. R. Shoenfield [Sho-1] and later independently by H. Putnam [Pu] and independently by E. M. Gold [Go]. As an application of this (...) result, we give a recursion theoretic analysis of clopen determinacy: there is a correlation given between the height α of a well-founded tree corresponding to a clopen game $A \subseteq \omega^\omega$ and the Turing degree of a winning strategy f for one of the players--roughly, f can be chosen to be recursive in 0 α and this is the best possible (see § 4 for precise results). (shrink)

In this paper I present a game-theoretical approach to the problem of induction. I investigate the comparative success of prediction methods by mathematical analysis and computer programming. Hume's problem lies in the fact that although the success of object-inductive prediction strategies is quite robust, they cannot be universally optimal. My proposal towards a solution of the problem of induction is meta-induction. I show that there exist meta-inductive prediction strategies whose success is universally optimal, modulo short-run losses which are upper-bounded. I (...) then turn to the implications of my approach for the evolution of cognition. In the final section I suggest a revision of the paradigm of bounded rationality by introducing the distinction between local, general and universal prediction strategies. (shrink)

Load monitoring in basketball is fundamental to develop training programs, maximizing performance while reducing injury risk. However, information regarding the load associated with specific activity patterns during competition is limited. This study aimed at assessing the external load associated with high-intensity activities recorded during official basketball games, with respect to different activity patterns, playing positions, and activities performed with or without ball. Eleven male basketball players competing in the Lithuanian third division were recruited for this study. Three in-season (...) class='Hi'>games were assessed via time-motion analysis and microsensors. Specifically, the high-intensity activities including sprints, high-intensity specific movements and jumps were identified and subsequently the external load [PlayerLoad™ and PlayerLoad™/min ] of each activity was determined. Linear mixed models were used to examine differences in PL, PL/min and mean duration between activity pattern, playing positions and activities performed with or without ball. Results revealed PL was lower in jumps compared to sprints [p < 0.001, effect size = 0.68] and HSMs, while PL/min was greater in sprints compared to jumps. Jumps displayed shorter duration compared to sprints and HSMs, with HSMs lasting longer than sprints. Jumps duration was longer in backcourt than frontcourt players. When considering activity patterns combined, PL and duration were greater without ball. Regarding HSMs, PL/min was higher with ball, while duration was longer without ball. The current findings suggest that external load differences in high-intensity activities exist among activity patterns and between activities performed with and without ball, while no differences were found between playing positions. Practitioners should consider these differences when designing training sessions. (shrink)

Internet services, such as review sites, FAQ sites, online auction sites, online flea markets, and social networking services, are essential to our daily lives. Each Internet service aims to promote information exchange among people who share common interests, activities, or goods. Internet service providers aim to have users of their services actively communicate through their services. Without active interaction, the service falls into disuse. In this study, we consider that an Internet service has a network externality as its main (...) feature, and we model user behavior in the Internet service with network externality as a dynamic game. In particular, we model the diffusion process of users of an ISNE as an infinite-horizon extensive-form game of complete information in which: each user can choose whether or not to use the ISNE in her/his turn and the network effect of the ISNE depends on the history of each player’s actions. We then apply Markov perfect equilibrium to analyze how to increase the number of active users. We derive the necessary and sufficient condition under which the state in which every player is an active user is the unique Markov perfect equilibrium outcome. Moreover, we propose an incentive mechanism that enables the number of active users to increase steadily. (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)

First of all I would like to describe inductive and abductive reasoning in the light of the agent–based framework to the aim of clarifying their fallacious character and the role of the so-called ideal systems (logical and computational). Then I will analyze some inductive and abductive types of reasoning that in the perspective of classical and informal logic are defined fallacies. I will describe how in an agent-based reasoning this kind of fallacious reasoning can in some cases be redefined and (...) considered as a good way of reasoning. Finally, I will illustrate how what I call manipulative abduction can be interpreted as a form of practical reasoning a better understanding of which can furnish a description of human beings as hybrid reasoners in so far they are users of ideal and computational agents. (shrink)

The paper has a twofold aim. On the one hand, it provides what appears to be the first game-theoretic modeling of Napoleon’s last campaign, which ended dramatically on 18 June 1815 at Waterloo. It is specifically concerned with the decision Napoleon made on 17 June 1815 to detach part of his army against the Prussians he had defeated, though not destroyed, on 16 June at Ligny. Military historians agree that this decision was crucial but disagree about whether it was rational. (...) Hypothesizing a zero-sum game between Napoleon and Blücher, and computing its solution, we show that it could have been a cautious strategy on the former's part to divide his army, a conclusion which runs counter to the charges of misjudgement commonly heard since Clausewitz. On the other hand, the paper addresses methodological issues. We defend its case study against the objections of irrelevance that have been raised elsewhere against “analytic narratives”, and conclude that military campaigns provide an opportunity for successful application of the formal theories of rational choice. Generalizing the argument, we finally investigate the conflict between narrative accounts – the historians' standard mode of expression – and mathematical modeling. (shrink)

In this paper we study the distribution of power in the Basque Parliament since the restoration of the Spanish democracy. The classic simple games do not fit with the particular voting rule that it is used to invest the president of the regional government. In order to model this voting mechanism we incorporate coalitional externalities to the game. We use the extensions of the most popular power indices to games with externalities that have been proposed in the most (...) recent literature. Moreover, we propose a method to estimate the probability of a given coalition based on the ideological positions of its members in a two-dimensional political spectrum. (shrink)

The theory of competition has held a central place in economic analysis since Adam Smith. This book, written by one of the most distinguished of contemporary economic theorists, reports on a major research program to provide strategic foundations for the theory of perfect competition. Beginning with a concise survey of how the theory of competition has evolved, Gale makes extensive and rigorous use of dynamic matching and bargaining models to provide a more complete description of how a competitive equlibrium is (...) achieved. Whereas economists have made use of a macroscopic description of markets in which certain behavioral characteristics, such as price-taking behavior, are taken for granted, Gale uses game theory to re-evaluate this assumption, beginning with individual agents and modelling their strategic interaction. A strategic foundation for competitive equilibrium shows how such interaction leads to competitive, price-taking behavior. Essential reading for graduate courses in game theory and general equilibrium. (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)

Many weaknesses of game theory are cured by new models that embody simple cognitive principles, while maintaining the formalism and generality that makes game theory useful. Social preference models can generate team reasoning by combining reciprocation and correlated equilibrium. Models of limited iterated thinking explain data better than equilibrium models do; and they self-repair problems of implausibility and multiplicity of equilibria.

This article presents two theorems: a generalization of Löb’s Theorem that applies to formal proof systems operating with bounded computational resources, such as formal verification software or theorem provers, and a theorem on the robust cooperation of agents that employ proofs about one another’s source code as unexploitable criteria for cooperation. The latter illustrates a capacity for outperforming classical Nash equilibria and correlated equilibria, attaining mutually cooperative program equilibrium in the Prisoner’s Dilemma while remaining unexploitable, i.e., sometimes achieving the outcome, (...) and never receiving the outcome as player 1. (shrink)

We prove a number of results on the determinacy of σ-projective sets of reals, i.e., those belonging to the smallest pointclass containing the open sets and closed under complements, countable unions, and projections. We first prove the equivalence between σ-projective determinacy and the determinacy of certain classes of games of variable length <ω^2 (Theorem 2.4). We then give an elementary proof of the determinacy of σ-projective sets from optimal large-cardinal hypotheses (Theorem 4.4). Finally, we show how to generalize the (...) proof to obtain proofs of the determinacy of σ-projective games of a given countable length and of games with payoff in the smallest σ-algebra containing the projective sets, from corresponding assumptions (Theorem 5.1, Theorem 5.4). (shrink)

Climate change mitigation has become a paradigm case both for externalities in general and for the game-theoretic model of the Tragedy of the Commons (ToC) in particular. This situation is worrying, as we have reasons to suspect that some models in the social sciences are apt to be performative to the extent that they can become self-fulfilling prophecies. Framing climate change mitigation as a hardly solvable coordination problem may force us into a worse situation, by changing real-world behaviour to fit (...) our model, rather than the other way around. But while this problem of the performativity of the ToC has been noted in a recent paper in this journal by Matthew Kopec, his proposed strategies for dealing with their self-fulfilling nature fall short of providing an adequate solution. Instead of relying on the idea that modelling assumptions are always strictly speaking false, this paper shows that the problem may be better framed as a problem of underdetermination between competing explanations. Our goal here is to provide a framework for choosing between this set of competing models that allows us to avoid a ‘Russian Roulette’-like situation in which we gamble with existential risk. (shrink)

Inquisitive first-order logic, InqBQ, is a system which extends classical first-order logic with formulas expressing questions. From a mathematical point of view, formulas in this logic express properties of sets of relational structures. This paper makes two contributions to the study of this logic. First, we describe an Ehrenfeucht–Fraïssé game for InqBQ and show that it characterizes the distinguishing power of the logic. Second, we use the game to study cardinality quantifiers in the inquisitive setting. That is, we study what (...) statements and questions can be expressed in InqBQ about the number of individuals satisfying a given predicate. As special cases, we show that several variants of the question how many individuals satisfy α(x) are not expressible in InqBQ, both in the general case and in restriction to finite models. (shrink)

Games, which philosophers commonly invoke as models for diverse phenomena, are plausibly understood in terms of rules and goals, but this gives rise to two puzzles. The first concerns the identity of a single game over time. Intuitively one and the same game can undergo a change in rules, as when the rules of chess were modified so that a pawn could be moved two squares forward on its first move. Yet if games are individuated in terms of (...) their constitutive rules and goals, this is incoherent—new rules mean a new game. The second concerns the individuation of games at a point in time. Intuitively, there can be different versions of a single game, where the versions differ in the details of their rules. I offer a solution to this problem that draws on an analogy with individuating languages. The resulting theory should illuminate the metaphysics of games more generally. (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)

Wittgenstein used the notion of a language game to illustrate how language is interwoven with action. Here we consider how successful linguistic discourse of the sort he described might emerge in the context of a self-assembling evolutionary game. More specifically, we consider how discourse and coordinated action might self-assemble in the context of two generalized signaling games. The first game shows how prospective language users might learn to initiate meaningful discourse. The second shows how more subtle varieties of (...) discourse might co-emerge with a meaningful language. (shrink)

We define an evolutionary process of “economic Darwinism” for playing the field, symmetric games. The process captures two forces. One is “economic selection”: if current behavior leads to payoff differences, behavior yielding lowest payoff has strictly positive probability of being replaced by an arbitrary behavior. The other is “mutation”: any behavior has at any point in time a strictly positive, very small probability of shifting to an arbitrary behavior. We show that behavior observed frequently is in accordance with “evolutionary (...) equilibrium”, a static equilibrium concept suggested in the literature. Using this result, we demonstrate that generally under positive (negative) externalities, economic Darwinism implies even more under- (over-)activity than does Nash equilibrium. (shrink)

Martial-arts practice is not quite anything else: it is like sport, but is not sport; it constantly refers to and as it were cohabits with violence, but is not violent; it is dance-like but not dance. It shares a common athleticism with sports and dance, yet stands apart from both, especially through its paradoxical commitment to the external value of being an instrument of violence. My discussion seeks to illuminate martial arts practice by systematic contrast to games of sport (...) and works of performance art, especially dance. (shrink)

Let Mn♯ denote the minimal active iterable extender model which has n Woodin cardinals and contains all reals, if it exists, in which case we denote by Mn the class-sized model obtained by iterating the topmost measure of Mn class-many times. We characterize the sets of reals which are Σ1-definable from R over Mn, under the assumption that projective games on reals are determined:1. for even n, Σ1Mn=⅁RΠn+11;2. for odd n, Σ1Mn=⅁RΣn+11.This generalizes a theorem of Martin and Steel for (...) L, that is, the case n=0. As consequences of the proof, we see that determinacy of all projective games with moves in R is equivalent to the statement that Mn♯ exists for all n∈N, and that determinacy of all projective games of length ω2 with moves in N is equivalent to the statement that Mn♯ exists and satisfies AD for all n∈N. (shrink)

This article considers how a generalized signalling game may self-assemble as the saliences of the agents evolve by reinforcement on those sources of information that in fact lead to successful action. On the present account, generalized signalling games self-assemble even as the agents co-evolve meaningful representations and successful dispositions for using those representations. We will see how reinforcement on successful information sources also provides a mechanism whereby simpler games might compose to form more complex games. (...) Along the way, I consider how an old game might be appropriated to a new context by reinforcement on successful associations between old and new saliences. (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)

How can _Wii Sports_ teach us about metaphysics? Can playing _World of Warcraft_ lead to greater self-consciousness? How can we learn about aesthetics, ethics and divine attributes from _Zork_, _Grand Theft Auto_, and _Civilization_? A variety of increasingly sophisticated video games are rapidly overtaking books, films, and television as America's most popular form of media entertainment. It is estimated that by 2011 over 30 percent of US households will own a Wii console - about the same percentage that owned (...) a television in 1953. In _Philosophy Through Video Games, _Jon Cogburn and Mark Silcox - philosophers with game industry experience - investigate the aesthetic appeal of video games, their effect on our morals, the insights they give us into our understanding of perceptual knowledge, personal identity, artificial intelligence, and the very meaning of life itself, arguing that video games are popular precisely because they engage with longstanding philosophical problems. Topics covered include: * The Problem of the External World * Dualism and Personal Identity * Artificial and Human Intelligence in the Philosophy of Mind * The Idea of Interactive Art * The Moral Effects of Video Games * Games and God's Goodness Games discussed include: _Madden Football_, _Wii Sports_, _Guitar Hero_, _World of Warcraft_, _Sims Online_, _Second Life_, _Baldur's Gate_, _Knights of the Old Republic_, _Elder Scrolls_, _Zork_, _EverQuest_ _Doom_, _Halo 2_, _Grand Theft Auto_, _Civilization_, _Mortal Kombat_, _Rome: Total War_, _Black and White_, _Aidyn Chronicles_. (shrink)

The approach used by physics is based on the identification and study of ideal objects, which is also the basis of biophysics, in combination with von Neumann heuristic modeling and functional fractionation according to R.Rosen is discussed as a tool for studying the properties of consciousness. The object of the study is a kind of line of analog systems: the human brain, the vertebrate brain, the invertebrate brain and artificial neural networks capable of reflection, which is a key property characteristic (...) of consciousness. Reflection in the broad sense of the word, understood as an internal representation of the external world, is characteristic of a wide range of animals, and some of them (bumblebees, fish) even demonstrate reflection in the narrow sense of the word, understood as an inner self-representation. This complex behavior is realized by miniature brains of ~1 million neurons. The use of simple recurrent neural networks (RNNs) to obtain answers to general questions is illustrated. For example, it has been shown a small RNS is able to pass delayed matching to sample (DMTS) test, forming an individual dynamic representation of the received stimulus, allowing decoding by a special external neural detector.. It has been demonstrated in the reflexive game “even-odd”, the RNS has a huge advantage over a multi-layered neural network, with the same and a larger number of neurons – reflection defeats regression. It was found that the asymmetry of outcomes in the odd-even game, which was explained by various causes, including psychological ones – “it’s easier to catch up than to run away”, is reproduced in the game of two RNNs. Obviously, there are no psychological causes here and the advantage of the player playing for “even” is explained by the more complex strategy of the “odd” player – he needs to predict the opponent’s move and choose the opposite one. (shrink)

In any survey of recent developments in semantics, the game-theoretic approach to the semantics of both formal and of natural languages which has been developed by Jaakko Hintikka and his associates must loom large. It is indeed well known by this time that the semantics of the usual first-order logic can be spelled out in terms of games. What is not equally generally known is that this game-theoretical semantics can be augmented so as to apply also to natural languages (...) and not only to some of the artificial languages studied by logicians. The results already reached by Hintikka and his associates in this direction nevertheless show that many important phenomena of natural language can be handled in the game-theoretical framework. In this paper I shall first try to outline the basic ideas of the game-theoretical approach to semantics, then discuss briefly some problems which have so far been left untouched and thereby try to provide some new evidence for the naturalness and adequacy of a game-theoretical semantics. (shrink)

I offer two potential diagnoses of the behavioral norms governing post‐truth politics by comparing the view of language, communication, and truth‐telling put forward by David Lewis (extended by game theorists), and John Searle. My first goal is to specify the different ways in which Lewis, and game theorists more generally, in contrast to Searle (in the company of Paul Grice and Jurgen Habermas), go about explaining the normativity of truthfulness within a linguistic community. The main difference is that for Lewis (...) and game theorists, “truthful” signaling follows from an align- ment of interests, and deception follows from mixed motives leading to the calculation that sending false information is better for oneself. Following in the Enlightenment tradition, Searle argues that practical reasoning, which involves mastery of at least one language, requires that actors intend to communicate. This intention includes constraining the content of statements to uphold veracity conditions. After distinguishing between these two accounts, I will artic- ulate the implications for explaining, and even informing actions, constitutive of post‐truth politics. I argue that the strategic view of communication is suffi- cient neither to model everyday conversation nor to reflect a public sphere useful for democratic govern- ment. Both the pedagogy of strategic communication as cheap talk, and its concordance with new digital information technologies, challenge norms of truthful- ness that underlie modern institutions essential to an effective public sphere. (shrink)

In The Interface Envelope, James Ash develops a series of concepts to understand how digital interfaces work to shape the spatial and temporal perception of players. Drawing upon examples from videogame design and work from post-phenomenology, speculative realism, new materialism and media theory, Ash argues that interfaces create envelopes, or localised foldings of space time, around which bodily and perceptual capacities are organised for the explicit production of economic profit. Modifying and developing Bernard Stiegler's account of psychopower and Warren Neidich's (...) account of neuropower, Ash argues the aim of interface designers and publishers is the production of envelope power. Envelope power refers to the ways that interfaces in games are designed to increase users perceptual and habitual capacities to sense difference. Examining a range of examples from specific videogames, Ash identities a series of logics that are key to producing envelope power and shows how these logics have intensified over the last thirty years. In turn, Ash suggests that the logics of interface envelopes in videogames are spreading to other types of interface. In doing so life becomes enveloped as the environments people inhabit becoming increasingly loaded with digital interfaces. Rather than simply negative, Ash develops a series of responses to the potential problematics of interface envelopes and envelope power and emphasizes their pharmacological nature. (shrink)