We argue that pedagogic authority relies on love, which is misunderstood if seen as a matter of actions and subjects. Love is based not on finite subjects and objects existing in Euclidean space and linear time, but, rather, on the non-finite ontology, space and time of relations. Loving authority is a matter of calling and vocation, arising from the spontaneous and simultaneous call-and-response of a lively relation. We make this argument through a reading of Buber’s I–You relation and Murdoch’ (...) s account of the responsiveness of ascetic discipline. In presenting this analysis, we draw upon a case study from a research project on Australian teachers and students. (shrink)

We present a game semantics in the style of Lorenzen for Girard's linear logic . Lorenzen suggested that the meaning of a proposition should be specified by telling how to conduct a debate between a proponent P who asserts and an opponent O who denies . Thus propositions are interpreted as games, connectives as operations on games, and validity as existence of a winning strategy for P. We propose that the connectives of linear logic can be naturally (...) interpreted as the operations on games introduced for entirely different purposes by Blass . We show that affine logic, i.e., linear logic plus the rule of weakening, is sound for this interpretation. We also obtain a completeness theorem for the additive fragment of affine logic, but we show that completeness fails for the multiplicative fragment. On the other hand, for the multiplicative fragment, we obtain a simple characterization of game-semantical validity in terms of classical tautologies. An analysis of the failure of completeness for the multiplicative fragment leads to the conclusion that the game interpretation of the connective is weaker than the interpretation implicit in Girard's proof rules; we discuss the differences between the two interpretations and their relative advantages and disadvantages. Finally, we discuss how Gödel's Dialectica interpretation , which was connected to linear logic by de Paiva , fits with game semantics. (shrink)

We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cut-free proof net. A key role is played by the notion of history-free strategy; strong connections are made between history-free strategies and the Geometry of Interaction. (...) Our semantics incorporates a natural notion of polarity, leading to a refined treatment of the additives. We make comparisons with related work by Joyal, Blass, et al. (shrink)

In recent work, semantic games of independence-friendly logic were studied in strategic form in terms of Nash equilibria. The class of strategic games of independence-friendly logic is contained in the class of win-loss, zero-sum two-player games. In this note we draw on the theory of linear programming to develop tools to analyze the value of such games. We give two applications of these tools to independence-friendly logic under the so-called equilibrium semantics.

§ 1. Introduction. Perhaps the most surprising recent development in complexity theory is the discovery that the class NP can be characterized using a form of randomized proof checker that only examines a constant number of bits of the “proof” that a string is in a language [6, 5, 31, 3, 4]. More specifically, writing ∣x∣ for the length of a string x, a language L in the class NP of languages recognizable in Nondeterministic polynomial time is traditionally given by (...) a polynomial p and a polynomial-time predicate P such that a string x is in L iff there is some string y satisfying P, where ∣y∣ ≤ p. Intuitively, we can think of a string y as a possible proof that x ϵ L, with the predicate P some kind of proof checker that distinguishes good proofs from bad ones. A string x is therefore in a language L ϵ NP if there is a short proof that x ϵ L, and not in L otherwise. The surprising discovery is that the deterministic proof checker that reads the entire input and proof can be replaced by a probabilistic verifier that on input x and possible proof y, where y is presented in a certain way, flips at most O coins and reads at most a constant number of bits of x and y. Obviously, a probabilistic verifier that does not read the whole proof will sometimes make mistakes. However, the surprising and essentially non-intuitive mathematical fact is that for each language L in NP, it is possible to find a polynomial q and verifier V flipping a logarithmic number of coins and reading a constant number of bits such that, for any x ϵ L, there exists y with ∣y∣ ≤ q and with V accepting with probability 1 and, for x ∉ L, there is no y with ∣y∣ ≤ q and with V accepting with probability ≥ 1/4. This idea canalsobeextended to PSPACE [10, 9], using a game that alternates between two players instead of a proof presented by a “single player.”. (shrink)

We describe the constructive content of proofs in a fragment of propositional Infinitary Linear Logic in terms of strategies for a suitable class of games. Such strategies interpret linear proofs as parallel algorithms as long as the asymmetry of the connectives ? and ! allows it.

Linear Logic was introduced by Girard as a resource-sensitive refinement of classical logic. In this paper we establish strong connections between natural fragments of Linear Logic and a number of basic concepts related to different branches of Computer Science such as Concurrency Theory, Theory of Computations, Horn Programming and Game Theory. In particular, such complete correlations allow us to introduce several new semantics for Linear Logic and to clarify many results on the complexity of natural fragments (...) of Linear Logic. As a main corollary, any non-deterministic and concurrent computation is proved to be simulated directly within the framework of each of these systems. (shrink)

I present a semantics for the language of first-order additive-multiplicative linear logic, i.e. the language of classical first-order logic with two sorts of disjunction and conjunction. The semantics allows us to capture intuitions often associated with linear logic or constructivism such as sentences = games, SENTENCES = resources or sentences = problems, where “truth” means existence of an effective winning strategy.The paper introduces a decidable first-order logic ET in the above language and gives a proof of its soundness (...) and completeness with respect to this semantics. Allowing noneffective strategies in the latter is shown to lead to classical logic.The semantics presented here is very similar to Blass's game semantics. Although there is no straightforward reduction between the two corresponding notions of validity, my completeness proof can likely be adapted to the logic induced by Blass's semantics to show its decidability, which was the main problem left open in Blass's paper.The reader needs to be familiar with classical logic and arithmetic. (shrink)

Two structures A and B are n-equivalent if Player II has a winning strategy in the n-move Ehrenfeucht-Fraïssé game on A and B. In earlier articles we studied n-equivalence classes of ordinals and coloured ordinals. In this article we similarly treat a class of scattered order-types, focussing on monomials and sums of monomials in ω and its reverse ω*.

What is a game? What are we doing when we play a game? What is the value of playing games? Several different philosophical subdisciplines have attempted to answer these questions using very distinctive frameworks. Some have approached games as something like a text, deploying theoretical frameworks from the study of narrative, fiction, and rhetoric to interrogate games for their representational content. Others have approached games as artworks and asked questions about the authorship of games, about the ontology of (...) the work and its performance. Yet others, from the philosophy of sport, have focused on normative issues of fairness, rule application, and competition. The primary purpose of this article is to provide an overview of several different philosophical approaches to games and, hopefully, demonstrate the relevance and value of the different approaches to each other. Early academic attempts to cope with games tried to treat games as a subtype of narrative and to interpret games exactly as one might interpret a static, linear narrative. A faction of game studies, self-described as “ludologists,” argued that games were a substantially novel form and could not be treated with traditional tools for narrative analysis. In traditional narrative, an audience is told and interprets the story, where in a game, the player enacts and creates the story. Since that early debate, theorists have attempted to offer more nuanced accounts of how games might achieve similar ends to more traditional texts. For example, games might be seen as a novel type of fiction, which uses interactive techniques to achieve immersion in a fictional world. Alternately, games might be seen as a new way to represent causal systems, and so a new way to criticize social and political entities. Work from contemporary analytic philosophy of art has, on the other hand, asked questions whether games could be artworks and, if so, what kind. Much of this debate has concerned the precise nature of the artwork, and the relationship between the artist and the audience. Some have claimed that the audience is a cocreator of the artwork, and so games are a uniquely unfinished and cooperative art form. Others have claimed that, instead, the audience does not help create the artwork; rather, interacting with the artwork is how an audience member appreciates the artist's finished production. Other streams of work have focused less on the game as a text or work, and more on game play as a kind of activity. One common view is that game play occurs in a “magic circle.” Inside the magic circle, players take on new roles, follow different rules, and actions have different meanings. Actions inside the magic circle do not have their usual consequences for the rest of life. Enemies of the magic circle view have claimed that the view ignores the deep integration of game life from ordinary life and point to gambling, gold farming, and the status effects of sports. Philosophers of sport, on the other hand, have approached games with an entirely different framework. This has lead into investigations about the normative nature of games—what guides the applications of rules and how those rules might be applied, interpreted, or even changed. Furthermore, they have investigated games as social practices and as forms of life. (shrink)

Purpose of the article is to partially describe underpinning economics for the circular economy. A circular economy is an advancement from the linear economy which behaves according to the hierarchy of 6R, preferring reuse, remanufacture or recycle solutions insead of disposal. This new approach is a trigger of new business models seeking many times vor various kinds of support from the side of government. However, governmental support is not neither the only option nor the most functional one. Underpinning economics (...) for the circular economy can be based also at market-based tools. What we have in mind under this term for the purspose of this paper is the game in the market being played between buyers and sellers. Methodology: We have analyzed this interaction using game theory tool. The scietific goal of our paper was to suggest a quick market-based solution how to support circular economy business models whilst helping to the society to solve certain social problems. Our findings have led to a newly proposed way, how the current game in pricing could be changed. An emphasis shall be placed on strategies how to rise prices of linear economy products whilst offering wider social benefits to small sellers of such products. The price increase of linear economy products is considered in this paper as a market-based incentive to support recycled, remanufactured ones, whilst circular economy products are becoming more economically feasible in comparison with more expensive linear economy products. (shrink)

A previous work by Friedman et al. (Theory and Decision, 61:305–318, 2006) introduces the concept of a hierarchy of a simple voting game and characterizes which hierarchies, induced by the desirability relation, are achievable in linear games. In this paper, we consider the problem of determining all hierarchies, conserving the ordinal equivalence between the Shapley–Shubik and the Penrose–Banzhaf–Coleman power indices, achievable in simple games. It is proved that only four hierarchies are non-achievable in simple games. Moreover, it is (...) also proved that all achievable hierarchies are already obtainable in the class of weakly linear games. Our results prove that given an arbitrary complete pre-ordering defined on a finite set with more than five elements, it is possible to construct a simple game such that the pre-ordering induced by the Shapley–Shubik and the Penrose–Banzhaf–Coleman power indices coincides with the given pre-ordering. (shrink)

ABSTRACT At the beginning of the 13th century Fibonacci described the rules for making mixtures of all kinds, using the Hindu-Arabic system of arithmetic. His work was repeated in the early printed books of arithmetic, many of which contained chapters on ‘alligation', as the subject became known. But the rules were expressed in words, so the subject often appeared difficult, and occasionally mysterious. Some clarity began to appear when Thomas Harriot introduced a modern form of algebraic notation around 1600, and (...) he was almost certainly the first to express the basic rule of alligation in algebraic terms. Thus a link was forged with the work on Diophantine problems that occupied mathematicians like John Pell and John Kersey in the 17th century. Joseph Fourier's work on mechanics led him to suggest a procedure for handling linear inequalities based on a combination of logic and algebra; he also introduced the idea of describing the set of feasible solutions geometrically. In 1898, inspired by Fourier’s work, Gyula Farkas proved a fundamental theorem about systems of linear inequalities. This topic eventually found many applications, and it became known as Linear Programming. The theorem of Farkas also plays a significant role in Game Theory. (shrink)

A statement of hyperarithmetic analysis is a sentence of second order arithmetic S such that for every Y⊆ω, the minimum ω-model containing Y of RCA0 + S is HYP, the ω-model consisting of the sets hyperarithmetic in Y. We provide an example of a mathematical theorem which is a statement of hyperarithmetic analysis. This statement, that we call INDEC, is due to Jullien [13]. To the author's knowledge, no other already published, purely mathematical statement has been found with this property (...) until now. We also prove that, over RCA0, INDEC is implied by [Formula: see text] and implies ACA0, but of course, neither ACA0, nor ACA 0+ imply it. We introduce five other statements of hyperarithmetic analysis and study the relations among them. Four of them are related to finitely-terminating games. The fifth one, related to iterations of the Turing jump, is strictly weaker than all the other statements that we study in this paper, as we prove using Steel's method of forcing with tagged trees. (shrink)

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 study an extension of Stackelberg’s model in which many firms can produce at many different times. Demand is affine, while cost is linear. In this setting, we investigate whether Stackelberg’s results in a two-firm game are robust when the number of firms increases. We show that firms may not need to anticipate further entries, leaders might earn less than in the simultaneous game, and, whatever its cost and its time of entry, the firm’s entry always improves (...) welfare. (shrink)

A comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game theory (...) and going on to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics. (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.

We re-express a previous general result in a way which seems easier to remember, using the terminology of infinite games. We show how this can be applied to construct recursive linear orderings, showing, for example, that if there is a ▵ 0 2β + 1 linear ordering of type τ, then there is a recursive ordering of type ω β · τ.

In this paper, we study the structural optimization of community governance in smart cities and optimize the structure based on the game analysis of dynamic planning evolution. Theoretically, the connotation and extension of the concept of “self-organization” are cleared, and the environment and conditions of community self-organization formation, the formation process of community self-organization, and the types of community self-organization are discussed. The so-called “self-organization” is a process of spontaneously moving from disorder to order, and the environment and conditions (...) of community self-organization are mainly the openness, nonequilibrium state, and nonlinearity of the system. The key parameters of the contract with the change of the values of each factor make up for the inability to collect data for the empirical study in this paper; then, it presents four linear stages along with the cause such as self-creation, self-expansion, self-maintenance, and self-degeneration, respectively. The types of community self-organization mainly include community self-organization with random aggregation, socialized community self-organization, and stable community self-organization with autonomy orientation. By systematically sorting out the relationship between community self-organization and government, while confirming the positive significance of community self-organization to community cultural governance, various complex conflicts and game relationships will deeply affect the actual effectiveness of cultural governance and provide useful knowledge reference for future community cultural governance. (shrink)

Human-Computer Interaction and games set a new domain in understanding people’s motivations in gaming, behavioral implications of game play, game adaptation to player preferences and needs for increased engaging experiences in the context of HCI serious games. When the latter relate with people’s health status, they can become a part of their daily life as assistive health status monitoring/enhancement systems. Co-designing HCI-SGs can be seen as a combination of art and science that involves a meticulous collaborative process. The (...) design elements in assistive HCI-SGs for Parkinson’s Disease patients, in particular, are explored in the present work. Within this context, the Game-Based Learning design framework is adopted here and its main game-design parameters are explored for the Exergames, Dietarygames, Emotional games, Handwriting games, and Voice games design, drawn from the PD-related i-PROGNOSIS Personalized Game Suite holistic approach. Two main data sources were involved in the study. In particular, the first one includes qualitative data from semi-structured interviews, involving 10 PD patients and four clinicians in the co-creation process of the game design, whereas the second one relates with data from an online questionnaire addressed by 104 participants spanning the whole related spectrum, i.e., PD patients, physicians, software/game developers. Linear regression analysis was employed to identify an adapted GBL framework with the most significant game-design parameters, which efficiently predict the transferability of the PGS beneficial effect to real-life, addressing functional PD symptoms. The findings of this work can assist HCI-SG designers for designing PD-related HCI-SGs, as the most significant game-design factors were identified, in terms of adding value to the role of HCI-SGs in increasing PD patients’ quality of life, optimizing the interaction with personalized HCI-SGs and, hence, fostering a collaborative human-computer symbiosis. (shrink)

Qualitative Coalitional Games are a variant of coalitional games in which an agent's desires are represented as goals that are either satisfied or unsatisfied, and each choice available to a coalition is a set of goals, which would be jointly satisfied if the coalition made that choice. A coalition in a QCG will typically form in order to bring about a set of goals that will satisfy all members of the coalition. Our goal in this paper is to develop and (...) study logics for reasoning about QCGs. We begin by introducing a logic for reasoning about “static” QCGs, where participants play a single game, and we then introduce and study Temporal QCGs , i.e., games in which a sequence of QCGs is played. In order to represent and reason about such games, we introduce a linear time temporal logic of QCGs, called ℒ. We give a complete axiomatisation of ℒ, use it to investigate the properties of TQCGs, identify its expressive power, establish its complexity, characterise classes of TQGCs with formulas from our logical language, and use it to formulate several solution concepts for TQCGs. (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)

The idea of this paper is to approach linear orderings as generalized ordinals and to study how they are made from their initial segments. First we look at how the equality of two linear orderings can be expressed in terms of equality of their initial segments. Then we shall use similar methods to define functions by recursion with respect to the initial segment relation. Our method is based on the use of a game where smaller and smaller (...) initial segments of linear orderings are considered. The length of the game is assumed to exceed that of the descending sequences of elements of the linear orderings considered. By use of such game-theoretical methods we can for example extend the recursive definitions of the operations of sum, product and exponentiation of ordinals in a unique and natural way for arbitrary linear orderings. Extensions coming from direct limits do not satisfy our game-theoretic requirements in general. We also show how our recursive definitions allow very simple constructions for fixed points of functions, giving rise to certain interesting linear orderings. (shrink)

“Unraveling Braid” analyzes how unconventional, non-linear narrative fiction can help explain the ways in which video games signify. Specifically, this essay looks at the links between the semiotic features of Jonathan Blow’s 2008 puzzle-platform video game Braid and similar elements in Georges Perec’s 1978 novel Life A User’s Manual, as well as in other puzzle-themed literary precursors. Blow’s game design concepts “dynamical meaning” and “game play rhetoric” are explained in relation to a number of Braid levels; (...) along side this analysis is a parallel examination of the relationship between puzzle-makers and puzzle-solvers in Life A User’s Manual, revealed from a close reading of textual and organizational elements of Perec’s novel. Ultimately, Braid and Life A User’s Manual are shown to draw upon the same signifying processes, which are understood by their authors to operate within an implicitly communicative model. “Unraveling Braid”develops this model by positing a theory of storytelling in the imperative mood, in which the representation and arrangement of objects in the visual/organizational space of the text or game world becomes a fundamental rhetorical technique and meaning-maker.This technique signal show the reader/player is meant to progress through the work and interpret it as narrative, telling the reader/player what to do (but not necessarily how to do it). An understanding of “imperative” storytelling, this essay concludes, allows for a discussion of games and other media that denies neither the importance of player interactivity nor that of authorial design. (shrink)

This paper examines the theoretical background and actual behavior in a gaming tournament with endogenous timing where a person has more incentive, structure, and time to form a strategy. The baseline treatment suggests that subgame perfection is a reasonable predictor of behavior –- subjects made 170 of 208 theoretically predicted choices of best actions, with the majority of mistakes made in timing choices by the players who did not survive the cut to the second round. Four sensitivity treatments established that (...) the design feature that lead to more predictable behavior was time to think –- 745 of 960 correctly predicted decisions with more time versus 595 of 960 with less time. A random effects Probit model suggests that the key design feature that closed the gap between predicted and observed behavior was not necessarily the non-linear payoffs created by the tournament design, but rather that the key was providing people with more time to think about their strategy. (shrink)

We tackle the problem of preservation of totality by composition in arena games. We first explain how this problem reduces to a finiteness theorem on what we call pointer structures, similar to the parity pointer functions of Harmer, Hyland and Mélliès and the interaction sequences of Coquand. We discuss how this theorem relates to normalization of linear head reduction in simply-typed lambda-calculus, leading us to a semantic realizability proof à la Kleene of our theorem. We then present another proof (...) of a more combinatorial nature. Finally, we discuss the exact class of strategies to which our theorems apply. (shrink)

This paper examines the theoretical background and actual behavior in a gaming tournament with endogenous timing where a person has more incentive, structure, and time to form a strategy. The baseline treatment suggests that subgame perfection is a reasonable predictor of behavior –- subjects made 170 of 208 theoretically predicted choices of best actions, with the majority of mistakes made in timing choices by the players who did not survive the cut to the second round. Four sensitivity treatments established that (...) the design feature that lead to more predictable behavior was time to think –- 745 of 960 correctly predicted decisions with more time versus 595 of 960 with less time. A random effects Probit model suggests that the key design feature that closed the gap between predicted and observed behavior was not necessarily the non-linear payoffs created by the tournament design, but rather that the key was providing people with more time to think about their strategy. (shrink)

Inexpressibility results in Finite Model Theory are often proved by showing that Duplicator, one of the two players of an Ehrenfeucht game, has a winning strategy on certain structures.In this article a new method is introduced that allows, under certain conditions, the extension of a winning strategy of Duplicator on some small parts of two finite structures to a global winning strategy.As applications of this technique it is shown that • — Graph Connectivity is not expressible in existential monadic (...) second-order logic , even in the presence of a built-in linear order,• — Graph Connectivity is not expressible in MonNP even in the presence of arbitrary built-in relations of degree n0, and• — the presence of a built-in linear order gives MonNP more expressive power than the presence of a built-in successor relation. (shrink)

We investigate the stability of mixed strategy equilibria in 2 person (bimatrix) games under perturbed best response dynamics. A mixed equilibrium is asymptotically stable under all such dynamics if and only if the game is linearly equivalent to a zero sum game. In this case, the mixed equilibrium is also globally asymptotically stable. Global convergence to the set of perturbed equilibria is shown also for (rescaled) partnership games, also known as potential games. Lastly, mixed equilibria of partnership games (...) are shown to be always unstable under all dynamics of this class. (shrink)

We investigate the stability of mixed strategy equilibria in 2 person (bimatrix) games under perturbed best response dynamics. A mixed equilibrium is asymptotically stable under all such dynamics if and only if the game is linearly equivalent to a zero sum game. In this case, the mixed equilibrium is also globally asymptotically stable. Global convergence to the set of perturbed equilibria is shown also for (rescaled) partnership games, also known as potential games. Lastly, mixed equilibria of partnership games (...) are shown to be always unstable under all dynamics of this class. (shrink)

Game semantics extends the Curry–Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this paper we describe a logical counterpart to this extension, in which proofs denote such strategies. The system is expressive: it contains all of the connectives of Intuitionistic Linear Logic, and first-order quantification. Use of Lairdʼs sequoid operator allows proofs with imperative behaviour to be expressed. Thus, we can (...) embed first-order Intuitionistic Linear Logic into this system, Polarized Linear Logic, and an imperative total programming language.The proof system has a tight connection with a simple game model, where games are forests of plays. Formulas are modelled as games, and proofs as history-sensitive winning strategies. We provide a strong full completeness result with respect to this model: each finitary strategy is the denotation of a unique analytic proof. Infinite strategies correspond to analytic proofs that are infinitely deep. Thus, we can normalise proofs, via the semantics. (shrink)

In cooperative Cournot oligopoly games, it is known that the β-core is equal to the α-core, and both are non-empty if every individual profit function is continuous and concave (Zhao, Games Econ Behav 27:153–168, 1999b). Following Chander and Tulkens (Int J Game Theory 26:379–401, 1997), we assume that firms react to a deviating coalition by choosing individual best reply strategies. We deal with the problem of the non-emptiness of the induced core, the γ-core, by two different approaches. The first (...) establishes that the associated Cournot oligopoly Transferable Utility (TU)-games are balanced if the inverse demand function is differentiable and every individual profit function is continuous and concave on the set of strategy profiles, which is a step forward beyond Zhao’s core existence result for this class of games. The second approach, restricted to the class of Cournot oligopoly TU-games with linear cost functions, provides a single-valued allocation rule in the γ-core called Nash Pro rata (NP)-value. This result generalizes Funaki and Yamato’s (Int J Game Theory 28:157–171, 1999) core existence result from no capacity constraint to asymmetric capacity constraints. Moreover, we provide an axiomatic characterization of this solution by means of four properties: efficiency, null firm, monotonicity, and non-cooperative fairness. (shrink)

We present a setting in which the search for a proof of B or a refutation of B can be carried out simultaneously: in contrast, the usual approach in automated deduction views proving B or proving ¬B as two, possibly unrelated, activities. Our approach to proof and refutation is described as a two-player game in which each player follows the same rules. A winning strategy translates to a proof of the formula and a counter-winning strategy translates to a refutation (...) of the formula. The game is described for multiplicative and additive linear logic . A game theoretic treatment of the multiplicative connectives is intricate and our approach to it involves two important ingredients. First, labeled graph structures are used to represent positions in a game and, second, the game playing must deal with the failure of a given player and with an appropriate resumption of play. This latter ingredient accounts for the fact that neither player might win. (shrink)

The lostness measure, an implicit and unobtrusive measure originally designed for assessing the usability of hypertext systems, could be useful in Virtual Reality (VR) games where players need to find information to complete a task. VR locomotion systems with node-based movement mimic actions for exploration and browsing found in hypertext systems. For that reason, hypertext usability measures, such as “lostness” can be used to identify how disoriented a player is when completing tasks in an educational game by examining steps (...) made by the player. An evaluation of two different lostness measures, global and local lostness, based on two different types of tasks, is described in a VR educational game using 13 college students between 14 and 18 years old in a first study and extended using 12 extra participants in a second study. Multiple Linear Regression analyses showed, in both studies, that local lostness, and not global lostness, had a significant effect on a post-game knowledge test. Therefore, we argued that local lostness was able to predict how well-participants would perform on a post-game knowledge test indicating how well they learned from the game. In-game experience aspects (engagement, cognitive interest, and presence) were also evaluated and, interestingly, it was also found that participants learned less when they felt more present in the game. We believe these two measures relate to cognitive overload, which is known to have an adverse effect on learning. Further research should investigate the lostness measure for use in an online adaptive game system and design the game system in such a way that the risk of cognitive overload is minimized when learning, resulting in higher retention of information. (shrink)

The conventional community sports facility allocation methods have high minimum costs, and a new community sports facility allocation performance optimization method is designed based on a linear programming model in order to reduce the performance capital investment. The standardized community sports facility allocation performance objective function is established, and a pairwise model is built to divide the feasible and optimal solutions, and the feasible solutions and their constraints are found out. Establish a community sports facility configuration performance optimization model, (...) delineate the boundaries of the optimal solution by bifurcation, and set the feasible domain of the performance optimization model. The performance optimization algorithm is designed to improve the speed of community sports facility allocation performance optimization. In the experiment, the method is compared with data-driven method, digital management method, and evolutionary game algorithm, which requires less capital investment in spring, autumn, and winter than digital management method and evolutionary game algorithm, and the minimum capital investment in summer is less than the other three methods. From the above experimental data, it is clear that the performance optimization method has the smallest minimum capital investment and achieves the purpose of reducing the input cost. (shrink)

The objective of this article is to investigate the impact of agent heterogeneity (as regards their attitude towards cooperation) and payoff structure on cooperative behaviour, using an experimental setting with incomplete information. A game of chicken is played considering two types of agents: ‘unconditional cooperators’, who always cooperate, and ‘strategic cooperators’, who do not cooperate unless it is in their interest to do so. Overall, our data show a much higher propensity to cooperate than predicted by theory. They also (...) suggest that agent heterogeneity matters: the higher the proportion of ‘strategic cooperators’ in the population, the higher their probability to cooperate. Finally, our data confirm that higher rewards to cooperation (embedded in the payoff structure) tend to lower defection. Taken together, our results suggest that the subjects might be non-expected utility maximizers, dealing with both outcomes and probabilities in a non-linear manner. (shrink)

C. Karp has shown that if α is an ordinal with ω α = α and A is a linear ordering with a smallest element, then α and $\alpha \bigotimes A$ are equivalent in L ∞ω up to quantifer rank α. This result can be expressed in terms of Ehrenfeucht-Fraïssé games where player ∀ has to make additional moves by choosing elements of a descending sequence in α. Our aim in this paper is to prove a similar result for (...) Ehrenfeucht-Fraïssé games of length ω 1 . One implication of such a result will be that a certain infinite quantifier language cannot say that a linear ordering has no descending ω 1 -sequences (when the alphabet contains only one binary relation symbol). Connected work is done by Hyttinen and Oikkonen in [H] and [O]. (shrink)

This study investigates simple games. A fundamental research question in this field is to determine necessary and sufficient conditions for a simple game to be a weighted majority game. Taylor and Zwicker showed that a simple game is non-weighted if and only if there exists a trading transform of finite size. They also provided an upper bound on the size of such a trading transform, if it exists. Gvozdeva and Slinko improved that upper bound; their proof employed (...) a property of linear inequalities demonstrated by Muroga. In this study, we provide a new proof of the existence of a trading transform when a given simple game is non-weighted. Our proof employs Farkas’ lemma, and yields an improved upper bound on the size of a trading transform. We also discuss an integer-weight representation of a weighted simple game, improving the bounds obtained by Muroga. We show that our bound on the quota is tight when the number of players is less than or equal to five, based on the computational results obtained by Kurz. Furthermore, we discuss the problem of finding an integer-weight representation under the assumption that we have minimal winning coalitions and maximal losing coalitions. In particular, we show a performance of a rounding method. Finally, we address roughly weighted simple games. Gvozdeva and Slinko showed that a given simple game is not roughly weighted if and only if there exists a potent certificate of non-weightedness. We give an upper bound on the length of a potent certificate of non-weightedness. We also discuss an integer-weight representation of a roughly weighted simple game. (shrink)

The ratio-bias (RB) phenomenon refers to the perceived likelihood of a low-probability event as greater when it is presented in the form of larger (e.g. 10-in-100) rather than smaller (e.g. 1-in-10) numbers. According to cognitive-experiential self-theory (CEST), the RB effect in a game of chance in a win condition, in which drawing a red jellybean is rewarded, can be accounted for by two facets of concrete thinking, the greater comprehension (at the intuitive-experiential level) of single numbers than of ratios, (...) and of smaller than of larger numbers. In a lose condition, in which drawing a red jellybean is punished, the assumption of a third facet of concrete thinking, the ''affirmative-representation principle'', is necessary, as many participants reverse their focus of attention from the undesirable red to the desirable white jellybeans. Results supported the CEST explanation of the RB effect by demonstrating a predicted negative linear relation between the magnitude of the RB effect and the magnitude of the probability-ratios in the win condition and a positive linear relation in the lose condition. Support was also found for the associative principle of experiential processing. (shrink)

We add a stage to Nash’s demand game by allowing the greedier player to revise his demand if the demands are not jointly feasible. If he decides to stick to his initial demand, then the game ends and no one receives anything. If he decides to revise it down to 1-x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1-x$$\end{document}, where x is his initial demand, the revised demand is implemented with certainty. The implementation probability changes linearly between (...) these two extreme cases. We derive a condition on the feasible set under which the two-stage game has a unique subgame perfect equilibrium. In this equilibrium, there is first-stage agreement on the egalitarian demands. We also study two n-player versions of the game. In either version, if the underlying bargaining problem is “divide-the-dollar,” then equal division is sustainable in a subgame perfect equilibrium if and only if the number of players is at most four. (shrink)

The aesthetic experience of Laurence Sterne’s The Life and Opinion of Tristram Shandy, Gentleman is not reducible to an interpretation of plot or a linear critical analysis on the level of structure. Instead, it is thematized around a particular paradox of “double chronology” of autobiography, which continues the unfolding of the text yet simultaneously disrupts it. As such, Tristram Shandy’s lack of plot is a secondary phenomenon to the textual game of detour and digression it plays. This essay (...) is less concerned with providing a closed argument and much more concerned with opening up inquiry into time and the aesthetics of reading with brief recourse to Paul Ricoeur and Hans-Georg Gadamer. Overall, I hope to indicate how Tristram Shandy provides a space wherein the pleasure of reading itself is disclosed. (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 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)

In the context of propositional logics, we apply semantics modulo satisfiability—a restricted semantics which comprehends only valuations that satisfy some specific set of formulas—with the aim to efficiently solve some computational tasks. Three possible such applications are developed.We begin by studying the possibility of implicitly representing rational McNaughton functions in Łukasiewicz Infinitely-valued Logic through semantics modulo satisfiability. We theoretically investigate some approaches to such representation concept, called representation modulo satisfiability, and describe a polynomial algorithm that builds representations in the newly (...) introduced system. An implementation of the algorithm, test results and ways to randomly generate rational McNaughton functions for testing are presented. Moreover, we propose an application of such representations to the formal verification of properties of neural networks by means of the reasoning framework of Łukasiewicz Infinitely-valued Logic.Then, we move to the investigation of the satisfiability of joint probabilistic assignments to formulas of Łukasiewicz Infinitely-valued Logic, which is known to be an NP-complete problem. We provide an exact decision algorithm derived from the combination of linear algebraic methods with semantics modulo satisfiability. Also, we provide an implementation for such algorithm for which the phenomenon of phase transition is empirically detected.Lastly, we study the game theory situation of observable games, which are games that are known to reach a Nash equilibrium, however, an external observer does not know what is the exact profile of actions that occur in a specific instance; thus, such observer assigns subjective probabilities to players actions. We study the decision problem of determining if a set of these probabilistic constraints is coherent by reducing it to the problems of satisfiability of probabilistic assignments to logical formulas both in Classical Propositional Logic and Łukasiewicz Infinitely-valued Logic depending on whether only pure equilibria or also mixed equilibria are allowed. Such reductions rely upon the properties of semantics modulo satisfiability. We provide complexity and algorithmic discussion for the coherence problem and, also, for the problem of computing maximal and minimal probabilistic constraints on actions that preserves coherence.prepared by Sandro Márcio da Silva Preto.E-mail: [email protected]:https://doi.org/10.11606/T.45.2021.tde-17062021-163257. (shrink)

ABSTRACTThis paper draws on Ian Bogost’s argument that video games constitute a form of ‘procedural rhetoric’, in order to re-examine the representation of heroic madness First-Person-Shooter games. Rejecting the idea that games attempt to recreate the experience of madness to the player through linear representation, the paper instead identifies two persistent commonplace figures which appear within the genre: the monstrous double, and the reaching tentacle. While Bogost’s notion of procedural rhetoric allows analysis to move away from the more facile (...) interpretations of gameplay, the paper argues that these figures also demand an account of the commonplace itself – the rhetorical ‘topic’ – which links the technical structure of gaming procedures with the tropes and figures that enable them to make sense within their wider cultural context and tradition. While the figures of the double and the tentacle purposefully draw on existing tropes and processes associated with the cultural meanings of mental healt... (shrink)