Communication is an inherently strategic matter. This paper introduces simple game theoretic models of information transmission to identify different forms of uncertainty which may pose a problem of trust in testimony. Strategic analysis suggests discriminating between trust in integrity, trust in competence, trust in (the will to invest) effort and trust in honesty. Whereas uncertainty about the sender's honesty or integrity may directly influence a rational receiver's readiness to rely on sender's statements, neither uncertainty about the competence of (...) a sender nor uncertainty about his willingness to invest effort has any direct impact on rational reliance on its own. In this regard, trust in honesty and trust in integrity appear to be more basic than trust in competence or effort. (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)

Consider a simple game with n players. Let ψi be the Shapley–Shubik power index for player i. Then 1-ψi measures his powerlessness. We break down this powerlessness into two components – a `quixote index' Q i (which measures how much of a `quixote' i is), and a `follower index' F i (which measures how much of a `follower' he is). Formulae, properties, and axiomatizations for Q and F are given. Examples are also supplied.

In this paper we study three-valued simple games as a natural extension of simple games. We analyze to which extent well-known results on the core and the Shapley value for simple games can be extended to this new setting. To describe the core of a three-valued simple game we introduce vital players, in analogy to veto players for simple games. Moreover, it is seen that the transfer property of Dubey can still be used to (...) characterize the Shapley value for three-valued simple games. We illustrate three-valued simple games and the corresponding Shapley value in a parliamentary bicameral system. (shrink)

A path scheme for a game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path. A path scheme is called population monotonic if a player’s payoff does not decrease as the path coalition grows. In this study, we focus on Shapley path schemes of simple games in which for every path coalition the Shapley value of the (...) associated subgame provides the allocation at hand. Obviously, each Shapley path scheme of a game is population monotonic if and only if the Shapley allocation scheme of the game is population monotonic in the sense of Sprumont (Games Econ Behav 2:378–394, 1990). We prove that a simple game allows for population monotonic Shapley path schemes if and only if the game is balanced. Moreover, the Shapley path scheme of a specific path is population monotonic if and only if the first winning coalition that is formed along the path contains every minimal winning coalition. We also show that each Shapley path scheme of a simple game is population monotonic if and only if the set of veto players of the game is a winning coalition. Extensions of these results to other efficient probabilistic values are discussed. (shrink)

This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in threshold logic in the (...) sixties and seventies for this problem. However, game theory has taken the lead and some new results have been obtained for the problem in the past two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures for future research. The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal winning coalitions. (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)

We discuss a simple logic to describe one of our favourite games from childhood, hide and seek, and show how a simple addition of an equality constant to describe the winning condition of the seeker makes our logic undecidable. There are certain decidable fragments of first-order logic which behave in a similar fashion with respect to such a language extension, and we add a new modal variant to that class. We discuss the relative expressive power of the proposed (...) logic in comparison to the standard modal counterparts. We prove that the model checking problem for the resulting logic is \(\textsf{P}\) -complete. In addition, by exploring the connection with related product logics, we gain more insight towards having a better understanding of the subtleties of the proposed framework. (shrink)

We introduce two new iteration games: the game , which is a strengthening of the weak iteration game, and the game , which is somewhat stronger than but weaker than the full iteration game of length ω1. For a countable M elementarily embeddable in some Vη, with two players I and II, we can show that II wins and that I does not win.

We address simple voting games as mathematical objects in their own right, and study structures made up of these objects, rather than focusing on SVGs primarily as co-operative games. To this end it is convenient to employ the conceptual framework and language of category theory. This enables us to uncover the underlying unity of the basic operations involving SVGs.

This paper applies the theoretical criteria laid out by D’Arms et al. to various aspects of evolutionary models of signalling. The question that D’Arms et al. seek to answer can be formulated as follows: Are the models that we use to explain the phenomena in question conceptually adequate? The conceptual adequacy question relates the formal aspects of the model to those aspects of the natural world that the model is supposed to capture. Moreover, this paper extends the analysis of D’Arms (...) et al. by asking the following additional question: Are the models that we use sufficient to explain the phenomena in question? The sufficiency question asks what formal resources are minimally required for the model to get the right results most of the time. (shrink)

Humans are incapable of acting as utility maximisers. In contrast, the evolutionary process had considerable time and computational power to select optimal heuristics from a set of alternatives. To view evolution as the optimising agent has revolutionised game theory. Gigerenzer and his co-workers can help us understand the circumstances under which evolution and learning achieve optimisation and Nash equilibria.

We discuss a simple logic to describe one of our favourite games from childhood, hide and seek, and show how a simple addition of an equality constant to describe the winning condition of the seeker makes our logic undecidable. There are certain decidable fragments of first-order logic which behave in a similar fashion and we add a new modal variant to that class of logics. We also discuss the relative expressive power of the proposed logic in comparison to (...) the standard modal counterparts. (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.

We investigate a simple game paradigm for intuitionistic logic, inspired by Wajsberg’s implicit inhabitation algorithm and Beth tableaux. The principal idea is that one player, ∃ros, is trying to construct a proof in normal form while his opponent, ∀phrodite, attempts to build a counter-model. The determinacy of the game implies therefore both completeness and semantic cut-elimination.

We completely characterize the simple majority weighted voting game achievable hierarchies, and, in doing so, show that a problem about representative government, noted by J. Banzhaf [Rutgers Law Review 58, 317–343 (1965)] cannot be resolved using the simple majority quota. We also demonstrate that all hierarchies achievable by any quota can be achieved if the simple majority quota is simply incremented by one.

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 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)

This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized assignment semantics for first order logic. The expressive strength, complete proof calculus and meta-properties of LFD are explored. Various language extensions are presented as well, up to undecidable modal-style logics for independence and dynamic logics of changing dependence models. Finally, more concrete settings for dependence are discussed: (...) continuous dependence in topological models, linear dependence in vector spaces, and temporal dependence in dynamical systems and games. (shrink)

We give a simple game-theoretic proof of Silver's theorem that every analytic set is Ramsey. A set P of subsets of ω is called Ramsey if there exists an infinite set H such that either all infinite subsets of H are in P or all out of P. Our proof clarifies a strong connection between the Ramsey property of partitions and the determinacy of infinite games.

We discuss games of both perfect and imperfect information at two levels of structural detail: players’ local actions, and their global powers for determining outcomes of the game. We propose matching logical languages for both. In particular, at the ‘action level’, imperfect information games naturally model a combined ‘dynamic-epistemic language’ – and we find correspondences between special axioms and particular modes of playing games with their information dynamics. At the ‘outcome level’, we present suitable notions of game equivalence, (...) plus some simple representation results. (shrink)

We represent truth sets for a variety of the well known semantic theories of truth as those sets consisting of all sentences for which a player has a winning strategy in an infinite two person game. The classifications of the games considered here are simple, those over the natural model of arithmetic being all within the arithmetical class of $\Sum_{3}^{0}$.

Why games? How could anyone consider action games an experimental paradigm for Cognitive Science? In 1973, as one of three strategies he proposed for advancing Cognitive Science, Allen Newell exhorted us to “accept a single complex task and do all of it.” More specifically, he told us that rather than taking an “experimental psychology as usual approach,” we should “focus on a series of experimental and theoretical studies around a single complex task” so as to demonstrate that our theories of (...) human cognition were powerful enough to explain “a genuine slab of human behavior” with the studies fitting into a detailed theoretical picture. Action games represent the type of experimental paradigm that Newell was advocating and the current state of programming expertise and laboratory equipment, along with the emergence of Big Data and naturally occurring datasets, provide the technologies and data needed to realize his vision. Action games enable us to escape from our field's regrettable focus on novice performance to develop theories that account for the full range of expertise through a twin focus on expertise sampling and longitudinal studies of simple and complex tasks. (shrink)

It is widely agreed that play and games contribute to the good life. One might naturally wonder how games in particular so contribute? Granted, games can be very good, what exactly is so good about them when they are good? Although a natural starting point, this question is perhaps naive. Games come in all shapes and sizes, and different games are often good in very different ways. Chess, Bridge, Bingo, Chutes and Ladders, Football, Spin the Bottle, Dungeons & Dragons, Pac-Man, (...) Minecraft and Charades are all games, and can all contribute to a good life, but each will characteristically enrich someone’s life in its own distinctive way. Some games facilitate socializing and sociability, other games improve physical fitness, some develop a sense of fair play and reciprocity, while others enhance concentration and analytic skills. Asking ‘what is good about games?’ and assuming a simple answer is as naïve as asking ‘what is good about fiction?’ or ‘what is good about sex?’ However, a less naïve question and philosophically interesting question is not hard to formulate. Plausibly, much of the heterogeneity of the value of games stems from the different kinds of instrumental value of different games. Perhaps we should therefore ask in what ways the activity of playing games is characteristically good for its own sake. Unfortunately, the philosophical literature on the non-instrumental value of playing games is sparse. One of the few sustained treatments of the topic can be found in an underappreciated exchange between Thomas Hurka and John Tasioulas. Interestingly, despite taking different views of what it is to play a game, they both make room for the non-instrumental value of play and achievement in game play and they both argue that these two goods stand in important an important explanatory relation. However, they take diametrically opposed views as to which of these good is more basic. Roughly, on Hurka’s view, the good of achievement is more basic, and it is because of the non-instrumental value of achievement that what Hurka calls “playing in a game,” which involves playing, is itself non-instrumentally good because of the non-instrumental value of achievement. The idea is that if something is non-instrumentally good then loving that thing is also non-instrumentally good, and that playing in a game involves loving the activity for its own sake. In this way, the value of achievement in a game grounds the value of playing in a game. Tasioulas takes exactly the opposite approach. He argues that there must be something independently good about playing a game which grounds the value of achievement in that game. On his view, the typical grounding good or “framing value” of games is play itself – what I am here calling “playing.” In this essay, I raise some objections to both Hurka’s view and Tasioulas’s view and develop a positive alternative conception of the non-instrumental value of games. I argue that while each view is insightful in its own way, neither gets things exactly right. For a start, the way in which they characterize the key concepts is problematic. Hurka’s definition of ‘play a game’, which he lifts from Suits, is problematic, while both of their characterizations of play are problematic for reasons I rehearse here. They also take an unduly narrow view of the possible role of achievement in game play, both effectively conflating achievement with “excellence.” I argue, by contrast, that there is an important sense in which even someone who is not very good at the game by any objective standard can still reap the goods of achievements in games. At the same time, those who play games typically do not do so for the sake of achievements as such, though they may do something which is in a sense tantamount to this, or so I shall argue. Finally, I argue that neither Hurka’s “achievement first” order of explanation nor Tasioulas’s “play first” order of explanation is fully correct. I argue for what I call a “variable priority” view. On this view, the value of play sometimes grounds the value of achievement in a game, while in other cases the independently grounded value of achievement in a game provides a further ground for the value of play, though even in that case play is independently good for its own sake. I begin by laying out Hurka’s and Tasioulas’s views. (shrink)

Various potential strategic interactions between a “strong” Artificial intelligence and humans are analyzed using simple 2 × 2 order games, drawing on the New Periodic Table of those games developed by Robinson and Goforth. Strong risk aversion on the part of the human player leads to shutting down the AI research program, but alternative preference orderings by the human and the AI result in Nash equilibria with interesting properties. Some of the AI-Human games have multiple equilibria, and in other (...) cases Pareto-improvement over the Nash equilibrium could be attained if the AI’s behavior towards humans could be guaranteed to be benign. The preferences of a superintelligent AI cannot be known in advance, but speculation is possible as to its ranking of alternative states of the world, and how it might assimilate the accumulated wisdom of humanity. (shrink)

We study the equilibrium behavior of informed traders interacting with market scoring rule (MSR) market makers. One attractive feature of MSR is that it is myopically incentive compatible: it is optimal for traders to report their true beliefs about the likelihood of an event outcome provided that they ignore the impact of their reports on the profit they might garner from future trades. In this paper, we analyze non-myopic strategies and examine what information structures lead to truthful betting by traders. (...) Specifically, we analyze the behavior of risk-neutral traders with incomplete information playing in a dynamic game. We consider finite-stage and infinite-stage game models. For each model, we study the logarithmic market scoring rule (LMSR) with two different information structures: conditionally independent signals and (unconditionally) independent signals. In the finite-stage model, when signals of traders are independent conditional on the state of the world, truthful betting is a Perfect Bayesian Equilibrium (PBE). Moreover, it is the unique Weak Perfect Bayesian Equilibrium (WPBE) of the game. In contrast, when signals of traders are unconditionally independent, truthful betting is not a WPBE. In the infinite-stage model with unconditionally independent signals, there does not exist an equilibrium in which all information is revealed in a finite amount of time. We propose a simple discounted market scoring rule that reduces the opportunity for bluffing strategies. We show that in any WPBE for.. (shrink)

The paper presents a simple game-theoretic model in which players decide on search procedures for a prize located in one of a set of labeled boxes. The prize is awarded to the player who finds it first. A player can decide on the number of (costly) search units he employs and on the order in which he conducts the search. It is shown that in equilibrium, the players employ an equal number of search units and conduct a completely (...) random search. The paper demonstrates that the search procedure is intrinsically inefficient. Journal of Economic Literature Classification.. (shrink)

The paper presents a simple game-theoretic model in which players decide on search procedures for a prize located in one of a set of labeled boxes. The prize is awarded to the player who finds it first. A player can decide on the number of (costly) search units he employs and on the order in which he conducts the search. It is shown that in equilibrium, the players employ an equal number of search units and conduct a completely (...) random search. The paper demonstrates that the search procedure is intrinsically inefficient. Journal of Economic Literature Classification Number: D83. (shrink)

In previous work I’ve defended an interest-relative theory of belief. This paper continues the defence. It has four aims. -/- 1. To offer a new kind of reason for being unsatis ed with the simple Lockean reduction of belief to credence. 2. To defend the legitimacy of appealing to credences in a theory of belief. 3. To illustrate the importance of theoretical, as well as practical, interests in an interest-relative account of belief. 4. To revise my account to cover (...) propositions that are practically and theoretically irrelevant to the agent. (shrink)

This chapter contains sections titled: “I started when there was no such thing as traditional” “Simple is Good”:10 An Affirmation of Authenticity Notes.

Genericity is the idea that the same program can work at many different data types. Longo, Milstead and Soloviev proposed to capture the inability of generic programs to probe the structure of their instances by the following equational principle: if two generic programs, viewed as terms of type , are equal at any given instance A[T], then they are equal at all instances. They proved that this rule is admissible in a certain extension of System F, but finding a semantically (...) motivated model satisfying this principle remained an open problem.In the present paper, we construct a categorical model of polymorphism, based on game semantics, which contains a large collection of generic types. This model builds on two novel constructions:•A direct interpretation of variable types as games, with a natural notion of substitution of games. This allows moves in games A[T] to be decomposed into the generic part from A, and the part pertaining to the instance T. This leads to a simple and natural notion of generic strategy.•A “relative polymorphic product” which expresses quantification over the type variable Xi in the variable type A with respect to a “universe” which is explicitly given as an additional parameter B. We then solve a recursive equation involving this relative product to obtain a universe in a suitably “absolute” sense.Full Completeness for ML types is proved for this model. (shrink)

Situational Design lays out a new methodology for designing and critiquing videogames. While most game design books focus on games as formal systems, Situational Design concentrates squarely on player experience. It looks at how playfulness is not a property of a game considered in isolation, but rather the result of the intersection of a game with an appropriate player. Starting from simple concepts, the book advances step-by-step to build up a set of practical tools for designing (...) player-centric playful situations. While these tools provide a fresh perspective on familiar design challenges as well as those overlooked by more transactional design paradigms. Key Features Introduces a new methodology of game design that concentrates on moment-to-moment player experience Provides practical design heuristics for designing playful situations in all types of games Offers groundbreaking techniques for designing non-interactive play spaces Teaches designers how to create games that function as performances Provides a roadmap for the evolution of games as an art form. (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)

In this chapter the author looks at how Wittgenstein applies his method of creating simple language games to discuss fundamental questions in the Philosophical Investigations and its preliminary works. Wittgenstein seems to think that numerals can be learned alone, demonstratively, without further linguistic context. He altogether ignores Frege's preferred interpretation “that the content of a statement of number is an assertion about a concept,” which, for Wittgenstein, would mean, among other things, that numerals can only be learned and used (...) in conjunction with other words. The chapter highlights that a simple language game becomes expanded through the introduction of expressions of the category of proper names with a consideration of the Philosophical Investigations, which at first glance appears to have something to say about the interplay of proper names and concept terms in the building of a sentence. (shrink)

Digraph games are cooperative TU-games associated to domination structures which can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles in social choice theory. The Shapley value, core, marginal vectors and selectope vectors of digraph games are characterized in terms of so-called simple score vectors. A general characterization of the class of (almost positive) TU-games where each selectope vector is a marginal vector is provided in terms of (...) game semi-circuits. Finally, applications to the ranking of teams in sports competitions and of alternatives in social choice theory are discussed. (shrink)

In this article I introduce a simple classroom exercise intended to help students better understand Robert Nozick’s famous Wilt Chamberlain thought experiment. I outline the setup and rules of the Basic Version of the Game and explain its primary pedagogical benefits. I then offer several more sophisticated versions of the Game which can help to illustrate the difference between Nozick’s libertarianism and luck egalitarianism.

Signaling games with reinforcement learning have been used to model the evolution of term languages (Lewis 1969, Convention. Cambridge, MA: Harvard University Press; Skyrms 2006, “Signals” Presidential Address. Philosophy of Science Association for PSA). In this article, syntactic games, extensions of David Lewis’s original sender–receiver game, are used to illustrate how a language that exploits available syntactic structure might evolve to code for states of the world. The evolution of a language occurs in the context of available vocabulary and (...) syntax—the role played by each component is compared in the context of simple reinforcement learning. (shrink)

Our understanding of communication and its evolution has advanced significantly through the study of simple models involving interacting senders and receivers of signals. Many theorists have thought that the resources of mathematical information theory are all that are needed to capture the meaning or content that is being communicated in these systems. However, the way theorists routinely talk about the models implicitly draws on a conception of content that is richer than bare informational content, especially in contexts where false (...) content is important. This article shows that this concept can be made precise by defining a notion of functional content that captures the degree to which different states of the world are involved in stabilizing senders’ and receivers’ use of a signal at equilibrium. A series of case studies is used to contrast functional content with informational content, and to illustrate the explanatory role and limitations of this definition of functional content. _1_ Introduction _2_ Modelling Framework _3_ Two Kinds of Content _3.1_ Informational content _3.2_ Functional content _4_ Cases _4.1_ Case 1: Simplest case _4.2_ Case 2: Partial pooling _4.3_ Case 3: Bottleneck _4.4_ Case 4: Partial common interest _4.5_ Case 5: Deception _4.6_ Case 6: A further problem arising from divergent interests _5_ Discussion Appendix. (shrink)

We describe a fully abstract semantics for a simple functional language with locally declared names which may be used as pointers to names. It is based on a category of dialogue games acted upon by the group of natural number automorphisms. This allows a formal, semantic characterization of the key properties of names such as freshness and locality.We describe a model of the call-by-value λ-calculus based on these games, and show that it can be used to interpret the nu-calculus (...) of Pitts and Stark. We then construct a model of our pointer-language by extending our category of games with an explicit representation of the store, using a notion of semantic garbage-collection to erase inaccessible pointers. Using factorization and decomposition techniques, we show that the compact elements of our model are definable as terms, and hence it is fully abstract. (shrink)

According to the Simple View of intentional action, I have intentionally switched on the light only if I intended to switch on the light. The idea that intending to is necessary for intentionally -ing has been challenged by Bratman (1984, 1987) with a counter-example in which a videogame player is trying to hit either of two targets while knowing that she cannot hit both targets. When a target is hit, the game finishes. And if both targets are about (...) to be hit simultaneously, the game shuts down. The player knows that she cannot hit both targets, but still she concludes that, given her skills, the best strategy is to have a go at each target at the same time. Suppose she hits target 1. It seems obvious that she has hit target 1 intentionally. But, Bratman argues, she could not have intended to hit target 1. Since the scenario is perfectly symmetrical, had the player intended to hit target 1, she would have also had to intend to hit target 2. But the player knows that she cannot hit both targets. (shrink)

Prospect theory emerged as one of the leading descriptive decision theories that can rationalize a large body of behavioral regularities. The methods for eliciting prospect theory parameters, such as its value function and probability weighting, are invaluable tools in decision analysis. This paper presents a new simple method for eliciting prospect theory’s value function without any auxiliary/simplifying parametric assumptions. The method is applicable both to choice under ambiguity (Knightian uncertainty) and risk (when events are characterized by objective probabilities). Our (...) new elicitation method is implemented in a simple paper-and-pencil experiment (via an iterative multiple price list format). This is one of the first experiments that elicits non-parametric prospect theory’s value function with salient rewards. The collected data generally confirm findings in the existing literature: the value function is S-shaped (concave in the gain domain and convex in the loss domain) though there is a weaker loss aversion on the aggregate level and a substantial heterogeneity in loss aversion on the individual level (41% loss averse, 6% loss neutral and 53% gain seeking). (shrink)

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

We give a complete axiomatization of the identities of the basic game algebra valid with respect to the abstract game board semantics. We also show that the additional conditions of termination and determinacy of game boards do not introduce new valid identities.En route we introduce a simple translation of game terms into plain modal logic and thus translate, while preserving validity both ways, game identities into modal formulae.The completeness proof is based on reduction of (...) game terms to a certain ‘minimal canonical form’, by using only the axiomatic identities, and on showing that the equivalence of two minimal canonical terms can be established from these identities. (shrink)