There have been two main lines in the literature on restricted games: the first line was started by Myerson (1977) that studied graph-restricted games an the second one was initiated by Faigle (1989). The present paper provides a unified way to look on the literature and establishes connections between the two different lines on restricted games. The strength and advantages of this unified approach becomes clear in the study of the inheritance of the convexity (...) from the game to the restricted game where an interesting result by Nouweland and Borm (1991) on the convexity of graph-restricted games is turned into a direct consequence of the corresponding result by Faigle (1989), by means of this relation. (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)

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)

Some theorists claim that games are “transmedial”, meaning that the same game can be played in different media. It is unclear, however, what are the limits of transmedial games. Are all games in-principle transmedial, or only some? One suggestion offered by Jesper Juul is that, if games are understood as sets of rules, then a game is transmedial if its rules can be either implemented or adapted into some new media. I argue against this view on (...) the grounds that the rules of many games are dependent on the game’s media such that they cannot be adapted to a new medium. As such the games-as-rules view of transmediality is not restrictive enough. To add the necessary restriction, I suggest that games are transmedial, not only when they contain the same rules, but also when it requires the same set of skills to play each. I further argue that a skill-set view of transmediality is better able to account for many common intuitions about games. (shrink)

Locality notions in logic say that the truth value of a formula can be determined locally, by looking at the isomorphism type of a small neighbourhood of its free variables. Such notions have proved to be useful in many applications. They all, however, refer to isomorphisms of neighbourhoods, which most local logics cannot test. A stronger notion of locality says that the truth value of a formula is determined by what the logic itself can say about that small neighbourhood. Since (...) the expressiveness of many logics can be characterized by games, one can also say that the truth value of a formula is determined by the type, with respect to a game, of that small neighbourhood. Such game-based notions of locality can often be applied when traditional isomorphism-based notions of locality cannot.Our goal is to study game-based notions of locality. We work with an abstract view of games that subsumes games for many logics. We look at three, progressively more complicated locality notions. The easiest requires only very mild conditions on the game and works for most logics of interest. The other notions, based on Hanf’s and Gaifman’s theorems, require more restrictions. We state those restrictions and give examples of logics that satisfy and fail the respective game-based notions of locality. (shrink)

An overview of different versions and applications of Lorenzen’s dialogue game approach to the foundations of logic, here largely restricted to the realm of manyvalued logics, is presented. Among the reviewed concepts and results are Giles’s characterization of Łukasiewicz logic and some of its generalizations to other fuzzy logics, including interval based logics, a parallel version of Lorenzen’s game for intuitionistic logic that is adequate for finite- and infinite-valued Gödel logics, and a truth comparison game for infinite-valued Gödel logic.

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

Logical omniscience states that the knowledge set of ordinary rational agents is closed for its logical consequences. Although epistemic logicians in general judge this principle unrealistic, there is no consensus on how it should be restrained. The challenge is conceptual: we must find adequate criteria for separating obvious logical consequences from non-obvious ones. Non-classical game-theoretic semantics has been employed in this discussion with relative success. On the one hand, with urn semantics [15], an expressive fragment of classical game semantics that (...) weakens the dependence relations between quantifiers occurring in a formula, we can formalize, for a broad array of examples, epistemic scenarios in which an individual ignores the validity of some first-order sentence. On the other hand, urn semantics offers a disproportionate restriction of logical omniscience. Therefore, an improvement of this system is needed to obtain a better solution of the problem. In this paper, I argue that our linguistic competence in using quantifiers requires a sort of basic hypothetical logical knowledge that can be formulated as follows: when inquiring after the truth-value of ∀xφ, an individual might be unaware of all substitutional instances this sentence accepts, but at least she must know that, if an element a is given, then ∀xφ holds only if φ is true. This thesis accepts game-theoretic formalization in terms of a refinement of urn semantics. I maintain that the system so obtained affords an improved solution of the logical omniscience problem. To do this, I characterize first-order theoremhood in US+. As a consequence of this result, we will see that the ideal reasoner depicted by US+ only knows the validity of first-order formulas whose Herbrand witnesses can be trivially found, a fact that provides strong evidence that our refinement of urn semantics captures a relevant sense of logical obviousness. (shrink)

Counterpossibles, counterfactuals conditional with impossible antecedents, are notoriously contested; while the standard view makes them trivially true, some authors argue that they can be non-trivially true. In this paper, I examine the use of counterfactuals in the context of games, and argue that there is a case to be made for their non-triviality in a restricted sense. In particular, I examine the case of retro problems in chess, where it can happen that one is tasked with evaluating counterfactuals (...) about illegal positions. If we understand illegality as a type of restricted impossibility, those counterfactuals are non-trivial counterpossibles. I suggest that their non-triviality stems from their role in practices of rule coordination and revision, and suggest that this model could be generalized to counterpossibles in different domains. I then compare the approach to the accounts of Vetter 2016 and Locke 2019. (shrink)

Oikkonen, J. and J. Väänänen, Game-theoretic inductive definability, Annals of Pure and Applied Logic 65 265-306. We use game-theoretic ideas to define a generalization of the notion of inductive definability. This approach allows induction along non-well-founded trees. Our definition depends on an underlying partial ordering of the objects. In this ordering every countable ascending sequence is assumed to have a unique supremum which enables us to go over limits. We establish basic properties of this induction and examine examples where it (...) emerges naturally. In the main results we prove an abstract Kleene Theorem and restricted versions of the Stage-Comparison Theorem and the Reduction Theorem. (shrink)

In this paper we introduce a game semantics for System P, one of the most studied axiomatic systems for non-monotonic reasoning, conditional logic and belief revision. We prove soundness and completeness of the game semantics with respect to the rules of System P, and show that an inference is valid with respect to the game semantics if and only if it is valid with respect to the standard order semantics of System P. Combining these two results leads to a new (...) completeness proof for System P with respect to its order semantics. Our approach allows us to construct for every inference either a concrete proof of the inference from the rules in System P or a countermodel in the order semantics. Our results rely on the notion of a witnessing set for an inference, whose existence is a concise, necessary and sufficient condition for validity of an inferences in System P. We also introduce an infinitary variant of System P and use the game semantics to show its completeness for the restricted class of well-founded orders. (shrink)

We consider a class of games, which we call “groups’ games”, in which players are partitioned into classes within which players may be considered indistinguishable. We compute explicit formulas for some of the principal values restricted to these games. This is particularly useful for dealing with games with a large number of players where the usual formulas would be impractical to compute. We give several examples that illustrate how this idea may be applied to concrete (...) situations. (shrink)

Without violating the spirit of Game-Theoretical semantics, its results can be re-worked in Martin-Löf''s Constructive Type Theory by interpreting games as types of Myself''s winning strategies. The philosophical ideas behind Game-Theoretical Semantics in fact highly recommend restricting strategies to effective ones, which is the only controversial step in our interpretation. What is gained, then, is a direct connection between linguistic semantics and computer programming.

I consider games with ambiguous payoffs played by non-Expected Utility decision makers. Three equilibrium solutions are studied. Nash equilibrium in which equilibrium mixed strategies must be best responses, Crawford equilibrium in beliefs and pure equilibrium in beliefs in which equilibrium strategies are mixtures of best responses, with the latter restricting best responses to pure actions. I study the interactions between ambiguity preferences on one side and equilibrium properties on the other. I show how the equilibrium concepts differ, computing necessary (...) and sufficient conditions for existence and equivalence. I also show how these solution concepts fare against two fundamental principles of Nash equilibrium in standard games: the principle of indifference and the reduction principle. Given both are central to the computation of Nash equilibrium in games with Expected Utility players, their failure indicates how relaxing the Expected Utility hypothesis may disrupt standard game theoretic results such as the characterization of equilibria in two-player games. (shrink)

This chapter argues that Westworld functions as a role‐play experience that continually entices its guests with suggested but unrealized layers of meaning and significance in its immersive western landscape. Where traditional role‐play experiences deliver meaning through player and Game Master group interaction, Westworld provides its guests with violent escapism, sexual fantasy, and nostalgic indulgence. Within the series, the Westworld park presents itself as a combination of two aspects of tabletop role‐playing game: sandbox format and Live Action Role‐play (LARP). Within the (...) role‐play experience, the cultivation of motivation on the part of the Game Master entices players to undertake or follow particular narrative threads. Gameplay was designed to cultivate certain personality traits and instincts. Herein the game's rules, style and structures “influence a user's behavior without forcing the change” ‐ essentially enacting education through restriction. In the case of role‐play games, these restrictions are less over by the narrative nature of the game. (shrink)

Traditionally, epistemologists have distinguished between epistemic and pragmatic goals. In so doing, they presume that much of game theory is irrelevant to epistemic enterprises. I will show that this is a mistake. Even if we restrict attention to purely epistemic motivations, members of epistemic groups will face a multitude of strategic choices. I illustrate several contexts where individuals who are concerned solely with the discovery of truth will nonetheless face difficult game theoretic problems. Examples of purely epistemic coordination problems and (...) social dilemmas will be presented. These show that there is a far deeper connection between economics and epistemology than previous appreciated. (shrink)

This paper theoretically and experimentally investigates the behavior of asymmetric players in guessing games. The asymmetry is created by introducing r>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r>1$$\end{document} replicas of one of the players. Two-player and restricted N-player cases are examined in detail. Based on the model parameters, the equilibrium is either unique in which all players choose zero or mixed in which the weak player (r=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r=1$$\end{document}) imitates (...) the strong player (r>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r>1$$\end{document}). A series of experiments involving two and three-player repeated guessing games with unique equilibrium is conducted. We find that equilibrium behavior is observed less frequently and overall choices are farther from the equilibrium in two-player asymmetric games in contrast to symmetric games, but this is not the case in three-player games. Convergence towards equilibrium exists in all cases but asymmetry slows down the speed of convergence to the equilibrium in two, but not in three-player games. Furthermore, the strong players have a slight earning advantage over the weak players, and asymmetry increases the discrepancy in choices (defined as the squared distance of choices from the winning number) in both games. (shrink)

Restricting attention to the class of extensive games defined by von Neumann and Morgenstern with the added assumption of perfect recall, we specify the information of each player at each node of the game-tree in a way which is coherent with the original information structure of the extensive form. We show that this approach provides a framework for a formal and rigorous treatment of questions of knowledge and common knowledge at every node of the tree. We construct a particular (...) information partition for each player and show that it captures the notion of maximum information in the sense that it is the finest within the class of information partitions that satisfy four natural properties. Using this notion of “maximum information” we are able to provide an alternative characterization of the meet of the information partitions. (shrink)

We consider strategic-form games with ordinal payoffs and provide a syntactic analysis of common belief/knowledge of rationality, which we define axiomatically. Two axioms are considered. The first says that a player is irrational if she chooses a particular strategy while believing that another strategy is better. We show that common belief of this weak notion of rationality characterizes the iterated deletion of pure strategies that are strictly dominated by pure strategies. The second axiom says that a player is irrational (...) if she chooses a particular strategy while believing that a different strategy is at least as good and she considers it possible that this alternative strategy is actually better than the chosen one. We show that common knowledge of this stronger notion of rationality characterizes the restriction to pure strategies of the iterated deletion procedure introduced by Stalnaker (1994). Frame characterization results are also provided. (shrink)

One might expect that, in pure coordination games, coordination would become less frequent as the number of options increases. Contrary to this expectation, we report an experiment which found more frequent coordination when the option set was unrestricted than when it was restricted. To try to explain this result, we develop a method for eliciting the general rules that subjects use to identify salient options in restricted and unrestricted sets. We find that each such rule, if used (...) by all subjects, would generate greater coordination in restricted sets. However, subjects tend to apply different rules to restricted and unrestricted sets. (shrink)

We provide eductive foundations for the concept of forward induction, in the class of games with an outside option. The formulation presented tries to capture in a static notion the rest point of an introspective process, achievable from some restricted preliminary beliefs. The former requisite is met by requiring the rest point to be a Nash equilibrium that yields a higher payoff than the outside option. With respect to the beliefs, we propose the Incentive Dominance Criterion. Players should (...) consider one action more likely than another whenever the former is better than getting the outside option for more conjectures over his rival's actions. We apply this model to the case where the subgame is a coordination game with a conflict between payoff dominance and risk dominance. Our results provide support for dominance solvability, but not for Van Damme's notion of forward induction. We show how the forward induction logic helps to select the Pareto dominant equilibrium. This is the case whenever player 1's act of giving up the outside option reverses the incentive dominance relations among 1's pure actions in the subgame. (shrink)

This paper investigates experimentally the effects of communication in distinct games with complete information. We design four games resulting from the interaction between two incentive elements: strategic complementarity and coordination. These incentive elements allow to analyse the use of cheap talk as an efficiency-enhancing and coordinating device. We implement a restricted communication protocol in repeated settings with fixed partners. Our findings provide robust evidence about how cheap talk interacts with incentives to explain strategic behaviour in a dynamic (...) way. As expected, cheap talk increases efficiency under complementarity incentives, and the coordination level under coordination incentives. As novelty, the use of limited communication in repeated interactions has led to identify specific time-varying message profiles as the most effective messages in the coordination games. While the content of messages is explained by the complementarity incentives, faithfulness to credible messages is determined by the coordination incentives. (shrink)

McGarvey (Econometrica, 21(4), 608–610, 1953) has shown that any irreflexive and anti-symmetric relation can be obtained as a relation induced by majority rule. We address the analogous issue for dominance relations of finite cooperative games with non-transferable utility (coalitional NTU games). We find any irreflexive relation over a finite set can be obtained as the dominance relation of some finite coalitional NTU game. We also show that any such dominance relation is induced by a non-cooperative game through β-effectivity. (...) Dominance relations obtainable through α-effectivity, however, have to comply with a more restrictive condition, which we refer to as the edge-mapping property. (shrink)

This essay argues that idleness as play and leisure would be recognised as an ideal over game playing in Bernard Suits’ Utopia. Idleness is unaccountably overlooked as an ideal by Suits, as is the problem that his description of game playing is an anachronism, pushing his Utopians into a pre-Utopian condition. There is room for playing games in an idle Utopia but in a less prominent and more restricted role. Idleness as play and leisure is not defended as (...) the sole ideal of Utopian existence though it is possibly that. Rather, it is presented as a compelling and preferable ideal for Suits’ Utopians, thus refuting his claim that game playing is ‘the only possible’ ideal of human existence in Utopia. (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)

Background Over the last decades, the neurosciences, behavioral sciences, and the social sciences have all seen a rapid development of innovative research methods. The field of bioethics, however, has trailed behind in methodological innovation. Despite the so-called “empirical turn” in bioethics, research methodology for project development, data collection and analysis, and dissemination has remained largely restricted to surveys, interviews, and research papers. We have previously argued for a “Design Bioethics” approach to empirical bioethics methodology, which develops purpose-built methods for (...) investigation of bioethical concerns. In this paper we compare a research tool created using a design bioethics approach to a “methods-as-usual” approach in empirical bioethics.Methods Our study compared dimensions of engagement with a digital game we created, called “Tracing Tomorrow,” to a standard vignette survey. The two tools investigated the same subject matter, digital phenotyping for mental health, in a sample of 301 UK adolescents.Results Participants who played the game reported a greater sense of presence, emotional engagement, cognitive absorption, and mental health ethics insight, compared to participants who completed the vignette survey. Perceived authenticity and curiosity/motivation to learn more was equivalent for both methods.Conclusion The results of this study highlights the importance of purpose-built methodology for empirical bioethics research. (shrink)

Bargaining games have played a prominent role in modeling the evolution of social conventions. Previous models assumed that agents must choose from a predetermined set of strategies. I present a new model of two agents learning in bargaining games in which new strategies must be invented and reinforced. I study the efficiency and fairness of the model outcomes. The outcomes are somewhat efficient, but a significant part of the resource is wasted nonetheless. I implement two forms of forgetting, (...) and restrictions to the set of strategies that can be invented. (shrink)

Can social phenomena be understood by analyzing their parts? Contemporary economic theory often assumes that they can. The methodology of constructing models which trace the behavior of perfectly rational agents in idealized environments rests on the premise that such models, while restricted, help us isolate tendencies, that is, the stable separate effects of economic causes that can be used to explain and predict economic phenomena. In this paper, I question both the claim that models in economics supply claims about (...) tendencies and also the view that economics, when successful, necessarily follows this method. When economics licenses successful policy interventions, as it did in the case of the Federal Communications Commission spectrum auctions, its method is not to study tendencies but rather to study the phenomenon as a whole. Key Words: economic models • tendencies • economic experiments • policy making • John Stuart Mill. (shrink)

Subjects communicated prior to playing trust games; the richness of the communication media and the topics of conversation were manipulated. Communication richness failed to produce significant differences in first-mover investments. However, the topics of conversation made a significant difference: the amounts sent were considerably higher in the unrestricted communication conditions than in the restricted communication and no-communication conditions. Most importantly, we find that first-movers' expectations of second-movers' reciprocation are influenced by communication and strongly predict their levels of investment.

North American Indians have often been perceived as violent, bloodthirsty human beings. The horrified fascination exerted by this violence on the European imagination takes hold of all historical accounts and lies at the heart of the smallest social productions. The sports games, whose imposing corpus is intriguing to the colonists, are also perceived as a cultural element of this gratuitous violence, a biological one, even, as inherent to their “wild nature”. And yet, far from being instinctual, this violence takes (...) on a ritual and propitiatory dimension that is at the same time at the service of private interests, but also, and especially so, of tribal ones. By taking possession of the lacrosse game through its institutionalization, Canadians hope to control the violence of this emblematic game-ritual. Despite a deep transformation of the game, the instinctual manifestations in the human relationships that are supposed to decline through the internalization of restrictions subsist. The original game still seems to express itself through this violence-based relationship, no matter how codified. Drawing on archives ranging from missiological writings to anthropological documents, as well as on recent academic studies, this article tries to dispel the defining halo of a violence sometimes confused with distinct forms of aggressivity. (shrink)

This paper discusses the relation between communication and preservation of social norms guarded by third-party sanctions. In 2001 Jonathan Bendor and Piotr Swistak derived deductively the existence of such norms from a simple boundedly rational choice model. Their analysis was based on a perfect public information case. We take into account communication and analyse at the micro level the process of production and interpretation of information on which decisions are based. We show that when information is fully private and we (...) allow for communication a state of anomie can result. If some social control mechanisms are available, social stability can be maintained. The less efficient the social control mechanisms however, the more restrictive rules will be needed to sustain the social norms. Furthermore not all cognitive strategies for interpreting received messages are equally effective. Strategies based on reputation are better than strategies based on profit analysis. (shrink)

ABSTRACT:Although a research focus on the increasing involvement of corporations in shaping and maintaining the global rules of the game points out promising avenues for future research, it simultaneously makes clear how little currently established, mostly managerial conceptual frameworks have to offer in making sense of these developments. It is argued that we need to expand the rather restricted perspectives that these frameworks provide, in order to explore new conceptual foundations that will not only enable us to travel the (...) confines of the different disciplines involved with the study of the changing role of business in shaping the global rules of the game, but that can also systematically connect normative and positive research questions at the conceptual level. Three directions for this search for new foundations are briefly explored. (shrink)

ABSTRACT:Although a research focus on the increasing involvement of corporations in shaping and maintaining the global rules of the game points out promising avenues for future research, it simultaneously makes clear how little currently established, mostly managerial conceptual frameworks have to offer in making sense of these developments. It is argued that we need to expand the rather restricted perspectives that these frameworks provide, in order to explore new conceptual foundations that will not only enable us to travel the (...) confines of the different disciplines involved with the study of the changing role of business in shaping the global rules of the game, but that can also systematically connect normative and positive research questions at the conceptual level. Three directions for this search for new foundations are briefly explored. (shrink)

Socialization theories suggest that, due to social change and technological transformation, peers and media have become important institutions of socialization for young people. Assuming that male adolescents use digital games for processes of peer self-socialization, this article investigates the values they mediate in digital games and how these values are related to their practice (with a focus on harassment) in digital games. Applying a qualitative research design, 36 male adolescents who frequently play various (multiplayer) online games (...) were interviewed about their values and practices when gaming. The results show that the young gamers share individualistic values promoting performance, competition, and achievement, which seem to facilitate practices of online harassment. We conclude that, in their gaming practices, male adolescents mediate and reproduce neoliberal values as increasingly shared by society. Regarding their practices of harassment, however, they seem to use digital games as a moratorium that lets them break free from societal restrictions. (shrink)

We extend Gurevich-Harrington's Restricted Memory Determinacy Theorem), which served in their paper as a tool to give their celebrated “short proof” of Robin's decision method for S2S. We generalize the determinacy problem by attaching to the game two opposing strategies called restraints, and by asking “which player has a strategy which is a refinement of the restraint for the player and such that it wins the game against the restraint of the opponent?” We give a solution for the Determinacy (...) with Restraints Problem in the class of strategies with restricted memory for the GH games. The solution includes a criterion for the winning player and an explicit class of winning strategies. A determinacy result which includes similar information was first discovered by Büchi and Landweber and extended by Büchi . However, these pioneering works do not consider the determinacy with restraints. Also, the explicit presentation of winning strategies in these insightful papers does not emphasize their modular construction as do GH's and our proofs. In our view, this is a source of a difficulty in understanding these papers. Games with restraints and modular construction of winning strategies have applications to the semantics, development and verification of concurrent programs. A concurrent program can be viewed as a strategy in a certain game and a program specification can be regarded as a combination of a winning condition and restraints for the game , A. Yakhnis and V. Yakhnis ). The modularity of a winning strategyfor the game helps to generate a concurrent program from the strategy that satisfies the specification ). It turns out that such program specification requirements as mutual exclusion and an absence of a lockout or a deadlock are naturally represented as Büchi's or Gurevich-Harrington's winning conditions. The present paper can be read independently of the paper by Gurevich and Harrington. (shrink)

An information completion of an extensive game is obtained by extending the information partition of every player from the set of her decision nodes to the set of all nodes. The extended partition satisfies Memory of Past Knowledge (MPK) if at any node a player remembers what she knew at earlier nodes. It is shown that MPK can be satisfied in a game if and only if the game is von Neumann (vN) and satisfies memory at decision nodes (the restriction (...) of MPK to a player's own decision nodes). A game is vN if any two decision nodes that belong to the same information set of a player have the same number of predecessors. By providing an axiom for MPK we also obtain a syntactic characterization of the said class of vN games. (shrink)

We propose in this paper a new family of belief merging operators, that is based on a game between sources : until a coherent set of sources is reached, at each round a contest is organized to find out the weakest sources, then those sources has to concede. This idea leads to numerous new interesting operators and opens new perspectives for belief merging. Some existing operators are also recovered as particular cases. Those operators can be seen as a special case (...) of Booth's Belief Negotiation Models [BOO 02], but the achieved restriction forms a consistent family of merging operators that worths to be studied on its own. (shrink)

Accountability is present in many types of social relations; for example, the accountability of elected representatives to voters is the key characteristic of representative democracy. We distinguish between two institutional mechanisms of accountability, i.e., opportunity to punish and requirement of a justification, and examine the separate and combined effects of these mechanisms on individual behavior. For this purpose, we designed a decision-making experiment where subjects engage in a three-player trust game with two senders and one responder. We ask whether holding (...) the responder accountable increases senders’ and responders’ contributions in a trust game. When restricting the analysis to the first round, the requirement of justification seems to have a positive impact on senders’ contributions. When the game is played repeatedly, the experience of previous rounds dominates the results and significant treatment effects are no longer seen. We also find that responders tend to justify their choices in terms of reciprocity, which is in line with observed behavior. Moreover, the treatment combining punishment and justification hinders justifications that appeal to pure self-interest. (shrink)

Kaneko-Suzuki developed epistemic logics of shallow depths with multiple players for investigations of game theoretical problems. By shallow depth, we mean that nested occurrences of belief operators of players in formulae are restricted, typically to be of finite depths, by a given epistemic structure. In this paper, we develop various methods of surgical operations (cut and paste) of epistemic world models. An example is a bouquet-making, i.e., tying several models into a bouquet. Another example is to engraft a model (...) to some branches of another model. By these methods, we obtain various meta-theorems on semantics and syntax on epistemic logics. To illustrate possible uses of our meta-theorems, we present one game theoretical theorem, which is also a meta-theorem in the sense of logic. (shrink)

We do not believe that logic is the sole answer to deep and intriguing questions about human behaviour, but we think that it might be a useful tool in simulating and understanding it to a certain degree and in specifically restricted areas of application. We do not aim to resolve the question of what rational behaviour in games with mistaken and changing beliefs is. Rather, we develop a formal and abstract framework that allows us to reason about behaviour (...) in games with mistaken and changing beliefs leaving aside normative questions concerning whether the agents are behaving “rationally”; we focus on what agents do in a game. In this paper, we are not concerned with the reasoning process of the (ideal) economic agent; rather, our intended application is artificial agents, e.g., autonomous agents interacting with a human user or with each other as part of a computer game or in a virtual world. We give a story of mistaken beliefs that is a typical example of the situation in which we should want our formal setting to be applied. Then we give the definitions for our formal system and how to use this setting to get a backward induction solution. We then apply our semantics to the story related earlier and give an analysis of it. Our final section contains a discussion of related work and future projects. We discuss the advantages of our approach over existing approaches and indicate how it can be connected to the existing literature. (shrink)

Specific to the NCSs where sensor signals can be processed centrally, a collaborative design scheme of dynamic game scheduling and advanced control theory was proposed in the present study. Firstly, by using the Jordan standard state space equation of the research object, the three elements of state noncooperative game were built, and the existence and uniqueness of Nash equilibrium solution were verified. In addition, the iterative equation of the scheduling matrix was derived by complying with the designed utility function. Secondly, (...) refer to the number of restricted states the order of sliding mode was determined. And based on it, the corresponding sliding surface was designed. Subsequently, the quadratic optimization theory was adopted to regulate the control value following the implementation of the scheduling strategy to ensure that the control quality was further enhanced in the limited network service. Lastly, a TrueTime simulation example is established to verify the effectiveness of the proposed scheme. (shrink)

The presence of sports fans in the stands is considered a natural and essential element of sporting events. Beyond the atmosphere fans create and the color they add to the game, their presence reflects the idea that the game is more than a competition between two teams —it is a grand battle between communities and identities, which is also the reason that fans are willing to sacrifice so much on behalf of their team. As is other areas of life, the (...) COVID-19 pandemic created an unusual situation, in which sporting events were held without spectators in the stadium stands. In many places around the world, professional sporting activities were permitted but spectators were not allowed into the stadiums due to social distancing restrictions. The current study examines this unique situation and through it, gains an understanding of fans’ beliefs concerning the significance of spectators and their presence in the stadium. Through in-depth interviews with football fans who regularly attend games, the current study explores football fans’ experiences as they viewed “ghost games”. Findings show that this unique situation, caused by the global pandemic, heightened fans’ deep-rooted connection to sports and to their favorite team, and also exacerbated the social, emotional, and professional implications of viewing football games with no spectators. (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)

We give some restrictions for the search for a model of the club principle with no Souslin trees. We show that ${\diamondsuit(2^\omega, [\omega]^\omega}$ , is almost constant on) together with CH and “all Aronszajn trees are special” is consistent relative to ZFC. This implies the analogous result for a double weakening of the club principle.

Lockdowns, or modern quarantines, involve the use of novel restrictive non-pharmaceutical interventions (NPIs) to suppress the transmission of COVID-19. In this paper, I aim to critically analyze the emerging history and philosophy of lockdowns, with an emphasis on the communication of health evidence and risk for informing policy decisions. I draw a distinction between evidence-based and modeling-based decision-making. I argue that using the normative framework of evidence-based medicine would have recommended against the use of lockdowns. I first review the World (...) Health Organization’s evidence-based pandemic preparedness plans for respiratory viruses. I then provide a very brief history of COVID-19 modeling, which was cited as justification for the use of lockdowns in the U.K., the U.S., and much of the world. I focus on the so-called Imperial College model designed by Neil Ferguson et al. as well as the so-called Oxford model designed by José Lourenço et al. I analyze the evidence-based pandemic response known as ‘mitigation’, and I compare it with Ferguson et al.’s experimental strategy known as ‘suppression’. I summarize the strengths and weaknesses of these strategies based on their diametric aims and each model’s parametric assumptions. Based on my critical analysis of the suppression strategy, I attempt to expose what has been called the ‘logic of lockdowns’, which Sunetra Gupta of the Oxford model group has suggested is flawed. Finally, I consider Trisha Greenhalgh’s objection to evidence-based policy based on the precautionary principle, and I attempt to offer a response. I conclude with a brief narrative review of the emerging randomized evidence on restrictive NPIs, which seems to support my claim that mitigation was the strategy that would have been recommended by evidence-based medicine. If this is true, then COVID-19 modeling may serve as an important reminder of the enduring lesson of evidence-based medicine: that one should always ‘Trust the Evidence!’ for better health policy. (shrink)