多值逻辑与语义赋值博弈

文章在扩展博弈上,给出了多值逻辑的语义赋值博弈的一般框架,避免了博弈者在多值逻辑的语义博弈中声明无穷对象的问题;然后通过Eloise赢的策略定义博弈的语义概念——赋值,证明了多值逻辑的博弈语义与Tarski语义是等价的;最后,根据语义赋值博弈框架对经典逻辑进行了博弈化。     

Hard and Soft Preparation Sets in Boolean Games

A fundamental problem in game theory is the possibility of reaching equilibrium outcomes with undesirable properties, e.g., inefficiency. The economics literature abounds with models that attempt to modify games in order to avoid such undesirable properties, for example through the use of subsidies and taxation, or by allowing players to undergo a bargaining phase before their decision. In this paper, we consider the effect of such transformations in Boolean games with costs, where players control propositional variables that they can set to true or false, and are primarily motivated to seek the satisfaction of some goal formula, while secondarily motivated to minimise the costs of their actions. We adopt (pure) preparation sets (prep sets) as our basic solution concept. A preparation set is a set of outcomes that contains for every player at least one best response to every outcome in the set. Prep sets are well-suited to the analysis of Boolean games, because we can naturally represent prep sets as propositional formulas, which in turn allows us to refer to prep formulas. The preference structure of Boolean games with costs makes it possible to distinguish between hard and soft prep sets. The hard prep sets of a game are sets of valuations that would be prep sets in that game no matter what the cost function of the game was. The properties defined by hard prep sets typically relate to goal-seeking behaviour, and as such these properties cannot be eliminated from games by, for example, taxation or subsidies. In contrast, soft prep sets can be eliminated by an appropriate system of incentives. Besides considering what can happen in a game by unrestricted manipulation of players’ cost function, we also investigate several mechanisms that allow groups of players to form coalitions and eliminate undesirable outcomes from the game, even when taxes or subsidies are not a possibility.     

A New Game Equivalence,its Logic and Algebra

We present a new notion of game equivalence that captures basic powers of interacting players. We provide a representation theorem, a complete logic, and a new game algebra for basic powers. In doing so, we establish connections with imperfect information games and epistemic logic. We also identify some new open problems concerning logic and games.

     

Keep ‘hoping’ for rationality: a solution to the backward induction paradox

We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on (doxastic) plausibility models. Similarly to other epistemic statements (e.g. negations of Moore sentences and of Muddy Children announcements), dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we “simulate” the play of a game as a succession of dynamic updates of the original plausibility model: the epistemic situation when a given node is reached can be thought of as the result of a joint act of learning (via public announcements) that the node is reached. We then use the notion of “stable belief”, i.e. belief that is preserved during the play of the game, in order to give an epistemic condition for backward induction: rationality and common knowledge of stable belief in rationality. This condition is weaker than Aumann’s and compatible with the implicit assumptions (the “epistemic openness of the future”) underlying Stalnaker’s criticism of Aumann’s proof. The “dynamic” nature of our concept of rationality explains why our condition avoids the apparent circularity of the “backward induction paradox”: it is consistent to (continue to) believe in a player’s rationality after updating with his irrationality.     

Subgames within Large Games and the Heuristic of Imitation

We study repeated normal form games where the number of players is large. We argue that it is interesting to look at such games as being divided into subgames, each of which we call a neighbourhood. The structure of such a game is given by a graph G whose nodes are players and edges denote visibility. The neighbourhoods are maximal cliques in G. The game proceeds in rounds where in each round the players of every clique X of G play a strategic form game among each other. A player at a node v strategises based on what she can observe, i.e., the strategies and the outcomes in the previous round of the players at vertices adjacent to v. Based on this, the player may switch strategies in the same neighbourhood, or migrate to another neighbourhood. We are interested in addressing questions regarding the eventual stability of such games. We incrementally impose constraints on the ‘types’ of the players. First, we look at players who are unconstrained in their strategising abilities, in that, players who may use unbounded memory. We then consider the case of memoryless players. We show that in both these cases the eventual stability of the game can be characterised in terms of potentials. We then introduce a simple modal logic in which the types of the players can be specified. We show that when the players play according to these specified types, it can be effectively decided whether the game stabilises. Finally, we look at the important heuristic of imitation. Simple imitative strategies can be specified in the logic introduced by us. We show that in a population of optimisers and imitators, we can decide how ‘worse-off’ the imitators are by playing imitative strategies rather than optimal ones.     

Selling Gender: Associations of Box Art Representation of Female Characters With Sales for Teen- and Mature-rated Video Games

Content analysis of video games has consistently shown that women are portrayed much less frequently than men and in subordinate roles, often in “hypersexualized” ways. However, the relationship between portrayal of female characters and videogame sales has not previously been studied. In order to assess the cultural influence of video games on players, it is important to weight differently those games seen by the majority of players (in the millions), rather than a random sample of all games, many of which are seen by only a few thousand people. Box art adorning the front of video game boxes is a form of advertising seen by most game customers prior to purchase and should therefore predict sales if indeed particular depictions of female and male characters influence sales. Using a sample of 399 box art cases from games with ESRB ratings of Teen or Mature released in the US during the period of 2005 through 2010, this study shows that sales were positively related to sexualization of non-central female characters among cases with women present. In contrast, sales were negatively related to the presence of any central female characters (sexualized or non-sexualized) or the presence of female characters without male characters present. These findings suggest there is an economic motive for the marginalization and sexualization of women in video game box art, and that there is greater audience exposure to these stereotypical depictions than to alternative depictions because of their positive relationship to sales.     

Prosocial video games reduce aggressive cognitions

Previous research has shown that playing violent video games increased aggressive tendencies. However, as pointed out by the General Learning Model (GLM) [Buckley, K. E., & Anderson, C. A. (2006). A theoretical model of the effects and consequences of playing video games. In: P. Vorderer & J. Bryant (Eds.), Playing video games motives responses and consequences (pp. 363-378). Mahwah, NJ: Lawrence Erlbaum], depending on their content, video games do not inevitably increase but may also decrease aggressive responses. Accordingly, the present research tested the hypothesis that playing prosocial video games decreases aggressive cognitions. In fact, playing a prosocial (relative to a neutral) video game reduced the hostile expectation bias (Experiment 1) and decreased the accessibility of antisocial thoughts (Experiment 2). Thus, these results lend credence to GLMs assumption that the effects of video game exposure depend to a great extent on the content of the game played.     

Friends, fun, frustration and fantasy: Child motivations for video game play

Although a considerable amount of attention has examined potential positive and negative consequences of video game play in children, relatively little research has examined children’s motivations for using games. The current study hopes to address this gap in the literature by examining children’s motivations for video game play in a large sample of youth (n = 1254). Results indicated that video game use was common, and often a social activity. Social play was mainly predicted by motivations related to socialization, fun/challenge and current stress level. Preference for violent games was more common in males and predicted by fun/challenge motivations and beliefs such games could be cathartic for stress. Children with clinically elevated levels of depressive and ADHD symptoms did not play more games, or more violent games, but were more inclined to endorse catharsis motivations for video game use. Results from this study provide understanding of what motivates children to use games, and how the motivations of children with symptoms of psychosocial problems (as identified via subscales of the Pediatric Symptom Checklist) may differ from others.     

A Characterization of von Neumann Games in Terms of Memory

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.     

Transition semantics: the dynamics of dependence logic

We examine the relationship between dependence logic and game logics. A variant of dynamic game logic, called Transition Logic, is developed, and we show that its relationship with dependence logic is comparable to the one between first-order logic and dynamic game logic discussed by van Benthem. This suggests a new perspective on the interpretation of dependence logic formulas, in terms of assertions about reachability in games of imperfect information against Nature. We then capitalize on this intuition by developing expressively equivalent variants of dependence logic in which this interpretation is taken to the foreground.     

Gender and Race Representation in Casual Games

This paper examines gender and race representation in casual games through content analysis. Study 1 looks at gender and race representation in a random sample (N?=?200) of casual games retrieved from the websites of the largest five casual game distributors. Study 2 looks at the most popular games on websites of the same five multinational distributors (N?=?54) and analyzes how primary characters are portrayed in terms of appearance and personality. Females are overly represented as primary characters but chi-square analyses indicate no significant differences between sexes in terms of how they are portrayed: of note, neither males nor females are depicted in a sexual manner. These results conflict with previous studies of gender representation in game characters: this paper suggests that sampling methodology and the relatively new trend of casual games excluded this subset of games from prior research. Implications are discussed using a social cognitive framework.     

On the Epistemic Foundation for Iterated Weak Dominance: An Analysis in a Logic of Individual and Collective attitudes

This paper proposes a logical framework for representing static and dynamic properties of different kinds of individual and collective attitudes. A complete axiomatization as well as a decidability result for the logic are given. The logic is applied to game theory by providing a formal analysis of the epistemic conditions of iterated deletion of weakly dominated strategies (IDWDS), or iterated weak dominance for short. The main difference between the analysis of the epistemic conditions of iterated weak dominance given in this paper and other analysis is that we use a semi-qualitative approach to uncertainty based on the notion of plausibility first introduced by Spohn, whereas other analysis are based on a quantitative representation of uncertainty in terms of probabilities.     

T-ECHO: model of decision making to explain behaviour in experiments and simulations under time pressure

Objectives: To explain the mechanisms of decision making in sports. The ‘Decision Field Theory’ by Townsend and Busemeyer ((1995). Dynamic representation of decision-making. In R. F. Port & T. von Gelder (Eds.), Mind as motion (p. 101). Cambridge: MIT Press) was applied to a ball game situation.Design/Method: A situation in basketball was simulated and used in two experiments. The simulation was realized using a local neural network (Behav. Brain Sci., 12 (1989) 435) and was based on a decision model T-ECHO (Tactical decision — Explanatory Coherence by Harmonic Optimization). Experiment 1 (n=53) tested decisions in a video-based laboratory decision task. Learning took place by watching video clips and was significantly better for implicit and explicit groups than for a control group. Experiment 2 (n=34) replicated the results by using incidental and intentional learning groups. Finally, comparisons between behaviour output of neural networks and participants' decision making were made.Results: A good fit between simulation and participant behaviour was shown. Time pressure explained preference reversals from a dynamic viewpoint.Conclusions: The use of simulations and decision experiments lead to a fruitful way to understand the mechanisms of decision making in ball games.     

Game outcome and elite Japanese women’s field hockey player’s experience of emotions and stress

Objectives: To measure the effects of game outcome on pleasant and unpleasant emotions and stress during elite-level competition.Design: Quasi-experimental repeated pre- and post-game measurement in a field setting.Methods: Participants were 16 members of the Japanese women’s field hockey team playing a world cup preliminary qualifying tournament in Trinidad. Players completed the Tension and Effort Stress Inventory (TESI), a measure of emotion and stress, at the seven games of the tournament (five wins, two losses).Results: The pattern of emotions after game 1 (a loss) were in sharp contrast to the results from the other six games (five wins, one loss). When compared to other games, significant increases in anxiety, humiliation and excitement pre- to post-game 1 were found, as were significantly higher scores in sullenness and lower scores in relaxation post-game 1. No significant decreases in external tension stress and somatic tension and effort stress pre- to post-game 1 were found. For the other games, athletes were significantly more relaxed and excited after games, increasing with each game in the tournament. Also, the unpleasant emotion and stress results, associated with game 1, significantly diminished as the team progressed to the tournament final. There was no evidence for a simple win/loss difference on post-game emotions and stress.Conclusions: The relationship between game outcome and emotional response is not straightforward. Other factors, such as cognition, may also play a role.     

Self-concept as a risky driver: Mediating the relationship between racing video games and on-road driving violations in a community-based sample

PurposeThe mediating relationship of self-conceptions as a risky driver on self-reported driving violations was examined for players of “drive’em up” and “circuit” racing video games using an Internet survey of automobile and racing club members. Structural equation modelling (SEM) tested Fischer et al. (2012) extended socio-cognitive model on the effects of risk-glorifying media on cognitions and actions.MethodAn Internet questionnaire was developed and relied upon validated instruments or questions derived from previous surveys. Driver club members were asked about: (1) their frequency of video game playing, (2) self-perceptions as a risky driver and (3) self-reported driving violations. SEM was performed to examine mediating effects of racing video game playing on self-reported driving violations.ResultsPlaying “drive‘em up” video games positively predicted risky self-concept (β = .15, t = 2.26), which in turn, positively predicted driving violations (β = .73, t = 8.63), while playing “circuit racing” games did not predict risky self-concept, although risky self-concept did predict driving violations (β = .72, t = 8.67).ConclusionsSelf-concept as a risky driver mediated the relationship between racing video game playing and self-reported driving violations for “drive’em up”, but not for “circuit racing” video games. These findings are congruent with Fischer and colleagues’ experimental model that self-concept as a reckless driver mediated the relationship between racing video game playing for “drive’em up”, but not for “circuit racing” games and risk-taking behavior in a video of road traffic scenarios.     

Rationality and indeterminate probabilities

We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required. Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with our describing a world that plausibly has indeterminate chances. Rationality requires a certain alignment of your credences with corresponding hypotheses about the chances. Thus, if you hypothesize the chances to be indeterminate, your will inherit their indeterminacy in your corresponding credences. Our third argument is motivated by a dilemma. Epistemic rationality requires you to stay open-minded about contingent matters about which your evidence has not definitively legislated. Practical rationality requires you to be able to act decisively at least sometimes. These requirements can conflict with each other-for thanks to your open-mindedness, some of your options may have undefined expected utility, and if you are choosing among them, decision theory has no advice to give you. Such an option is playing Nover and Hájek??s Pasadena Game, and indeed any option for which there is a positive probability of playing the Pasadena Game. You can serve both masters, epistemic rationality and practical rationality, with an indeterminate credence to the prospect of playing the Pasadena game. You serve epistemic rationality by making your upper probability positive-it ensures that you are open-minded. You serve practical rationality by making your lower probability 0-it provides guidance to your decision-making. No sharp credence could do both.     

Having it Both Ways: Consciousness, Unique Not Otherworldly

I respond to Chalmers’ (2006, 2010) objection to the Phenomenal Concept Strategy (PCS) by showing that his objection is faced with a dilemma that ultimately undercuts its force. Chalmers argues that no version of PCS can posit psychological features that are both physically explicable and capable of explaining our epistemic situation. In response, I show that what Chalmers calls ‘our epistemic situation’ admits either of a phenomenal or of a topic-neutral characterization, neither of which supports Chalmers’ objection. On the one hand, if our epistemic situation is characterized phenomenally, then Chalmers’ demand that PCS should explain our epistemic situation is misplaced. PCS can explain our epistemic situation only if there is a reductive explanation of consciousness. But according to PCS, no reductive explanation of consciousness can be given. On the other hand, if our epistemic situation is characterized topic-neutrally, then PCS is not only physically explicable, but it also explains our epistemic situation. Either way, PCS is safe.     

Effects of Violent Video Games on Aggressive Behavior: Potential Sex Differences

Evidence of the effects of playing violent video games on subsequent aggression has been mixed. This study examined how playing a violent video game affected levels of aggression displayed in a laboratory. A total of 43 undergraduate students (22 men and 21 women) were randomly assigned to play either a violent (Mortal Kombat) or nonviolent (PGA Tournament Golf) video game for 10 min. Then they competed with a confederate in a reaction time task that allowed for provocation and retaliation. Punishment levels set by participants for their opponents served as the measure of aggression. The results confirmed our hypothesis that playing the violent game would result in more aggression than would playing the nonviolent game. In addition, a Game × Sex interaction showed that this effect was larger for men than for women. Findings are discussed in light of potential differences in aggressive style between men and women.     

Discovery in complex adaptive systems

The distinction between ontological ground-truth phenomena and epistemic measurements of those phenomena is discussed and analyzed in the context of complex cognitive systems research. A common style of computational simulation is identified as a Dissect-the-Simulation motif. In this style, a model of cognition is designed and when it generally mimics some cognitive behavior, its own ontic processes (which are fully accessible because it is a simulation) are proposed as potential ontic processes inside actual human cognition. I propose here a second style of modeling, which might be called Measure-the-Simulation. In this style, simulated versions of coarse-grained epistemic measurements are performed on the model with the intent of discovering how those epistemic measurements themselves may transform the actual ontic data, and thus induce a variety of mis-categorizations of phenomena. When our epistemic measurements are better understood, such mis-categorizations can perhaps be avoided. As a proof of concept, Conway’s Game of Life is analyzed and measured with two different types of coarse-grained epistemic measures. Dramatic differences are identified in how a binary coarse-graining, versus a graded coarse-graining, transforms the discovery process for activity patterns on the lattice of this cellular automaton.     

Changing Types: Information Dynamics for Qualitative Type Spaces

Many different approaches to describing the players’ knowledge and beliefs can be found in the literature on the epistemic foundations of game theory. We focus here on non-probabilistic approaches. The two most prominent are the so-called Kripkeor Aumann- structures and knowledge structures (non-probabilistic variants of Harsanyi type spaces). Much of the recent work on Kripke structures has focused on dynamic extensions and simple ways of incorporating these. We argue that many of these ideas can be applied to knowledge structures as well. Our main result characterizes precisely when one type can be transformed into another type by a specific type of information update. Our work in this paper suggest that it would be interesting to pursue a theory of “information dynamics” for knowledge structures (and eventually Harsanyi type spaces).