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.     

Socially Constructed Technology

The concepts of omniscience and omnipotence are defined in 2 × 2 ordinal games, and implications for the optimal play of these games, when one player is omniscient or omnipotent and the other player is aware of his omniscience or omnipotence, are derived. Intuitively, omniscience allows a player to predict the strategy choice of an opponent in advance of play, and omnipotence allows a player, after initial strategy choices are made, to continue to move after the other player is forced to stop. Omniscience and its awareness by an opponent may hurt both players, but this problem can always be rectified if the other player is omniscient. This pathology can also be rectified if at least one of the two players is omnipotent, which can override the effects of omniscience. In some games, one player's omnipotence ‐ versus the other's ‐ helps him, whereas in other games the outcome induced does not depend on which player is omnipotent. Deducing whether a player is superior (omniscient or omnipotent) from the nature of his game playing alone raises several problems, however, suggesting the difficulty of devising tests for detecting superior ability in games.     

What's My Motivation? Video Games and Interpretative Performance

The interpretation of character motivations is a crucial part of the understanding of many narratives, including those found in video games. This interpretation can be complicated in video games by the player performing the role of a player‐character within the game narrative. Such performance finds the player making choices for the character and also interpreting the resulting character actions and their effect on the game's narrative. This can lead to interpretative difficulties for game narratives and their players: if a decision to act is made by the player, is it that the player's own imaginative reasons for acting warrant some narrative interpretations and exclude others? To answer this I argue that we need to investigate (a) the interactive ontology of video game narratives, (b) the notion of game playing as interpretative performance, and (c) the player‐character, an artifact through which performance is focused in narrative games. Doing so shows there to be at least two problems with the notion of the correct interpretation of narrative games. Neither of these problems entirely negates the normativity of game narratives, however, and so players are left with the problem of how they might decide which of the possible playings are warranted. I end by making some practical suggestions for the thoughtful and narratively interested game player.     

From reasonable preferences,via argumentation,to logic

This article demonstrates that typical restrictions which are imposed in dialogical logic in order to recover first-order logical consequence from a fragment of natural language argumentation are also forthcoming from preference profiles of boundedly rational players, provided that these players instantiate a specific player type and compute partial strategies. We present two structural rules, which are formulated similarly to closure rules for tableaux proofs that restrict players' strategies to a mapping between games in extensive forms (i.e., game trees) and proof trees. Both rules are motivated from players' preferences and limitations; they can therefore be viewed as being player-self-imposable. First-order logical consequence is thus shown to result from playing a specific type of argumentation game. The alignment of such games with the normative model of the Pragma-dialectical theory of argumentation is positively evaluated. But explicit rules to guarantee that the argumentation game instantiates first-order logical consequence have now become gratuitous, since their normative content arises directly from players' preferences and limitations. A similar naturalization for non-classical logics is discussed.     

Information and the complementarity game

Complementarity games are explorative games between two players. The deterministic rules of the game are known to both players. The first player freely chooses among a finite number of states of the game but tells nobody of this decision. The second player accesses the game only by primitive, symbolic input‐output interfaces. The task of the second player is to find out the unknown state by input‐output experiments. The logic resulting from this scenario resembles‐ quantum logic in many aspects. It is the empirical logic of choice for virtual realities.     

Is behavioral pro-sociality game-specific? Pro-social preference and expectations of pro-sociality

We observed the behaviors of the same people across five games – two prisoner’s dilemma games, a trust game (in which the subject took on the role of both truster and trustee), a dictator game, and a faith game – any pair of which was separated by an interval of several months to reduce potential carry-over effects, and found strong consistency in behaviors among these games. We also found consistency between the expectations of other players’ behaviors and the player’s own behavior across games. We further found that the consistent behavioral pro-sociality observed across different games was related to the general measures of pro-social value orientation and perceiving the game situations. These findings suggest that individual and cultural differences in game behaviors can reflect both the ways in which people perceive game situations and their general social preferences.     

Game Theory and Rational Decision

In its classical conception, game theory aspires to be a determinate decision theory for games, understood as elements of a structurally specified domain. Its aim is to determine for each game in the domain a complete solution to each player's decision problem, a solution valid for all real-world instantiations, regardless of context. “Permissiveness” would constrain the theory to designate as admissible for a player any conjecture consistent with the function's designation of admissible strategies for the other players. Given permissiveness and other appropriate constraints, solution sets must contain only Nash equilibria and at least one pure-strategy equilibrium, and there is no solution to games in which no symmetry invariant set of pure-strategy equilibria forms a Cartesian product. These results imply that the classical program is unrealizable. Moreover, the program is implicitly committed to permissiveness, through its common-knowledge assumptions and its commitment to equilibrium. The resulting incoherence deeply undermines the classical conception in a way that consolidates a long series of contextualist criticisms. This revised version was published online in July 2006 with corrections to the Cover Date.     

On fairness and learning agents in a bargaining model with uncertainty

The emergence of fair divisions in a repeated bargaining game is investigated in a computational model. Individuals of human societies often appeal to some norm of fairness in situations where an agreement over the division of a surplus is required. The employed framework consists of players alternating offers that describe possible ways to share a certain commodity. The players are allowed a limited number of offers to reach an agreement; if they fail to agree, the player who made the first offer, the lucky player, wins the whole lot at stake. Uncertainty is introduced in the process by randomly choosing the lucky player at the beginning of each iteration. In the experiments, the players acquired strategies by employing a variant of Q-learning, a reinforcement learning algorithm. Experiments were performed with different configurations of utility functions on the players’ preferences in taking actions in risky situations. Analysis of the results shows that the game theoretical model of a single shot of the bargaining game used in the experiments closely matches the outcomes obtained in the simulated framework, despite the differences in the quality of the players, who are assumed to be fully rational in the theoretical model. Learning agents that are timid toward risky situations manage to acquire strategies that lead to fair outcomes when playing against each other, but find themselves in a disadvantageous position when confronting bolder types.     

Why are online games so self‐involving: A social identity analysis of massively multiplayer online role‐playing games

This article investigates the ways in which players of massively multiplayer online role‐playing games (MMORPGs) internalize being a player into their self‐concept. In accordance with the social identity framework, we assume that being a player and being a member of a guild within the game can both shape the social identity of members. In two studies, we survey players inside or outside the MMORPG. Players are interviewed either at an interguild comparison level or at the more inclusive level of MMORPG players. Study 1 (n = 84) reveals favoritism for the in‐group guild in a within‐game context, and Study 2 (n = 200) shows that valuation of and identification with the in‐group are moderated by the interview context and the level of category inclusion: Inside the game, the guild is more valued and identification is emphasized. In contrast, valuation of and identification with MMORPG players is not influenced by the interview context. Together, by examining both valuation and identification processes, this research reveals that playing online games may be self‐involving because being a player, but also being a member of a guild, directly contribute to the social identity. Copyright © 2015 John Wiley & Sons, Ltd.     

The Intrinsic Quantum Nature of Nash Equilibrium Mixtures

In classical game theory the idea that players randomize between their actions according to a particular optimal probability distribution has always been viewed as puzzling. In this paper, we establish a fundamental connection between n-person normal form games and quantum mechanics (QM), which eliminates the conceptual problems of these random strategies. While the two theories have been regarded as distinct, our main theorem proves that if we do not give any other piece of information to a player in a game, than the payoff matrix—the axiom of “no-supplementary data” holds—then the state of mind of a rational player is algebraically isomorphic to a pure quantum state. The “no supplementary data” axiom is captured in a Lukasiewicz’s three-valued Kripke semantics wherein statements about whether a strategy or a belief of a player is rational are initially indeterminate i.e. neither true, nor false. As a corollary, we show that in a mixed Nash equilibrium, the knowledge structure of a player implies that probabilities must verify the standard “Born rule” postulate of QM. The puzzling “indifference condition” wherein each player must be rationally indifferent between all the pure actions of the support of his equilibrium strategy is resolved by his state of mind being described by a “quantum superposition” prior a player is asked to make a definite choice in a “measurement”. Finally, these results demonstrate that there is an intrinsic limitation to the predictions of game theory, on a par with the “irreducible randomness” of quantum physics.     

Video Games can Increase Creativity,but with Caveats

Although many studies have focused on aggression or visual-spatial cognition effects of video games, the problem-solving aspects have been largely ignored. This study sought to expand the existing literature on video game effects by focusing on a rarely-tested outcome: creative production. As a game with few rules and a high amount of player freedom, Minecraft exemplifies a game that fosters players’ abilities for creative expression. This experimental study included 352 undergraduates and it compared the effect of playing Minecraft on creativity measures compared to watching a TV show (passive control), a driving game (game control), and playing Minecraft with specific instructions (an instructional control). A within-subjects analysis found a significant correlation between trait creativity and game play habits. Between-groups experimental analyses showed that players randomly assigned to play Minecraft without instruction demonstrated significantly higher scores on post-game creativity measures compared to those who played Minecraft with instructions to “be creative,” those who played a driving game, or those who watched a television show. Results indicate that effects are not solely predicted by game mechanics, but also by the way the player plays.     

National security games

Issues that arise in using game theory to model national security problems are discussed, including positing nation-states as players, assuming that their decision makers act rationally and possess complete information, and modeling certain conflicts as two-person games. A generic two-person game called the Conflict Game, which captures strategic features of such variable-sum games as Chicken and Prisoners' Dilemma, is then analyzed. Unlike these classical games, however, the Conflict Game is a two-stage game in which each player can threaten to retaliate — and carry out this threat in the second stage — if its opponent chose noncooperation in the first stage.Conditions for the existence of different pure-strategy Nash equilibria, or stable outcomes, are found, and these results are extended to situations in which the players can select mixed strategies (i.e., make probabilistic threats or choices). Although the Conflict Game sheds light on the rational foundations underlying arms races, nuclear deterrence, and other strategic situations, more detailed assumptions are required to tie this generic game to specific conflicts.Steven J. Brams gratefully acknowledges the financial support of the National Science Foundation under Grant No. SES85-20154, the Sloan Foundation, and the Guggenheim Foundation.D. Marc Kilgour gratefully acknowledges the financial support of the Natural Sciences and Engineering Research Council of Canada under Grant No. A8974.     

How perceiving additional targets modifies teams’ tactical behavior during football small-sided games

This study aimed to measure how the change on targets information modifies teams’ tactical behavior during football small-sided games. 20 male senior professional players divided in 4 teams of 5 players participated in the study. Each team played two small-sided games, one with 2 official targets with goalkeeper and one with 6 small targets. Positional data of each player were recorded using a 15 Hz portable GPS. The distance between the centers of gravity (CG) of both team, the stretch index and the relative stretch index were measured and differences accessed via standardized differences, coefficient intervals and meta-analysis procedures. A moderate increase on the distance between the CG of each team and a small decrease on the stretch index and on the relative stretch index from 2 targets to the 6 targets games was observed. It was also identified that pitch location affected the interaction between teams. When the game was played in lateral corridors or defensive sectors, the differences between game conditions increased. Emphasizing the information for attacking team to shoot at goal, by manipulating the number of targets constrained tactical behavior of teams. The amplification of specific information on small-sided games can help coaches to promote players and teams’ emergent adapted behaviors.     

Message Exchange Games in Strategic Contexts

When two people engage in a conversation, knowingly or unknowingly, they are playing a game. Players of such games have diverse objectives, or winning conditions: an applicant trying to convince her potential employer of her eligibility over that of a competitor, a prosecutor trying to convict a defendant, a politician trying to convince an electorate in a political debate, and so on. We argue that infinitary games offer a natural model for many structural characteristics of such conversations. We call such games message exchange games, and we compare them to existing game theoretic frameworks used in linguistics—for example, signaling games—and show that message exchange games are needed to handle non-cooperative conversation. In this paper, we concentrate on conversational games where players’ interests are opposed. We provide a taxonomy of conversations based on their winning conditions, and we investigate some essential features of winning conditions like consistency and what we call rhetorical cooperativity. We show that these features make our games decomposition sensitive, a property we define formally in the paper. We show that this property has far-reaching implications for the existence of winning strategies and their complexity. There is a class of winning conditions (decomposition invariant winning conditions) for which message exchange games are equivalent to Banach- Mazur games, which have been extensively studied and enjoy nice topological results. But decomposition sensitive goals are much more the norm and much more interesting linguistically and philosophically.     

Manipulating Games by Sharing Information

We address the issue of manipulating games through communication. In the specific setting we consider (a variation of Boolean games), we assume there is some set of environment variables, the values of which are not directly accessible to players; the players have their own beliefs about these variables, and make decisions about what actions to perform based on these beliefs. The communication we consider takes the form of (truthful) announcements about the values of some environment variables; the effect of an announcement is the modification of the beliefs of the players who hear the announcement so that they accurately reflect the values of the announced variables. By choosing announcements appropriately, it is possible to perturb the game away from certain outcomes and towards others. We specifically focus on the issue of stabilisation: making announcements that transform a game from having no stable states to one that has stable configurations.     

Three ancient problems solved by using the game theory logic based on the Shapley value

The ancient problems of bankruptcy, contested garment, and rights arbitration have generated many studies, debates, and controversy. The objective of this paper is to show that the Shapley value from game theory, measuring the power of each player in a game, may be consistently applied for getting the general one-step solution of all these three problems viewed as n-person games. The decision making is based on the same tool, namely the game theory logic based on the use of the Shapley value, but the specific games involved are slightly different in each problem. The kind of claims of the players, the relationship between the given claims and the given resources available, and the particular way of calculating the generalized characteristic function of the game determine the specific type of game which has to be solved in each of the three ancient problems mentioned. The iterative use of the Shapley value may also justify the well-known Aumann–Maschler step-by-step procedure for solving the bankruptcy problem.

     

Play as co‐created narrative in computer game consumption: The hero's journey in Warcraft III

Computer games are now a significant consumption activity in consumer culture. Informed by interdisciplinary studies and drawing on data from in‐depth interviews with players of the Warcraft III computer game, we explore the relationship between play and storytelling during digital play. Understanding that such play is determined by systems of game rules and that computer game characters and settings are capable of conveying cultural meanings to players, we found that the rules of play in computer games can be designed in ways that encourage consumers to co‐create meaningful story plots derived from their knowledge of myth and fiction. In the case of Warcraft, these plots resembled the archetypal plot of the hero's journey. We conclude that computer games immerse consumers in a form of playful consumption that engages them in memorialised, co‐authored storytelling. Copyright © 2012 John Wiley & Sons, Ltd.     

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.