Game Playing

We introduce a new isomorphic quantity for Banach spaces, the index ΘX , based on finite convex coverings of the unit ball. This index is closely related to the asymptotic moduli of uniform convexity and uniform smoothness, so that it can be calculated for several classical Banach spaces.

The polymorphic fungus Candida albicans can live as an aggressive pathogen that causes a wide variety of diseases in humans. Host resistance against these infections is mediated predominantly by phagocytes, namely neutrophils and macrophages. This report provides two game theoretical models of ingested Candida albicans cells in macrophages. Two strategies are available for each pathogenic yeast cell: avoiding lysis transiently (called silencing) or forming hyphae and escaping (called piercing because the macrophage is pierced from inside). In dependence on parameter values, two different outcomes can be derived from the model: when the difference of the costs of the two strategies is low, all fungal cells inside a macrophage will play the piercing strategy, while in the high-cost case, a mixed population of piercing and silencing cells is the only stable solution. Further, the role of the SAP gene family encoding secreted proteinases and the Sap proteins is investigated with the help of known studies and is put in relation to the costs of the strategies, the most important parameter of this model. Our results are in agreement with wet-lab results presented by other groups and the model parameters can be estimated from experimental data.

We study a quantum version of a penny flip game played using control parameters of the Hamiltonian in the Heisenberg model. Moreover, we extend this game by introducing auxiliary spins which can be used to alter the behaviour of the system. We show that a player aware of the complex structure of the system used to implement the game can use this knowledge to gain higher mean payoff.

We study a quantum version of a penny flip game played using control parameters of the Hamiltonian in the Heisenberg model. Moreover, we extend this game by introducing auxiliary spins which can be used to alter the behaviour of the system. We show that a player aware of the complex structure of the system used to implement the game can use this knowledge to gain higher mean payoff.

On 24. i. d4 Black has the very strong reply 24 ... J:Id4. But now the devastated residence of the white king creates a painful impression. 24 .. Jlh3 25.tbg3 'fid5 26.St.b6 St.e5 13 ... b5 I sensed that it was on the solution to this particu lar problem that if not everything, then a great deal , depended. I thought for almost an hour, and found a refutation ... 14.-tfG! ..tf6 No better is 14 ... gf6 15.f5! b4 16. t2J e2, when Black cannot maintain his pawn at e6. If Black had attempted to repair the basic defect of his position, and had defended his light-squared bishop by 15 ... l:tac8, then White had prepared 16.e5! .!';lfd8 17. 'ii c5!, andif17 ... .i g2, then 18. 'ii gl !

Improving teaching in universities is a worthy aim, but how will the Teaching Excellence Framework recognise and reward quality? Marty Chamberlain looks at how teaching is currently assessed. Peer review of teaching tends to operate superficially when it is decoupled from formal staff development and employee feedback processes. Further complicating matters, in professions underpinned by tacit knowledge, experts tend to rely on personal and often idiosyncratic judgements about competency.

Central banks, in executing monetary policy, while pursuing traditional objectives, such as the control of inflation, may try also to promote financial stability. In this paper, we explore a simple monetary policy game played between the central bank and the financial sector. The ...

Engagement with computer games causes children and adolescent users to spend a substantial amount of time at sedentary game playing activity. We hypothesise that this engagement can be leveraged to motivate users to increase their amount of physical activity. In this paper, we present a novel approach for designing computer games, according to which the users' physical activity reinforces their game character. This way the users are seamlessly motivated to perform physical activity while maintaining their enjoyment of playing the game.

A theory of heuristic game tree search and evaluation functions for estimating minimax values is developed. The result is quite different from the traditional minimsx approach to game playing, and it leads to product-propagation rules for backing up values when subpositions in the game are independent. In this theory Nau's paradox is avoided and deeper searching leads to better moves if one has reasonable evaluation functions.

The Layered Pareto Coevolution Archive (LAPCA) was recently proposed as an effective Coevolutionary Memory (CM) which, under certain assumptions, approximates monotonic progress in coevolution. In this paper, a technique is developed that interfaces the LAPCA algorithm with NeuroEvolution of Augmenting Topologies (NEAT), a method to evolve neural networks with demonstrated efficiency in game playing domains. In addition, the behavior of LAPCA is analyzed for the first time in a complex game-playing domain: evolving neural network controllers for the game Pong. The technique is shown to keep the total number of evaluations in the order of those required by NEAT, making it applicable to complex domains. Pong players evolved with a LAPCA and with the Hall of Fame (HOF) perform equally well, but the LAPCA is shown to require significantly less space than the HOF. Therefore, combining NEAT and LAPCA is found to be an effective approach to coevolution.

Discrete optimization problems (DOPs) arise in various applications such as planning, scheduling, computer aided design, robotics, game playing and constraint directed reasoning. Often, a DOP is formulated in terms of nding a (minimum cost) solution path in a graph from an initial node to a goal node and solved by graph/tree search methods such as branch-and-bound and dynamic programming. Availability of parallel computers has created substantial interest in exploring the use of parallel processing for solving discrete optimization problems. This article provides an overview of parallel search algorithms for solving discrete optimization problems. 1 Introduction. Discrete optimization problems (DOPs) arise in various applications such as planning, scheduling, computer aided design, robotics, game playing and constraint directed reasoning. Formally, a DOP can be stated as follows : Given a nite discrete set X and a function f(x) de ned on the elements of X, nd an optimal element x opt , such that, f(x opt ) = minff(x)=x Xg. In

We propose the use of a new design-first approach called Problem Stereotypes and Solution Frameworks, for teaching CS1 and CS2. A problem stereotype is a category of problems that can be solved using similar techniques. A solution framework is a typical solution to a problem, parts of which can be reused to solve other problems of this stereotype. Students are introduced to a stereotype through a selection of related problems, and common features among these are identified. Homework problems are selected from the same stereotype, with students expected to follow the "recipe" provided by the given examples to generate their own solutions. Using this approach reduces the stress level for beginner students, and prevents them falling prey to the "CS is HARD" myth. We present the results of our experience with this approach in two introductory classes and an upper-division Artificial Intelligence (AI) class at SUNY Brockport.

Writing puzzle-solving and game-playing programs can generate excitement in students. Such programs are usually assigned as projects in an AI course. These are major software projects expected to be completed by students who usually have had no prior instruction in SE concepts. Often, these are required to be implemented in languages and paradigms in which the students have minimal expertise resulting in frustration among students as well as faculty. We discuss a "problem stereotypes and solution frameworks" approach to teaching CS1/2 (most likely prerequisites to AI) which ensures that the students have exposure to a judicious amount of SE methodology. We extend this approach to teaching an AI course by identifying the State-Space-Search and Two-Person-Zero-Sum-Game stereotypes. We have developed a solution framework (consisting of Java abstract classes) that can be used to solve typical problems falling into these stereotypes. Using the framework, a student will be able to develop a puzzle-solver or a game-player program mainly by focusing on problemspecific details. Preliminary experimentation has revealed that the students found it easy to use the framework and were successful in developing puzzle-solvers. We believe that our approach based on reusable software infrastructure enables students to develop interesting programs early in their undergraduate careers.

We present a model of a purchaser of electricity in Norway, bidding into a wholesale electricity pool market that operates a day ahead of dispatch. The purchaser must arrange purchase for an uncertain demand that occurs the following day. Deviations from the day-ahead purchase are bought in a secondary market at a price that differs from the day-ahead price by virtue of regulating offers submitted by generators. Under an assumption that arbitrageurs are absent in these markets, we study conditions under which the purchaser should bid their expected demand, and examine the two-period game played between a single generator and purchaser in the presence of a competitive fringe. In all our models it is found that purchasers have an incentive to underbid their expected demand, and so the day-ahead prices will be below expected real-time prices. We also derive conditions on the optimal demand curve that purchasers should bid if the behavior of the other participants is unknown, but can be modeled by a market distribution function.

In this paper, we introduce the concept of generalized pseudo-base in generalized topological spaces, and using this concept, we study the product of g-Volterra space and weakly g-Volterra space in generalized topological spaces. In addition, we study the product of g-Baire space with g-Volterra space in generalized topological spaces.

In a small-scale study we have analyzed the genderscripts of the toys of three Dutch toy producing companies and we have interviewed owners and directors of these companies. We found large differences in the 'genderedness' of the games they were producing. We have found explanations for these differences in differences in the (feminist) values that the directors of these companies had. Moreover, we have interviewed eight girls (9-13 years old) on their game playing behaviour and observed them while they played masculine connotated games, to see how they dealt with the genderedness of these games. Indeed, although gender specific games may play an important part in the gendering of children and computer games may help to present computer science as something 'for boys', children also have some agency in dealing with the dominant discourses around gendered games.

We prove that if X is a subspace of Lp (2 < p < ∞), then either X embeds isomorphically into ℓp ⊕ ℓ2 or X contains a subspace Y, which is isomorphic to ℓp(ℓ2). We also give an intrinsic characterization of when X embeds into ℓp ⊕ℓ2 in terms of weakly null trees in X or, equivalently, in terms of the "infinite asymptotic game" played in X. This solves problems concerning small subspaces of Lp originating in the 1970's. The techniques used were developed over several decades, the most recent being that of weakly null trees developed in the 2000's.

Alice Mitchell Ultralab, Anglia Ruskin University Bishop Hall Lane, Chelmsford, CM1 1SG, UK e-mail: [email protected], web page : http://www.ultralab.net ... Paolo Inchingolo, Federica Vatta DEEI, University of Trieste Via Valerio 10, 34127 Trieste, Italy e-mail: paolo.inchingolo@ ...

If you would like to make any comments on this working paper please contact the author directly within 90 days of publication. Disclaimer This article has been written as part of a series of publications issued from the Centre for Tax System Integrity. The views contained in this article are representative of the author only. The publishing of this article does not constitute an endorsement of or any other expression of opinion by the Australian National University or the Commissioner of Taxation of the author's opinion. The Australian National University and the Commissioner of Taxation do not accept any loss, damage or injury howsoever arising that may result from this article. This article does not constitute a public or private ruling within the meaning of the Taxation Administration Act 1953, nor is it an advance opinion of the Commissioner of Taxation. iii THE CENTRE FOR TAX SYSTEM INTEGRITY WORKING PAPERS The Centre for Tax System Integrity (CTSI) is a specialised research unit set up as a partnership between the Australian National University (ANU) and the Australian Taxation Office (Tax Office) to extend our understanding of how and why cooperation and contestation occur within the tax system. This series of working papers is designed to bring the research of the Centre for Tax System Integrity to as wide an audience as possible and to promote discussion among researchers, academics and practitioners both nationally and internationally on taxation compliance. The working papers are selected with three criteria in mind: (1) to share knowledge, experience and preliminary findings from research projects; (2) to provide an outlet for policy focused research and discussion papers; and (3) to give ready access to previews of papers destined for publication in academic journals, edited collections, or research monographs.

We introduce a game of complete information with multiple principals and multiple agents. Each agent makes a decision that can affect the payoffs of all principals. Each principal offers monetary transfers to each agent conditional on the action taken by the agent. We characterize pure-strategy equilibria and we provide conditionsin terms of game balancedness-for the existence of an equilibrium with an efficient outcome. Games played through agents display a type of strategic inefficiency which is absent when either there is a unique principal or there is a unique agent.

Evolutionary theorizing has a long tradition in economics. Only recently has this approach been brought into the framework of noncooperative game theory. Evolutionary game theory studies the robustness of strategic behavior with respect to evolutionary forces in the context of games played many times in large populations of boundedly rational agents. This new strand in economic theory has lead to new predictions and opened up doors to other social sciences. The discussion will be focused on the following questions: What distinguishes the evolutionary approach from the rationalistic? What are the most important …ndings in evolutionary game theory so far? What are the next challenges for evolutionary game theory in economics? Doc: esem.tex ¤ This essay is composed of notes for an invited talk held 30 August 1997 at the Econometric Society European Meeting in Toulouse. I am grateful for comments from Eric van Damme and Fernando Vega-Redondo to an early draft.

The main objective of this paper is to provide an empirical assessment of the production process in a basketball team. We estimate a logit model in which the output produced by a team is the game outcome (win or loss) and the inputs are those play characteristics that impact on that outcome. From the results obtained it is clear that, on average, there is a substantial difference between the impact of each play characteristic on a basketball team's winning probability and that probability varies as the quality/quantity of the inputs used changes, albeit not proportionally.

Abstract. We introduce a computational method for semi-automatical detecting fortresses in the game of chess. It is based on computer heuristic search and can be easily used with any state-of-the-art chess program. We also demonstrate a method for avoiding fortresses and show how to find a break-through plan when one exists. Although the paper is not concerned with the question whether it is practical or not to implement the method within the state-of-the-art chess programs, the method can be useful, for example, in correspondence chess or in composing chess studies, where a human-computer interaction is of great importance, and the time available is significantly longer than in ordinary chess competitions.

In Artificial Intelligence (AI), there exist formalised approaches and algorithms for general problem solving. These approaches address problems that require combinatorial search among alternatives, such as planning, scheduling, or playing of games like chess. ...

Agents learning to act autonomously in realworld domains must acquire a model of the dynamics of the domain in which they operate. Learning domain dynamics can be challenging, especially where an agent only has partial access to the world state, and/or noisy external sensors. Even in standard STRIPS domains, existing approaches cannot learn from noisy, incomplete observations typical of real-world domains. We propose a method which learns STRIPS action models in such domains, by decomposing the problem into first learning a transition function between states in the form of a set of classifiers, and then deriving explicit STRIPS rules from the classifiers' parameters. We evaluate our approach on simulated standard planning domains from the International Planning Competition, and show that it learns useful domain descriptions from noisy, incomplete observations.

The game board is represented by an array `b[]` containing characters '0' to '9' representing the positions on the Tic-Tac-Toe grid. 2. Functions: ➢ `printboard()`: Prints the current state of the Tic-Tac-Toe board. ➢ `checkwin()`: Checks if any player has won the game based on the current board configuration. ➢ `aiMove()`: Represents the AI (Player 2) making a random move by generating a random number between 1 and 9. 3. Main Function: ➢ The `main()` function controls the flow of the game. ➢ It alternates between Player 1 and Player 2 (where Player 2 is the AI). ➢ Each player is prompted to make a move by entering a number corresponding to an empty position on the board. ➢ Player moves are denoted by 'X' and AI moves by 'O'. ➢ The game continues until there's a win, a draw, or an invalid move.

This article focuses on the techniques of evolutionary computation for generating players performing tasks cooperatively. However, in using evolutionary computation for generating players performing tasks cooperatively, one faces fundamental and difficult decisions, including the one regarding the so-called credit assignment problem. We believe that there are some correlations among design decisions, and therefore a comprehensive evaluation of them is essential. We first list three fundamental decisions and possible options in each decision in designing methods for evolving a cooperative team. We find that there are 18 typical combinations available. Then we describe the ultimately simplified soccer game played on a one-dimensional field as a testbed for a comprehensive evaluation for these 18 candidate methods. It has been shown that some methods perform well, while there are complex correlations among design decisions. Also, further analysis has shown that cooperative behavior can be evolved, and is a necessary requirement for the teams to perform well even in such a simple game.

Several approaches have been developed for answering users' specific questions about AI behavior and for assessing their core functionality in terms of primitive executable actions. However, the problem of summarizing an AI agent's broad capabilities for a user is comparatively new. This paper presents an algorithm for discovering from scratch the suite of high-level "capabilities" that an AI system with arbitrary internal planning algorithms/policies can perform. It computes conditions describing the applicability and effects of these capabilities in user-interpretable terms. Starting from a set of user-interpretable state properties, an AI agent, and a simulator that the agent can interact with, our algorithm returns a set of high-level capabilities with their parameterized descriptions. Empirical evaluation on several game-based scenarios shows that this approach efficiently learns descriptions of various types of AI agents in deterministic, fully observable settings. User studies show that such descriptions are easier to understand and reason with than the agent's primitive actions.

While current General Game Playing (GGP) systems facilitate useful research in Artificial Intelligence (AI) for game-playing, they are often somewhat specialized and computationally inefficient. In this paper, we describe an initial version of a "ludemic" general game system called Ludii, which has the potential to provide an efficient tool for AI researchers as well game designers, historians, educators and practitioners in related fields. Ludii defines games as structures of ludemes, i.e. highlevel, easily understandable game concepts. We establish the foundations of Ludii by outlining its main benefits: generality, extensibility, understandability and efficiency. Experimentally, Ludii outperforms one of the most efficient Game Description Language (GDL) reasoners, based on a propositional network, for all available games in the Tiltyard GGP repository.

We analyze further the Magnus-Derek game, a two-player game played on a round table with n positions. The players jointly control the movement of a token. One player, Magnus, aims to maximize the number of positions visited while minimizing the number of rounds. The other player, Derek, attempts to minimize the number of visited positions. We present a new strategy for Magnus that succeeds in visiting the maximal number of positions in 3(n − 1) rounds, which is the optimal number of rounds up to a constant factor.

We study Maker-Breaker games played on the edge set of a random graph. Specifically, we consider the random graph process and analyze the first time in a typical random graph process that Maker starts having a winning strategy for his final graph to admit some property P. We focus on three natural properties for Maker's graph, namely being k-vertex-connected, admitting a perfect matching, and being Hamiltonian. We prove the following optimal hitting time results: with high probability Maker wins the k-vertex connectivity game exactly at the time the random graph process first reaches minimum degree 2k; with high probability Maker wins the perfect matching game exactly at the time the random graph process first reaches minimum degree 2; with high probability Maker wins the Hamiltonicity game exactly at the time the random graph process first reaches minimum degree 4. The latter two statements settle conjectures of Stojaković and Szabó.

While current General Game Playing (GGP) systems facilitate useful research in Artificial Intelligence (AI) for game-playing, they are often somewhat specialized and computationally inefficient. In this paper, we describe an initial version of a "ludemic" general game system called Ludii, which has the potential to provide an efficient tool for AI researchers as well game designers, historians, educators and practitioners in related fields. Ludii defines games as structures of ludemes, i.e. highlevel, easily understandable game concepts. We establish the foundations of Ludii by outlining its main benefits: generality, extensibility, understandability and efficiency. Experimentally, Ludii outperforms one of the most efficient Game Description Language (GDL) reasoners, based on a propositional network, for all available games in the Tiltyard GGP repository.

Dynamic programs, or xpoint iteration schemes, are useful for solving many problems on state spaces, including model checking on Kripke structures (\veri cation"), computing shortest paths on weighted graphs (\optimization"), computing the value of games played on game graphs (\control"). For Kripke structures, a rich xpoint theory is available in the form of the-calculus. Yet few connections have been made between di erent interpretations of xpoint algorithms. We study the question of when a particular xpoint iteration scheme ' for verifying an !-regular property on a Kripke structure can be used also for solving a two-player game on a game graph with winning objective. We provide a su cient and necessary criterion for the answer to be a rmative in the form of an extremal-model theorem for games: under a game interpretation, the dynamic program ' solves the game with objective i f and only if both (1) under an existential interpretation on Kripke structures, ' is equivalent t o 9 , and (2) under a universal interpretation on Kripke structures, ' is equivalent to 8. In other words, ' is correct on all two-player game graphs i it is correct on all extremal game graphs, where one or the other player has no choice of moves. The theorem generalizes to quantitative interpretations, where it connects two-player games with costs to weighted graphs. While the standard translations from !-regular properties to the-calculus violate (1) or (2), we give a translation that satis es both conditions. Our construction, therefore, yields xpoint iteration schemes that can be uniformly applied on Kripke structures, weighted graphs, game graphs, and game graphs with costs, in order to meet or optimize a given !-regular objective.

We consider 2-player games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players choose their moves independently and simultaneously; the current state and the two moves determine the successor state. We consider ω-regular winning conditions specified as parity objectives on the resulting infinite state sequence. Both players are allowed to use randomization when choosing their moves. We study the computation of the limit-winning set of states, consisting of the states where the sup-inf value of the game for player 1 is 1: in other words, a state is limit-winning if player 1 can ensure a probability of winning arbitrarily close to 1. We show that the limit-winning set can be computed in O(n 2m+2) time, where n is the size of the game structure and 2m is the number of parities; membership of a state in the limit-winning set can be decided in NP ∩ coNP. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms are considerably more involved than those for turn-based games. This is because concurrent games violate two of the most fundamental properties of turn-based parity games. First, in concurrent games limit-winning strategies require randomization; and second, they require infinite memory.

Three-color parity games capture the disjunction of a Büchi and a co-Büchi condition. The most efficient known algorithm for these games is the progress measures algorithm by Jurdziński. We present an acceleration technique that, while leaving the worst-case complexity unchanged, often leads to considerable speed-ups in games arising in practice. As an application, we consider games played in discrete real time, where players should be prevented from stopping time by always choosing moves with delay zero. The time progress condition can be encoded as a three-color parity game. Using the tool TICC as a platform, we compare the performance of a BDD-based symbolic implementation of the progress measure algorithm with acceleration, and of the symbolic implementation of the classical μ-calculus algorithm of Emerson and Jutla.

We consider two-player games played for an infinite number of rounds, with ω-regular winning conditions. The games may be concurrent, in that the players choose their moves simultaneously and independently, and probabilistic, in that the moves determine a probability distribution for the successor state. We introduce quantitative game µ-calculus, and we show that the maximal probability of winning such games can be expressed as the fixpoint formulas in this calculus. We develop the arguments both for deterministic and for probabilistic concurrent games; as a special case, we solve probabilistic turn-based games with ω-regular winning conditions, which was also open. We also characterize the optimality, and the memory requirements, of the winning strategies. In particular, we show that while memoryless strategies suffice for winning games with safety and reachability conditions, Büchi conditions require the use of strategies with infinite memory. The existence of optimal strategies, as opposed to ε-optimal, is only guaranteed in games with safety winning conditions.

We consider two-player games played for an infinite number of rounds, with ω-regular winning conditions. The games may be concurrent, in that the players choose their moves simultaneously and independently, and probabilistic, in that the moves determine a probability distribution for the successor state. We introduce quantitative game µ-calculus, and we show that the maximal probability of winning such games can be expressed as the fixpoint formulas in this calculus. We develop the arguments both for deterministic and for probabilistic concurrent games; as a special case, we solve probabilistic turn-based games with ω-regular winning conditions, which was also open. We also characterize the optimality, and the memory requirements, of the winning strategies. In particular, we show that while memoryless strategies suffice for winning games with safety and reachability conditions, Büchi conditions require the use of strategies with infinite memory. The existence of optimal strategies, as opposed to ε-optimal, is only guaranteed in games with safety winning conditions.

We consider two-player infinite games played on graphs. The games are concurrent, in that at each state the players choose their moves simultaneously and independently, and stochastic, in that the moves determine a probability distribution for the successor state. The value of a game is the maximal probability with which a player can guarantee the satisfaction of her objective. We show that the values of concurrent games with ω-regular objectives expressed as parity conditions can be computed in NP ∩ coNP. This result substantially improves the best known previous bound of 3EXPTIME. It also shows that the full class of concurrent parity games is no harder than the special cases of turnbased deterministic parity games (Emerson-Jutla) and of turn-based stochastic reachability games (Condon), for both of which NP ∩ coNP is the best known bound. While the previous, more restricted NP ∩ coNP results for graph games relied on the existence of particularly simple (pure memoryless) optimal strategies, in concurrent games with parity objectives optimal strategies may not exist, and ε-optimal strategies (which achieve the value of the game within a parameter ε > 0) require in general both randomization and infinite memory. Hence our proof must rely on a more detailed analysis of strategies and, in addition to the main result, yields two results that are interesting on their own.

We consider concurrent games played on graphs. At every round of the game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety objective: "stay forever in a set F of states", and its dual, the reachability objective, "reach a set R of states". We present in this paper a strategy improvement algorithm for computing the value of a concurrent safety game, that is, the maximal probability with which player 1 can enforce the safety objective. The algorithm yields a sequence of player-1 strategies which ensure probabilities of winning that converge monotonically to the value of the safety game. The significance of the result is twofold. First, while strategy improvement algorithms were known for Markov decision processes and turn-based games, as well as for concurrent reachability games, this is the first strategy improvement algorithm for concurrent safety games. Second, and most importantly, the improvement algorithm provides a way to approximate the value of a concurrent safety game from below (the known value-iteration algorithms approximate the value from above). Thus, when used together with value-iteration algorithms, or with strategy improvement algorithms for reachability games, our algorithm leads to the first practical algorithm for computing converging upper and lower bounds for the value of reachability and safety games.

We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose probability distributions over moves, rather than single moves. Given a goal, for example, reach a target state, the question of winning is thus a probabilistic one: what is the maximal probability of winning from a given state? On these game structures, two fundamental notions are those of equivalences and metrics. Given a set of winning conditions, two states are equivalent if the players can win the same games with the same probability from both states. Metrics provide a bound on the difference in the probabilities of winning across states, capturing a quantitative notion of state similarity. We introduce equivalences and metrics for two-player game structures, and we show that they characterize the difference in probability of winning games whose...

We consider two-player games played for an infinite number of rounds, with ω-regular winning conditions. The games may be concurrent, in that the players choose their moves simultaneously and independently, and probabilistic, in that the moves determine a probability distribution for the successor state. We introduce quantitative game µ-calculus, and we show that the maximal probability of winning such games can be expressed as the fixpoint formulas in this calculus. We develop the arguments both for deterministic and for probabilistic concurrent games; as a special case, we solve probabilistic turn-based games with ω-regular winning conditions, which was also open. We also characterize the optimality, and the memory requirements, of the winning strategies. In particular, we show that while memoryless strategies suffice for winning games with safety and reachability conditions, Büchi conditions require the use of strategies with infinite memory. The existence of optimal strategies, as opposed to ε-optimal, is only guaranteed in games with safety winning conditions.

Our work is intended to model and solve artificial planning problems with logic based planning, using the novel semantics called p-stable, which is an alternative of stable semantics. Also we present a method to encode a general planning problem and then we present an example, which is the blocks world problem. This can be applied in a variety of tasks including robotics, process planning, updates, making evacuation plans and so on.

We analyze the number of games played in a seven-game playoff series under various homeaway sequences. In doing so, we employ a simple Bernoulli model of home-field advantage in which the outcome of each game in the series depends only on whether it is played at home or away with respect to a designated home team. Considering all such sequences that begin and end at home, we show that, in terms of the number of games played, there are four classes of stochastically different formats, including the popular 2-3 and 2-2 formats both currently used in National Basketball Association (NBA) playoffs. Characterizing the regions in parametric space that give rise to distinct stochastic and expected value orderings of series length among these four format classes, we then investigate where in this parametric space that teams actually play. An extensive analysis of historical 7-game playoff series data from the NBA reveals that this homeaway model is preferable to the simpler, well-studied but ill-fitting binomial model that ignores home-field advantage. The model suggests that switching from the 2-2 series format used for most of the playoffs to the 2-3 format that has been used in the NBA Finals since a switch in 1985 would stochastically lengthen these playoff series, creating an expectation of approximately one extra game per playoff season. Such evidence should encourage television sponsors to lobby for a change of playoff format in order to garner additional television advertising revenues while reducing team and media travel costs.

I lavori riflettono esclusivamente le opinioni degli autori e non impegnano la responsabilità del Dipartimento. SERIES e MATEF vogliono promuovere la circolazione di studi ancora preliminari e incompleti, per suscitare commenti critici e suggerimenti. Si richiede di tener conto della natura provvisoria dei lavori per eventuali citazioni o per ogni altro uso.

We study the strategic choice of compatibility between two initially incompatible network goods in a two-stage game played by an incumbent and an entrant firm. Compatibility may be achieved by means of a converter. We derive a number of results under different assumptions about the nature of the converter (one-way vs two-way) and the existence of property rights. In the case of a two-way converter, which can only be supplied by the incumbent, incompatibility will result in equilibrium. When both firms can build a one-way converter and there are no property rights on the necessary technical specifications, the unique equilibrium involves full compatibility. Finally, when each firm has property rights on its technical specifications, full incompatibility and preemption are again observed at the equilibrium. With incompatibility, entry deterrence occurs for sufficiently strong network effects. The welfare analysis shows that the equilibrium compatibility regime is socially inefficient for most levels of the network effects.

Economic theory suggests that multiple financial and non-financial measures (i.e., a strategic performance measurement system ''SPMS") be used in compensation contracting to properly direct employees' attention and motivate behavior aligned with organizational goals. Conversely, linking incentives to the SPMS can result in various dysfunctional behaviors, including game playing by employees, the achievement of unbalanced performance, and the potential of basing compensation on an incomplete performance measurement system. Prior literature has investigated the use of subjectivity in compensation contracting as a means of potentially mitigating these problems; however, subjectivity can introduce other problems including claims of favoritism and bias. Economic theorists have recently begun expanding the traditional agency model to include the notion of fairness or justice. In this study, we obtain data from an organization that uses an SPMS as the basis for the allocation of bonuses and investigate whether characteristics of the SPMS are associated with perceived organizational fairness. Specifically, we hypothesize and show that the extent to which employees perceive that the SPMS reflects a strategic causal model and the degree to which it is technically valid are positively associated with their perceptions of organizational justice. We also provide evidence that heightened levels of organizational justice are the mechanism though which the perceived characteristics of the SPMS are associated with employee performance. The implication is that firms do not necessarily need to introduce subjectivity into the incentive contracting system, but can enhance performance by linking incentive contracts to their SPMS if the system contains characteristics that enhance employees' perceptions of justice.

Automatically creating opening books is a natural step towards the building of strong game-playing programs, especially when there is little available knowledge about the game. However, while recent popular Monte-Carlo Tree-Search programs showed strong results for various games, we show here that programs based on such methods cannot efficiently use opening books created using algorithms based on minimax. To overcome this issue, we propose to use an MCTS-based technique, Meta-MCTS, to create such opening books. This method, while requiring some tuning to arrive at the best opening book possible, shows promising results to create an opening book for the game of the Amazons, even if this is at the cost of removing its Monte-Carlo part.