Strategic Game

8. HANDBOOK OF MONETARY ECONOMICS (in 2 volumes) Edited by Benjamin Friedman and Frank Hahn 9. HANDBOOK OF DEVELOPMENT ECONOMICS (in 4 volumes) Volumes 1 and 2 edited by Hollis B. Chenery and TN Srinivasan Volumes 3A and 3B edited by Jere ...

In this paper we explore the use of Hierarchical-Task-Network (HTN) representations to model strategic game AI. We will present two case studies. The first one reports on an experiment using HTNs to model strategies for Unreal Tournament® (UT) bots. We will argue that it is possible to encode strategies that coordinate teams of bots in first-person shooter games using

Preference is a basic notion in human behaviour, underlying such varied phenomena as individual rationality in the philosophy of action and game theory, obligations in deontic logic (we should aim for the best of all possible worlds), or collective decisions in social choice theory. Also, in a more abstract sense, preference orderings are used in conditional logic or non-monotonic reasoning as a way of arranging worlds into more or less plausible ones. The field of preference logic (cf. Hansson ) studies formal systems that can express and analyze notions of preference between various sorts of entities: worlds, actions, or propositions. The art is of course to design a language that combines perspicuity and low complexity with reasonable expressive power. In this paper, we take a particularly simple approach. As preferences are binary relations between worlds, they naturally support standard unary modalities. In particular, our key modality ♦ϕ will just say that is ϕ true in some world which is at least as good as the current one. Of course, this notion can also be indexed to separate agents. The essence of this language is already in [4], but our semantics is more general, and so are our applications and later language extensions. Our modal language can express a variety of preference notions between propositions. Moreover, as already suggested in [9], it can "deconstruct" standard conditionals, providing an embedding of conditional logic into more standard modal logics. Next, we take the language to the analysis of games, where some sort of preference logic is evidently needed ([23] has a binary modal analysis different from ours). We show how a qualitative unary preference modality suffices for defining Nash Equilibrium in strategic games, and also the Backward Induction solution for finite extensive games. Finally, from a technical perspective, our treatment adds a new twist. Each application considered in this paper suggests the need for some additional access to worlds before the preference modality can unfold its true power. For this purpose, we use various extras from the modern literature: the global modality, further hybrid logic operators, action modalities from propositional dynamic logic, and modalities of individual and distributed knowledge from epistemic logic. The total package is still modal, but we can now capture a large variety of new notions. Finally, our emphasis in this paper is wholly on expressive power. Axiomatic completeness results for our languages can be found in the follow-up paper [27].

Los juegos de estrategia abstracta constituyen un recurso educativo muy importante para desarrollar aptitudes de representación espacial y de pensamiento estratégico. En este sentido, y de forma específica, el juego del QUORIDOR permite adquirir aptitudes relacionadas con la accesibilidad diferencial ("barreras") y la representación espacial.

In a recent paper ͓D. A. Meyer, Phys. Rev. Lett. 82, 1052 ͑1999͔͒, it has been shown that a classical zero-sum strategic game can become a winning quantum game for the player with a quantum device. Nevertheless, it is well known that quantum systems easily decohere in noisy environments. In this paper, we show that if the handicapped player with classical means can delay his action for a sufficiently long time, the quantum version reverts to the classical zero-sum game under decoherence.

Game theory provides a useful framework for studying Multi-Criteria Decision Making problems. This paper suggests modeling Multi-Criteria Decision Making problems as strategic games and solving them using non-cooperative game theory concepts. The suggested method can be used to prescribe non-dominated solutions and also can be used as a method to predict the outcome of a decision making problem. Non-cooperative stability definitions for solving the games allow consideration of non-cooperative behaviors, often neglected by other methods which assume perfect cooperation among decision makers. To deal with the uncertainty in input variables a Monte-Carlo Game Theory (MCGT) approach is suggested which maps the stochastic problem into many deterministic strategic games. The games are solved using non-cooperative stability definitions and the results include possible effects of uncertainty in input variables on outcomes. The method can handle multi-criteria multi-decision-maker problems with uncertainty. The suggested method does not require criteria weighting, developing a compound decision objective, and accurate quantitative (cardinal) information as it simplifies the decision analysis by solving problems based on qualitative (ordinal) information, reducing the computational burden substantially. The MCGT method is applied to analyze California's Sacramento-San Joaquin Delta problem. The suggested method provides insights, identifies non-dominated alternatives, and predicts likely decision outcomes.

Issues of responsibility in the world of nanotechnology are becoming explicit with the emergence of a discourse on ‘responsible development’ of nanoscience and nanotechnologies. Much of this discourse centres on the ambivalences of nanotechnology and of promising technology in general. Actors must find means of dealing with these ambivalences. Actors’ actions and responses to ambivalence are shaped by their position and context, along with strategic games they are involved in, together with other actors. A number of interviews were conducted with industrial actors with the aim of uncovering their ethical stances towards responsible development of nanotechnology. The data shows that standard repertoires of justification of nanotechnological development were used. Thus, the industrial actors fell back on their position and associated responsibilities. Such responses reinforce a division of moral labour in which industrial actors and scientists can focus on the progress of science and technology, while other actors, such as NGOs, are expected to take care of broader considerations, such as ethical and social issues.

We extend the consistency principle for strategic games ) to apply to solutions which assign to each game a collection of product sets of strategies. Such solutions turn out to satisfy desirable properties that solutions assigning to each game a collection of strategy pro®les lack. Our ®ndings lead us to propose a new direction for normative game theory.

We study a strategic game where every node of a graph is owned by a player who has to choose a color. A player's payoff is 0 if at least one neighbor selected the same color, otherwise it is the number of players who selected the same color. The social cost of a state is defined as the number of distinct colors that the players use. It is ideally equal to the chromatic number of the graph but it can substantially deviate because every player cares about his own payoff, whatever how bad the social cost is. Following a previous work done by Panagopoulou and Spirakis [15] on the Nash equilibria of the coloring game, we give worst case bounds on the social cost of stable states. Our main contribution is an improved (tight) bound for the worst case social cost of a Nash equilibrium, and the study of strong equilibria, their existence and how far they are from social optima.

Too few students consider mathematics to be interesting, not to mention enjoyable or challenging. Integrating strategy games into mathematics classes can make them more exiting, enabling students to learn or practice various topics in a different manner while developing their mathematical thinking and improving their knowledge. 
One example of such a game is NIM, which is a two-player game, and according to Gardner (1983), one of the oldest mathematical games in the world. In this paper, I present a different perspective for the analysis of the game, using more common school knowledge – arithmetic series.

This book is an outgrowth of courses we have taught and discussions we have had with many friends and colleagues. Some of the material in Chapters 5, 8, and 9 is based on parts of a draft of a book on models of bounded rationality by ar. mjo I had the privilege of being educated in game theory by Robert Aumann, Sergiu Hart, Mordecai Kurz, and Robert Wilson at Stanford University. It is a great pleasure to acknowledge my debt to them.

Standard growth theory is based on atomistic agents with no strategic interactions among them. In contrast, we model growth as resulting from a one-off, strategic game between "workers" and owners of capital ("capitalists") on factor shares, in an otherwise standard "AK" growth model. The resulting distribution of income between factors further determines the marginal revenue product of capital and the rate of growth. We analyse the properties of four equilibria: competitive, Stackelberg equilibrium, a hybrid noncooperative regime, and cooperative (Nash) solution. We show that our model provides a potentially richer view of the growth process than comparable models, and endogenises a key aspect of the "social contract".

Many social situations require a mental model of the knowledge, beliefs, goals, and intentions of others: a Theory of Mind (ToM). If a person can reason about other people's beliefs about his own beliefs or intentions, he is demonstrating second-order ToM reasoning. A standard task to test second-order ToM reasoning is the second-order false belief task. A different approach to investigating ToM reasoning is through its application in a strategic game. Another task that is believed to involve the application of second-order ToM is the comprehension of sentences that the hearer can only understand by considering the speaker's alternatives. In this study we tested 40 children between 8 and 10 years old and 27 adult controls on (adaptations of) the three tasks mentioned above: the false belief task, a strategic game, and a sentence comprehension task. The results show interesting differences between adults and children, between the three tasks, and between this study and previous research. L. Flobbe (B)

Large value payment and securities settlement systems are important components of an economy's nancial system. Many such systems are operated by central banks and are liquidity intensive. Central banks often provide inexpensive liquidity to facilitate settlement. This leads to a number of policy questions about the provision of such liquidity. To answer these questions, central banks need to understand what factors in uence the timing of settlement. This paper o ers a model to better understand intraday patterns of settlement and identi es three factors that in uence the timing of settlement: the cost of intraday liquidity, a participant's exposure to settlement risk, and system design. Incorporating all three factors enables our model to explain a number of stylized facts concerning behavior within the Federal Reserve's Fedwire fund and securities systems around a major policy change. In particular, the model captures the di erent responses of the two systems in both the pattern of settlement and the use of intraday liquidity. The results map out how policy interacts with participants' incentives to in uence the use of intraday liquidity and the resultant credit exposure of a central bank. The model, therefore, can inform decision-making at central banks.

Purpose -Using Brandenburger and Nalebuff's 1995 co-opetition model as a reference, the purpose of this paper is to seek to develop a tool that, based on the tenets of classical game theory, would enable scholars and managers to identify which games may be played in response to the different conflict of interest situations faced by companies in their business environments. Design/methodology/approach -The literature on game theory and business strategy are reviewed and a conceptual model, the strategic games matrix (SGM), is developed. Two novel games are described and modeled. Findings -The co-opetition model is not sufficient to realistically represent most of the conflict of interest situations faced by companies. It seeks to address this problem through development of the SGM, which expands upon Brandenburger and Nalebuff's model by providing a broader perspective, through incorporation of an additional dimension (power ratio between players) and three novel, respectively, (rival, individualistic, and associative). Practical implications -This proposed model, based on the concepts of game theory, should be used to train decision-and policy-makers to better understand, interpret and formulate conflict management strategies. Originality/value -A practical and original tool to use game models in conflict of interest situations is generated. Basic classical games, such as Nash, Stackelberg, Pareto, and Minimax, are mapped on the SGM to suggest in which situations they could be useful. Two innovative games are described to fit four different types of conflict situations that so far have no corresponding game in the literature. A test application of the SGM to a classic Intel Corporation strategic management case, in the complex personal computer industry, shows that the proposed method is able to describe, to interpret, to analyze, and to prescribe optimal competitive and/or cooperative strategies for each conflict of interest situation.

Standard growth theory is based on atomistic agents with no strategic interactions among them. In contrast, we model growth as resulting from a one-off, strategic game between 'workers' and owners of capital ('capitalists') on factor shares, in an otherwise standard 'AK' growth model. The resulting distribution of income between factors further determines the marginal revenue product of capital and the rate of growth. We analyse the properties of four equilibria: competitive, Stackelberg equilibrium, a hybrid non-cooperative regime and cooperative, in terms of labour shares, growth and welfare. Our model thus endogenizes key aspects of the 'social contract'.

Behavioral studies suggest that making a decision involves representing the overall desirability of all available actions and then selecting that action that is most desirable. Physiological studies have proposed that neurons in the parietal cortex play a role in selecting movements for execution. To test the hypothesis that these parietal neurons encode the subjective desirability of making particular movements, we exploited Nash's game theoretic equilibrium, during which the subjective desirability of multiple actions should be equal for human players. Behavior measured during a strategic game suggests that monkeys' choices, like those of humans, are guided by subjective desirability. Under these conditions, activity in the parietal cortex was correlated with the relative subjective desirability of actions irrespective of the specific combination of reward magnitude, reward probability, and response probability associated with each action. These observations may help place many recent findings regarding the posterior parietal cortex into a common conceptual framework.

We study an economic model where agents trade a variety of products by using one of three competing rules: "need", "greed" and "noise". We find that the optimal strategy for any agent depends on both product composition in the overall market and composition of strategies in the market. In particular, a strategy that does best on pairwise competition may easily do much worse when all are present, leading, in some cases, to a "paper, stone, scissors" circular hierarchy.

Artykuł ten jest czwartym z serii artykułów poświęconych przeglądowej prezentacji poszczególnych metod sztucznej inteligencji (AI) prezentowanych jako wyspy archipelagu, co zostało skomentowane i wyjaśnione w pierwszym artykule tego cyklu. Warto dodać, że wszystkie wcześniejsze artykuły z tej serii są także dostępne w serwisie Academia.edu. W prezentowanym tu artykule przedstawione są programy sztucznej inteligencji grające z ludźmi w gry strategiczne (warcaby, szachy, Go), dalej omówiona jest obszerna dziedzina komputerowego przetwarzania języka naturalnego, a na końcu omówione są uczące się drzewa decyzyjne.

We present a logic for reasoning about strategic games. The logic is a modal formalism, based on the Coalition Logic of Propositional Control, to which we add the notions of outcomes and preferences over outcomes. We study the underlying structure of powers of coalitions as they are expressed in their effectivity function, and formalise a collection of solution concepts. We provide a sound and complete axiomatisation for the logic, and we demonstrate its features by applying it to some problems from social choice theory.

In this paper we use defense trees, an extension of attack trees with countermeasures, to represent attack scenarios and game theory to detect the most promising actions attacker and defender. On one side the attacker wants to break the system (with as little efforts as possible), on the opposite side the defender want to protect it (sustaining the minimum cost). As utility function for the attacker and for the defender we consider economic indexes (like the Return on Investment (ROI) and the Return on Attack (ROA)). We show how our approach can be used to evaluate effectiveness and economic profitability of countermeasures as well as their deterrent effect on attackers, thus providing decision makers with a useful tool for performing better evaluation of IT security investments during the risk management process.

We propose strategic games wherein the strategies consist of players asking each other questions and answering those questions. We study simplifications of such games wherein two players simultaneously ask each other a question that the opponent is then obliged to answer. The motivation for our research is to model conversation including the dynamics of questions and answers, to provide new links between game theory and dynamic logics of information, and to exploit the dynamic/strategic structure that, we think, lies implicitly inside epistemic models for epistemic languages, and to make that structure an explicit subject of logical study. Our main contributions are: the notion of a two-person question-answer game with information goals, the existence and computation of equilibria for these games, the correspondence with Bayesian games and their equilibria, and a connection between logic and game theory namely the existence of equilibria for positive goal formulae.

In recent decades, the concept of subjective probability has been increasingly applied to an adversary's choices in strategic games. A careful examination reveals that the standard construction of subjective probabilities does not apply in this context. We show how the difficulty may be overcome by means of a different construction, and provide an axiomatic foundation for it.

This paper focuses on the competitively optimal power-control, signal-shaping and interference mitigation for wireless mesh networks composed by Multiple-Antenna noncooperative transmit terminals and a base station affected by spatially colored Multi-Access Interference (MAI). The target is the competitive maximization of the information throughput of the uplink of each link active over the network. For this purpose, the MAI-impaired network is modelled as a noncooperative strategic game. Specifically, the main contribution of this paper may be so summarized. First, we consider power-control, signal-shaping and interference mitigation algorithms allowing the implementation of asynchronous Space-Division Multiple Access (SDMA) strategies able to guarantee the competitive maximization of the users' rate under both Quality of Service (QoS) guaranteed and QoS contracted access policies. Second, we give evidence that the developed SDMA outperforms (in terms of aggregate throughput) the conventional orthogonal ones, specially in operating scenarios affected by strong MAI. The proposed access scheme can be considered as an Active Networking strategy where the nodes try to "sense" the channel and to access according to a space-division policy.

This article examines the role of ambiguity in processes of institutional change. One challenge for understanding institutional change is to overcome the rather "oversocialized" view of action within Institutional theory. Drawing upon recent work in sociology, the paper introduces a nonteleological model of action that stresses the ambiguity of institutionalized beliefs. Ambiguity is then applied to Masahiko Aoki`s concept of institutions as "summary representation" of a strategic game. Rather than institutional break down, ambiguity is associated with incremental modes of institutional change through creative reinterpretation and redeployment of old institutions for new purposes.

In this paper, we introduce a game-theoretic framework to address the community detection problem based on the structures of social networks. We formulate the dynamics of community formation as a strategic game called community formation game: Given an underlying social graph, we assume that each node is a selfish agent who selects communities to join or leave based on her own utility measurement. A community structure can be interpreted as an equilibrium of this game. We formulate the agents' utility by the combination of a gain function and a loss function. We allow each agents to select multiple communities, which naturally captures the concept of "overlapping communities". We propose a gain function based on the modularity concept introduced by Newman , and a simple loss function that reflects the intrinsic costs incurred when people join the communities. We conduct extensive experiments under this framework, and our results show that our algorithm is effective in identifying overlapping communities, and are often better then other algorithms we evaluated especially when many people belong to multiple communities. To the best of our knowledge, this is the first time the community detection problem is addressed by a game-theoretic framework that considers community formation as the result of individual agents' rational behaviors.

c Continuous games are increasingly popular to study evolutionary phenomena. c Leading models of continuous games have led to confusion and errors in the literature. c A favorite model of the continuous prisoners dilemma actually models other games. c A favorite model of the continuous snow drift game also models other games.

The day-ahead electricity market is modeled as a multi-agent system with interacting agents including supplier agents, load serving entities, and a market operator. Simulation of the market clearing results under the scenario in which agents have learning capabilities is compared with the scenario where agents report true marginal costs. It is shown that, with Q-Learning, electricity suppliers are making more profits compared to the scenario without learning due to strategic gaming. As a result, the LMP at each bus is substantially higher.

In this paper we explore the use of Hierarchical-Task-Network (HTN) representations to model strategic game AI. We will present two case studies. The first one reports on an experiment using HTNs to model strategies for Unreal Tournament® (UT) bots. We will argue that it is possible to encode strategies that coordinate teams of bots in first-person shooter games using

We use a laboratory experiment to compare the way groups and individuals behave in an inter-temporal common pool dilemma. The experimental design distinguishes between a non-strategic problem where players (individuals or groups of three) make decisions without interaction and a strategic part where players harvest from a common pool. This allows us to correct for differences between individuals and groups in the quality of decisions when testing for differences in competitiveness. Group decisions are either made by majority rule or unanimity. The results show that groups are less myopic than individuals (i.e., they make qualitatively better decisions) but that they are more competitive than individuals when placed in a strategic setting. The net result for groups deciding by majority rule is that they make less efficient decisions in the strategic game than individuals do. We are able to show that this is caused by the median voter departing from her original preference in early periods with a shrinking pool. When groups have to make unanimous decisions they start playing the strategic game more efficiently then individuals do, but they rapidly become more competitive with repetition of the game.

Resumen La racionalidad limitada es un fenómeno observado de manera frecuente tanto en juegos experimentales como en situaciones cotidianas. La Neuroeconomía puede mejorar la comprensión de los procesos mentales que caracterizan la racionalidad limitada; en paralelo nos puede ayudar a comprender comportamientos que violan el equilibrio. Nuestro trabajo presenta resultados recientes sobre la bases neuronales del razonamiento estratégico (y sus límite) en juegos competitivos—como el juego del “beauty contest”. ...

Bounded rational behaviour is commonly observed in experimental games and in real life situations. Neuroeconomics can help to understand the mental processing underlying bounded rationality and out-of-equilibrium behaviour. Here we report results from recent studies on the neural basis of limited steps of reasoning in a competitive setting -the beauty contest game. We use functional magnetic resonance imaging (fMRI) to study the neural correlates of human mental processes in strategic games. We apply a cognitive hierarchy model to classify subject's choices in the experimental game according to the degree of strategic reasoning so that we can identify the neural substrates of different levels of strategizing. We found a correlation between levels of strategic reasoning and activity in a neural network related to mentalizing, i.e. the ability to think about other's thoughts and mental states. Moreover, brain data showed how complex cognitive processes subserve the higher level of reasoning about others. We describe how a cognitive hierarchy model fits both behavioural and brain data.

Much of experimental research in marketing has focused on individual choices. Yet in many contexts, the outcomes of one’s choices depend on the choices of others. Furthermore, the results obtained in individual decision making context may not be applicable to these strategic choices. In this paper, we discuss three avenues for further advancing our understanding of strategic choices. First, there is a need to develop theories about how people learn to play strategic games. Second, there is an opportunity to enrich standard economic models of strategic behavior by allowing for different types of bounded rationality and by relaxing assumptions about utility formulation. These new models can help us to more accurately predict strategic choices. Finally, future research can improve marketing practice by designing better mechanisms and validating them using experiments.

This paper explores the issues faced in creating a system that can learn tactical human behavior merely by observing a human perform the behavior in a simulation. More specifically, this paper describes a technique based on fuzzy ARTMAP (FAM) neural networks to discover the criteria that cause a transition between contexts during a strategic game simulation. The approach depends on existing context templates that can identify the high-level action of the human, given a description of the situation along with his action. The learning task then becomes the identification and representation of the context sequence executed by the human. In this paper, we present the FAM/Template-based Interpretation Learning Engine (FAMTILE). This system seeks to achieve this learning task by constructing rules that govern the context transitions made by the human. To evaluate FAMTILE, six test scenarios were developed to achieve three distinct evaluation goals: 1) to assess the learning capabilities of FAM; 2) to evaluate the ability of FAMTILE to correctly predict human and context selections, given an observation; and 3) more fundamentally, to create a model of the human's behavior that can perform the high-level task at a comparable level of proficiency.

We propose two variations of the non-cooperative bargaining model for games in coalitional form, introduced by Hart and Mas-Colell (Econometrica 64:357– 380, 1996a). These strategic games implement, in the limit, two new NTU-values: the random marginal and the random ...

We focus on axiomatizations of the Pareto equilibrium concept in multicriteria games based on consistency. Axiomatizations of the Nash equilibrium concept by Peleg and Tijs (1996) and Peleg, Potters, and Tijs (1996) have immediate generalizations. The axiomatization of Norde et al. (1996) cannot be generalized without the use of an additional axiom.

In this paper game theory is used to analyse the effect of a number of service failures during the execution of a grid orchestration. A service failure may be catastrophic in that it causes an entire orchestration to fail. Alternatively, a grid manager may utilise alternative services in the case of failure, allowing an orchestration to recover. A risk profile provides a means of modelling situations in a way that is neither overly optimistic nor overly pessimistic. Risk profiles are analysed using angel and daemon games. A risk profile can be assigned a valuation through an analysis of the structure of its associated Nash equilibria. Some structural properties of valuation functions, that show their validity as a measure for risk, are given. Two main cases are considered, the assessment of Orc expressions and the arrangement of a meeting using reputations.

This paper focuses on the competitively optimal power-control, signal-shaping and interference mitigation for wireless mesh networks composed by Multiple-Antenna noncooperative transmit terminals and a base station affected by spatially colored Multi-Access Interference (MAI). The target is the competitive maximization of the information throughput of the uplink of each link active over the network. For this purpose, the MAI-impaired network is modelled as a noncooperative strategic game. Specifically, the main contribution of this paper may be so summarized. First, we consider power-control, signal-shaping and interference mitigation algorithms allowing the implementation of asynchronous Space-Division Multiple Access (SDMA) strategies able to guarantee the competitive maximization of the users' rate under both Quality of Service (QoS) guaranteed and QoS contracted access policies. Second, we give evidence that the developed SDMA outperforms (in terms of aggregate throughput) the conventional orthogonal ones, specially in operating scenarios affected by strong MAI. The proposed access scheme can be considered as an Active Networking strategy where the nodes try to "sense" the channel and to access according to a space-division policy.

In this paper we use defense trees, an extension of attack trees with countermeasures, to represent attack scenarios and game theory to detect the most promising actions attacker and defender. On one side the attacker wants to break the system (with as little efforts as possible), on the opposite side the defender want to protect it (sustaining the minimum cost). As utility function for the attacker and for the defender we consider economic indexes (like the Return on Investment (ROI) and the Return on Attack (ROA)). We show how our approach can be used to evaluate effectiveness and economic profitability of countermeasures as well as their deterrent effect on attackers, thus providing decision makers with a useful tool for performing better evaluation of IT security investments during the risk management process.