Extensive Games Research Articles

Game design documentation

Changes in technology, development philosophy, and scale have required game designers to change how they communicate and mediate design decisions. Traditional game design studios used an extensive game design document (GDD), a meta-genre that described most of the game before it was developed. Current studies suggest that this is no longer the case. We conducted interviews at four independent game studios in order to share their game design documentation processes, revealing that, while an exhaustive GDD is rare, the meta-genre functions are preserved in a variety of mediated ways.

XGFX: eXtensible Game Framework through XMPP

XGFX: eXtensible Game Framework through XMPP

Sequential Competition and the Strategic Origins of Preferential Attachment

There exists a wide gap between the predictions of strategic models of network formation and empirical observations of the characteristics of socio-economic networks. Empirical observations underline a complex structure characterized by fat-tailed degree distribution, short average distance, large clustering coefficient and positive assortativity. Game theoretic models offer a detailed representation of individuals’ incentives but they predict the emergence of much simpler structures than these observed empirically. Random network formation processes, such as preferential attachment, provide a much better fit to empirical observations but generally lack micro-foundations. In order to bridge this gap, we propose to model network formation as extensive games and investigate under which conditions equilibria of these games are observationally equivalent with random network formation process. In particular, we introduce a class of games in which players compete with their predecessors and their successors for the utility induced by the links they form with other nodes in the network. Such sequential competition games can represent a number of strategic economic interactions such as oligopolistic competition in supply networks or diffusion of influence in opinion networks. We show that the focal equilibrium that emerges in this setting is one where players use probability distributions with full support and target the whole network with probabilities inversely proportional, to the utility of each node. Notably, when the utility of a node is inversely proportional to its degree, equilibrium play induces a preferential attachment process.

On equilibria in games with imperfect recall

We generalize the modified multiselves approach of Piccione and Rubinstein to (multiplayer) games of imperfect recall. Four solution concepts are introduced: the multiselves agent equilibrium, the multiselves Nash equilibrium, the multiselves sequential equilibrium, and the multiselves perfect equilibrium. These modified equilibrium notions satisfy two important properties not fulfilled by the original ones. First, they always exist: every finite extensive game has at least one multiselves equilibrium of each type. Second, they form a strict hierarchy: every multiselves perfect equilibrium is a multiselves sequential equilibrium, every multiselves sequential equilibrium is a multiselves Nash equilibrium, and every multiselves Nash equilibrium is a multiselves agent equilibrium—but not conversely. Finally, in games of perfect recall, the multiselves equilibrium notions reduce to their original counterparts.

Formative Knowledge Assessment Through Games Using Concept Map and Game Theory

This paper presents the results of a research work carried out in order to develop a novel gaming model for formative knowledge assessment (FKA). The benefits of FKA are well acknowledged by educators as it aids for better learning. As FKA is more frequent, the students’ willingness to take frequent assessments is poor. Often the students expressed that they felt uncomfortable and this resulted in lack of active participation. These are considered as major challenges to be addressed. Hence, this research aimed to find a way to make the assessments interesting. Based on the positive responses for game-based learning, a theoretical model that integrates the principles of extensive games (EGs) and concept map (CM), namely concept tree game (CTG), has been defined and developed. Further, a qualitative research has been performed to evaluate the impact of the FKA model. Major data gathering techniques used in this work were a class test, proposed FKA method, participant observation, survey and focussed team interview. The data were analysed statistically and the results revealed that it has been effective and useful for educators in assessing the knowledge of students and for students, it aided them to know where they stand and helped them to learn effectively.

Subgame Perfect Equilibria Under the Deferred Acceptance Algorithm

We analyze a subgame perfect equilibrium (SPE) of an extensive game with perfect information induced by the firm-oriented deferred acceptance (DA) algorithm in a one-to-one matching market between firms and workers. When no agents are strategic, the resulting outcome is the firm-optimal stable matching. We show that the worker-optimal stable matching is the unique SPE outcome when only workers are strategic. By contrast, multiple SPE outcomes may exist, possibly including unstable matchings when only firms are strategic. We show that every firm weakly prefers any SPE outcome to the worker-optimal stable matching and that the matching induced by Kesten's efficiency-adjusted DA algorithm can be achieved as a SPE. When both workers and firms are strategic, we also show that the worker-optimal stable matching is still the unique SPE outcome. Hence, the strategic behavior of workers yields the worker-optimal stable matching in a dynamic implementation of the firm-oriented DA algorithm. Our results reveal that the workers strategic behavior yields a reversal property in a dynamic implementation of the firm-oriented DA algorithm.

A Survey on the Relationship Between the Game of Cops and Robbers and Other Game Representations

This paper surveys the similarities and differences between the game of cops and robbers and classes of related games. The game of cops and robbers is a class of pursuit–evasion games played on a finite graph. The players comprise a set of cops and a robber located on vertices of the graph, and they move alternately along edges of the graph. The cops win the game if at least one cop occupies the same vertex of the robber in finite time; otherwise, the robber wins. Quilliot (Jeux de points fixes sur les graphes, These de 3ieme Cycle, Universite de Paris VI, Paris, pp 131–145, 1978) and Nowakowski and Winkler (Discrete Math 43:235–239, 1983) were among the first to study this class of games. The main questions studied in the literature of cops and robbers games are on the class of graphs that characterize cop-win games, on the minimum number of cops needed for classes of graphs to be cop-win, on a conjecture due Meyniel (Personal communication, 1985) about the cop number of a graph and more recently on the game played on random and/or infinite graphs (Bonato and Nowakowski in The game of cops and robbers, Student mathematical library, vol 61, American Mathematical Society, Providence, 2010; Bonato and Pralat in Graph searching games and probabilistic methods, CRC Press, Boca Raton, 2017). While the game of cops and robbers is not traditionally modeled in the language of extensive game theory (Kuhn, in: Kuhn, Tucker (eds) Contributions to the theory of games II, Princeton University Press, Princeton, 1953), Kehagias et al. (The role of visibility in pursuit/evasion games, 2014) give a general framework for the game of cops and robbers that relate to extensive games. By using the notion of “capture time,” they are able to represent the game using a standard discrete dynamic game model with explicit payoff functions for the cops and the robber. More recently, the game of cops and robbers has also been related to dynamic games with state variables (Bonato and Macgillivray in Contrib Discrete Math, 2017) and discounted stochastic games (Konstantinidis and Kehagias in Selfish cops and adversarial robber: multi-player pursuit evasion on graphs, 2017a, arXiv:1703.07695 ; Theor Comput Sci 680:25–35, 2017b). In this survey, we study these connections.

Acute and long-lasting cortical thickness changes following intensive first-person action videogame practice

Recent evidence shows how an extensive gaming experience might positively impact cognitive and perceptual functioning, leading to brain structural changes observed in cross-sectional studies. Importantly, changes seem to be game-specific, reflecting gameplay styles and therefore opening to the possibility of tailoring videogames according to rehabilitation and enhancement purposes. However, whether if such brain effects can be induced even with limited gaming experience, and whether if they can outlast the gaming period, is still unknown. Here we quantified both cognitive and grey matter thickness changes following 15 daily gaming sessions based on a modified version of a 3D first-person shooter (FPS) played in laboratory settings. Twenty-nine healthy participants were randomly assigned to a control or a gaming group and underwent a cognitive assessment, an in-game performance evaluation and structural magnetic resonance imaging before (T0), immediately after (T1) and three months after the end of the experiment (T2). At T1, a significant increase in thickness of the bilateral parahippocampal cortex (PHC), somatosensory cortex (S1), superior parietal lobule (SPL) and right insula were observed. Changes in S1 matched the hand representation bilaterally, while PHC changes corresponded to the parahippocampal place area (PPA). Surprisingly, changes in thickness were still present at T2 for S1, PHC, SPL and right insula as compared to T0. Finally, surface-based regression identified the lingual gyrus as the best predictor of changes in game performance at T1. Results stress the specific impact of core game elements, such as spatial navigation and visuomotor coordination on structural brain properties, with effects outlasting even a short intensive gaming period.

Response time optimization for cloudlets in Mobile Edge Computing

Mobile Edge computing (MEC) and caching are new forms of computing architecture which brings network functions to the network edge or physical proximity of the users. In MEC, the mobile cloudlets are smart phones which offer computational services to other smart phones available in the physical proximity. Selection of the device for offloading computationally intensive tasks is a very important criterion for end-users Quality of Service. This work focuses on optimal selection of devices which receives offloaded computational tasks. This paper presents a non-cooperative extensive game model where players maximize their pay-offs which leads to minimization of response time. Further, we make our proposed model to implicitly depend upon the battery life of the computational task receivers. The game model achieves Nash Equilibrium by using backward induction technique. This work also takes care of the device availability by clustering the previous availability data. Finally, we evaluate the performance of the proposed model upon response time, end-users utility and memory utilizations. We also see that the proposed work out performs the different schemes which we used for comparisons.

Dependent Types for Extensive Games

Extensive games are tools largely used in economics to describe decision processes of a community of agents. In this paper we propose a formal presentation based on the proof assistant COQ which focuses mostly on infinite extensive games and their characteristics. COQ proposes a feature called types'', which means that the type of an object may depend on the type of its components. For instance, the set of choices or the set of utilities of an agent may depend on the agent herself. Using dependent types, we describe formally a very general class of games and strategy profiles, which corresponds somewhat to what game theorists are used to. We also discuss the notions of infiniteness in game theory and how this can be precisely described.

A Dynamic-Logical Characterization of Solutions to Sight-limited Extensive Games

An unrealistic assumption in classical extensive game theory is that the complete game tree is fully perceivable by all players. To weaken this assumption, a class of games (called games with short sight) was proposed in literature, modelling the game scenarios where players have only limited foresight of the game tree due to bounded resources and limited computational ability. As a consequence, the notions of equilibria in classical game theory were refined to fit games with short sight. A crucial issue that thus arises is to determine whether a strategy profile is a solution for a game. To study this issue and address the underlying idea and theory on players’ decisions in such games, we adopt a logical way. Specifically, we develop a logic through which features of these games are demonstrated. More importantly, it enables us to characterize the solutions of these games via formulas of this logic. This work not only provides an insight into a more realistic model in game theory, but also enriches the possible applications of logic.

Modeling of Agent Cognition in Extensive Games via Artificial Neural Networks.

The decision-making process, which is regarded as cognitive and ubiquitous, has been exploited in diverse fields, such as psychology, economics, and artificial intelligence. This paper considers the problem of modeling agent cognition in a class of game-theoretic decision-making scenarios called extensive games. We present a novel framework in which artificial neural networks are incorporated to simulate agent cognition regarding the structure of the underlying game and the goodness of the game situations therein. An algorithmic procedure is investigated to describe the process for solving games with cognition, and then, a new equilibrium concept is proposed as a refinement of the classical one-subgame perfect equilibrium-by involving players' cognitive reasoning. Moreover, a series of results concerning the computational complexity, soundness, and completeness of the algorithm, as well as the existence of an equilibrium solution, is obtained. This framework, which is shown to be general enough to model the way in which AlphaGo plays Go, may offer a means for bridging the gap between theoretical models and practical problem-solving.

Impossibilities for strategy-proof committee selection mechanisms with vetoers

When a group of voters selects a committee out of a set of candidates, it is common and often desirable to endow these voters with some veto power. I present impossibility results showing that even limited veto power makes many mechanisms of interest manipulable. This applies in particular (i) to mechanisms the range of which contains a degenerate lottery in which a committee is chosen for sure and (ii) to mechanisms that are constructed from extensive game forms with a finite number of strategies. These impossibilities hold on a large set of domains including the domain of additive preferences, and even when probabilistic mechanisms are allowed and voters can report cardinal preferences.

On the use of game theory to study the planning and profitability of industrial microgrids connected to the distribution network

This study deals with the long-term planning of industrial microgrids (MGs) in order to decrease the electricity bill (compared with the current situation) for participating companies. In such industrial MGs, the distribution system operator, the industrial estate operator and prosumers' objectives, which can be conflicting, need to be taken into account at the same time. The planning problem is formulated as a multi-agent and multi-objective problem which is solved by computing a Nash equilibrium of an extensive game from game theory. Different time horizons of the decision process are taken into account. In this study, the planning tool principle is presented and some applications are provided.

Uncertain extensive game with application to resource allocation of national security

Uncertain theory is a powerful tool for describing human uncertainty, especially in social economic studies. In this paper, we consider finite extensive games with payoffs being uncertain variables. We introduce three different criteria: the expected value criterion, the optimistic value criterion and the pessimistic value criterion to describe players’ behaviors in different decision-making situations. Accordingly, three types of uncertain equilibria and uncertain subgame perfect equilibria for the uncertain extensive game are proposed. Moreover, we provide theorems to prove the existence of uncertain equilibria and uncertain subgame perfect equilibria. Finally, the resource allocation problem for national security is formulated and analyzed using the uncertain extensive game. Results show that different decision criteria may lead to different subgame perfect equilibria, demonstrating the significance of introducing different uncertain subgame perfect equilibria.

Computational ability in games: Individual difference and dynamics

In games especially large scale extensive games, players’ actual views of the game might be different from the real one, because of the limit of their computational power. Moreover, players’ views on the underlying game vary from person to person. Based on some existing work on modelling players’ limited foresight in games, we study several interesting types of players in terms of the characteristics of their actual views. The underlying model is closely connected to the well-known algorithm called α−β pruning, and an algorithmic procedure refining classical backward-induction is designed for strategy choosing in the actual process of playing such games. Further, we study the dynamic evolution of players’ foresight and show the resulting preference change.

Irrationality and ambiguity in extensive games

Based on a model where deviations from equilibrium play are assumed to identify irrational players who are characterized by ambiguous set-valued strategies, this paper introduces an equilibrium notion for extensive games with ambiguity averse players that yields a precise interpretation for the counterfactual reasoning usually associated with backward induction. The resulting equilibria are always Nash equilibria, but may not satisfy the conditions required for various refinements of Nash equilibrium, including those for subgame perfection. Existence of such equilibria is proved for all two-player games, and for N-player games with perfect information.

Positional Power in Hierarchies

Power is a core concept in the analysis and design of organisations. In this paper we consider positional power in hierarchies. One of the problems with the extant literature on positional power in hierarchies is that it is mainly restricted to the analysis of power in terms of the bare positions of the actors. While such an analysis informs us about the authority structure within an organisation, it ignores the decision-making mechanisms completely. The few studies which take into account the decision-making mechanisms make all use of adaptations of well-established approaches for the analysis of power in non-hierarchical organisations such as the Banzhaf measure; and thus they are all based on the structure of a simple game, i.e. they are 'membership based'. We demonstrate that such an approach is in general inappropriate for characterizing power in hierarchies as it cannot be extended to a class of decision-making mechanisms which allow certain actors to terminate a decision before all other members have been involved. As this kind of sequential decision-making mechanism turns out to be particularly relevant for hierarchies, we suggest an action-based approach - represented by an extensive game form - which can take the features of such mechanisms into account. Based on this approach we introduce a power score and measure that can be applied to ascribe positional power to actors in sequential decision making mechanisms.

Kuhn's Theorem for Extensive Games with Unawareness

We extend Kuhn's Theorem to extensive games with unawareness. This extension is not entirely obvious: First, extensive games with non-trivial unawareness involve a forest of partially ordered game trees rather than just one game tree. An information set at a history in one tree may consist of histories in a less expressive tree. Consequently, perfect recall takes a more complicated form as players may also become aware of new actions during the play. Second, strategies can only be partially an object of ex-ante choice in games with unawareness. Finally, histories that a player may expect to reach with a strategy profile may not be the histories that actually occur with this strategy profile, requiring us to define appropriate notions of equivalence of strategies.

Extensive Game of Horse Race: A Research on <i>Tian Ji's Horse Race</i> Based on Static Games of Complete Information

There are many ways to develop of the classical problem about Tian Ji's Horse Race so that this problem may be researched deeply using theory of games. Therefore, this paper designs n-order extensive game of horse race by changing a rule of traditional problem. After analysis, this paper holds a belief that this game is a kind of static games of complete information, which means theory of static games of complete information can be used to research Tian Ji's Horse Race . With showing all of the strategy profiles of third-order extensive game of horse race and calculating Nash equilibrium of this game, this paper finds some characteristics of the strategy profiles and Nash equilibrium of extensive game of horse race and give the expression of Nash equilibrium of mixed strategy of this game. A new concept of layout is introduced to reveal how strategy profiles influence the outcome of this game. Then the characteristic of the layouts of extensive game of horse race and the layout that can make Tian Ji’s payoff biggest are found and proved, which is drawn from the result of some simulations about fourth-order and fifth-rank extensive games of horse race using a Java program.