Nonlocal sets of orthogonal multipartite product states with less members

Repeated quantum game theory addresses long-term relations among players who choose quantum strategies. In the conventional quantum game theory, single-round quantum games or at most finitely repeated games have been widely studied; however, less is known for infinitely repeated quantum games. Investigating infinitely repeated games is crucial since finitely repeated games do not much differ from single-round games. In this work, we establish the concept of general repeated quantum games and show the Quantum Folk Theorem, which claims that by iterating a game one can find an equilibrium strategy of the game and receive reward that is not obtained by a Nash equilibrium of the corresponding single-round quantum game. A significant difference between repeated quantum prisoner’s dilemma and repeated classical prisoner’s dilemma is that the classical Pareto optimal solution is not always an equilibrium of the repeated quantum game when entanglement is sufficiently strong. When entanglement is sufficiently strong and reward is small, mutual cooperation cannot be an equilibrium of the repeated quantum game. In addition, we present several concrete equilibrium strategies of the repeated quantum prisoner’s dilemma.

     

Noise and the magic square game

A pseudo-telepathy game is a game for two or more players for which there is no classical winning strategy, but there is a winning strategy based on sharing quantum entanglement by the players. Since it is generally very hard to perfectly implement a quantum winning strategy for a pseudo-telepathy game, quantum players are almost certain to make errors even though they use a winning strategy. After introducing a model for pseudo-telepathy games, we investigate the impact of erroneously performed unitary transformations and also of noisy measurement devices on the quantum winning strategy for the magic square game. The question of how strong both types of noise can be so that quantum players would still be better than classical ones is also dealt with.     

A quantum approach to play asymmetric coordination games

We present a quantum approach to play asymmetric coordination games, which are more general than symmetric coordination games such as the Battle of the Sexes game, the Chicken game and the Hawk–Dove game. Our results show that quantum entanglement can help the players to coordinate their strategies.     

A value for games with a priori incompatible players

ABSTRACT

Numerous situations in decision-making deal with a set of agents who need to work together but they have some a priori bilateral problems among them. This paper introduces cooperative games with a priori incompatibilities using particular coalition systems. In these games, there are some red lines between some players, so that the negotiation has two stages. In the first stage, players can only negotiate with those with whom they are compatible. After that, the grand coalition will be formed. A value for these games is defined by using cooperative games with coalition configuration. A characterization of this value is obtained.     

e-Sports: Playing just for fun or playing to satisfy life goals?

Purposee-Sports is an area of the game scene, in which computer game players specialize in a specific game, form game teams (clans), compete together in tournaments and meet at so-called LAN (Local Area Network) parties. The objective of this study was to compare the different types of e-Sports players from the perspective of their personality traits and explicit motives and to compare e-Sports players with casual players in selected life goals.MethodsA questionnaire assessing life goals (Pöhlmann & Brunstein, 1997) and basic personality traits (Personality inventory KUD, 1986) were administered to 108 e-Sports players and 54 casual computer game players.ResultsIn the group of e-Sports players, only clan leaders significantly differed in life goal power from those who were not members of any clan. Significant differences were also found between e-Sports players and casual players in terms of life goals affiliation and diversion.Conclusionse-Sports seem not only to be about playing computer games, but can also serve as a means of satisfying the need to belong. They do this by creating friendly relationships through membership in game teams and participation in LAN parties, or satisfying the need for power by upholding a position of a game team leader and determining its course of action.     

Influence of initial conditions in 2\times 2 symmetric games

It is known that quantum game is characterized by the payoff matrix as well as initial states of the quantum objects used as carriers of information in a game. Further, the initial conditions of the quantum states influence the strategies adopted by the quantum players. In this paper, we identify the necessary condition on the initial states of quantum objects for converting symmetric games into potential games, in which the players acquire the same payoff matrix. The necessary condition to preserve the symmetric type and potential type of the game is found to be the same. The present work emphasizes the influence of the initial states in the quantization of games.     

Avoiding game‐tree pathology in 2‐player adversarial search

Adversarial search, or game‐tree search, is a technique for analyzing an adversarial game to determine what moves a player should make in order to win a game. Until recently, lookahead pathology (in which deeper game‐tree search results in worse play) has been thought to be quite rare. We provide an analysis that shows that every game should have some sections that are locally pathological, assuming that both players can potentially win the game. We also modify the minimax algorithm to recognize local pathologies in arbitrary games and cut off search accordingly (shallower search is more effective than deeper search when local pathologies occur). We show experimentally that our modified search procedure avoids local pathologies and consequently provides improved performance, in terms of decision accuracy, when compared with the minimax algorithm. In addition, we provide an experimental evaluation on the African game of Kalah, which shows the improved performances of our suggested error‐minimizing minimax algorithm when there is a large degree of pathology.     

Quantum game simulator, using the circuit model of quantum computation

We present a general two-player quantum game simulator that can simulate any two-player quantum game described by a 2×2 payoff matrix (two strategy games).The user can determine the payoff matrices for both players, their strategies and the amount of entanglement between their initial strategies. The outputs of the simulator are the expected payoffs of each player as a function of the other player's strategy parameters and the amount of entanglement. The simulator also produces contour plots that divide the strategy spaces of the game in regions in which players can get larger payoffs if they choose to use a quantum strategy against any classical one. We also apply the simulator to two well-known quantum games, the Battle of Sexes and the Chicken game.

Program summary

Program title: Quantum Game Simulator (QGS)Catalogue identifier: AEED_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEED_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 3416No. of bytes in distributed program, including test data, etc.: 583 553Distribution format: tar.gzProgramming language: Matlab R2008a (C)Computer: Any computer that can sufficiently run Matlab R2008aOperating system: Any system that can sufficiently run Matlab R2008aClassification: 4.15Nature of problem: Simulation of two player quantum games described by a payoff matrix.Solution method: The program calculates the matrices that comprise the Eisert setup for quantum games based on the quantum circuit model. There are 5 parameters that can be altered. We define 3 of them as constant. We play the quantum game for all possible values for the other 2 parameters and store the results in a matrix.Unusual features: The software provides an easy way of simulating any two-player quantum games.Running time: Approximately 0.4 sec (Region Feature) and 0.3 sec (Payoff Feature) on a Intel Core 2 Duo GHz with 2 GB of memory under Windows XP.     

Localization of two-particle quantum walk on glued-tree and its application in generating Bell states

Studies on two-particle quantum walks show that the spatial interaction between walkers will dynamically generate complex entanglement. However, those entanglement states are usually on a large state space and their evolutions are complex. It makes the entanglement states generated by quantum walk difficult to be applied directly in many applications of quantum information, such as quantum teleportation and quantum cryptography. In this paper, we firstly analyse a localization phenomena of two-particle quantum walk and then introduce how to use it to generate a Bell state. We will show that one special superposition component of the walkers’ state is localized on the root vertex if a certain interaction exists between walkers. This localization is interesting because it is contrary to our knowledge that quantum walk spreads faster than its classical counterpart. More interestingly, the localized component is a Bell state in the coin space of two walkers. By this method, we can obtain a Bell state easily from the quantum walk with spatial interaction by a local measurement, which is required in many applications. Through simulations, we verify that this method is able to generate the Bell state \(\frac{1}{\sqrt{2}}(|A \rangle _1|A\rangle _2 \pm |B\rangle _1|B\rangle _2)\) in the coin space of two walkers with fidelity greater than \(99.99999\,\%\) in theory, and we have at least a \(50\,\%\) probability to obtain the expected Bell state after a proper local measurement.     

An Efficient Synchronization Mechanism for Mirrored Game Architectures

Existing online multiplayer games typically use a client-server model, which introduces added latency as well as a single bottleneck and single point of failure to the game. Distributed multiplayer games minimize latency and remove the bottleneck, but require special synchronization mechanisms to provide a consistent game for all players. Current synchronization methods have been borrowed from distributed military simulations and are not optimized for the requirements of fast-paced multiplayer games. In this paper we present a new synchronization mechanism, trailing state synchronization (TSS), which is designed around the requirements of distributed first-person shooter games.We look at TSS in the environment of a mirrored game architecture, which is a hybrid between traditional centralized architectures and the more scalable peer-to-peer architectures. Mirrored architectures allow for improved performance compared to client-server architectures while at the same time allowing for a greater degree of centralized administration than peer-to-peer architectures.We evaluate the performance of TSS and other synchronization methods through simulation and examine heuristics for selecting the synchronization delays needed for TSS.     

Ambidextrous Innovation and Game Market Fit Performance: Feedback from Game Testers

ABSTRACT

The dynamics of the market pose a challenge for the digital game industry. Game development firms must develop innovative games to satisfy game players’ ever-changing needs and sustain a suitable product/market fit. To realize such innovation, developers tend to adopt an ambidextrous approach that includes exploratory and exploitative activities to develop games. In addition, game development teams must rely on feedback from game testers to enhance development and meet game players’ needs. However, the effect of feedback on innovation is subject to debate. Some studies have proposed that feedback has potentially negative effects on creativity. Given the prevalence of ambidextrous innovation and the utilization of feedback from game testers, no study to date has investigated the effects of feedback on game development quality. A survey of 119 paired game producers and developers revealed that “feedback timing” from game testers positively enhances the relationship between ambidextrous innovation and a game’s final development performance, whereas “feedback specificity” impairs the effectiveness of ambidextrous innovation. This paper discusses the implications of this study.     

Characterizing the Nash equilibria of a three-player Bayesian quantum game

Quantum games with incomplete information can be studied within a Bayesian framework. We consider a version of prisoner’s dilemma (PD) in this framework with three players and characterize the Nash equilibria. A variation of the standard PD game is set up with two types of the second prisoner and the first prisoner plays with them with probability p and \(1-p\), respectively. The Bayesian nature of the game manifests in the uncertainty that the first prisoner faces about his opponent’s type which is encoded either in a classical probability or in the amplitudes of a wave function. Here, we consider scenarios with asymmetric payoffs between the first and second prisoner for different values of the probability, p, and the entanglement. Our results indicate a class of Nash equilibria (NE) with rich structures, characterized by a phase relationship on the strategies of the players. The rich structure can be exploited by the referee to set up rules of the game to push the players toward a specific class of NE. These results provide a deeper insight into the quantum advantages of Bayesian games over their classical counterpart.     

Learning results and terminal values from the players of SimCity and The Sims

Most research on the topic conducted in the past did not elaborate in depth on the attributes of games that correspond to specific learning results. In this study, the means-end chain theory has been adopted as the theoretical basis to focus on the players of SimCity and The Sims (two of the most representative titles of the simulation game genre) as the subjects of the research. Through in-depth interviews conducted using the Soft Laddering approach, the study aims to examine the key attributes that would trigger learning results for players when playing games and the terminal values that the players would experience internally. The study also featured group comparison of subjects based on their gender. Results of the study showed that gamers still emphasise on the key aspects of Simulated reality and Self-created game content for simulation games. These two attributes have been found to lead to the learning results of Gain authentic experience and Cultivate imagination and creativity, ultimately leading to the terminal value of Sense of accomplishment.     

Towards affective camera control in games

Information about interactive virtual environments, such as games, is perceived by users through a virtual camera. While most interactive applications let users control the camera, in complex navigation tasks within 3D environments users often get frustrated with the interaction. In this paper, we propose inclusion of camera control as a vital component of affective adaptive interaction in games. We investigate the impact of camera viewpoints on psychophysiology of players through preference surveys collected from a test game. Data is collected from players of a 3D prey/predator game in which player experience is directly linked to camera settings. Computational models of discrete affective states of fun, challenge, boredom, frustration, excitement, anxiety and relaxation are built on biosignal (heart rate, blood volume pulse and skin conductance) features to predict the pairwise self-reported emotional preferences of the players. For this purpose, automatic feature selection and neuro-evolutionary preference learning are combined providing highly accurate affective models. The performance of the artificial neural network models on unseen data reveals accuracies of above 80% for the majority of discrete affective states examined. The generality of the obtained models is tested in different test-bed game environments and the use of the generated models for creating adaptive affect-driven camera control in games is discussed.     

When Can Limited Randomness Be Used in Repeated Games?

The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at generating random-like sequences, and true random bits may be unavailable. Even if the players have access to enough random bits for a single instance of the game their randomness might be insufficient if the game is played many times. In this work, we ask whether randomness is necessary for equilibria to exist in finitely repeated games. We show that for a large class of games containing arbitrary two-player zero-sum games, approximate Nash equilibria of the n-stage repeated version of the game exist if and only if both players have Ω(n) random bits. In contrast, we show that there exists a class of games for which no equilibrium exists in pure strategies, yet the n-stage repeated version of the game has an exact Nash equilibrium in which each player uses only a constant number of random bits. When the players are assumed to be computationally bounded, if cryptographic pseudorandom generators (or, equivalently, one-way functions) exist, then the players can base their strategies on “random-like” sequences derived from only a small number of truly random bits. We show that, in contrast, in repeated two-player zero-sum games, if pseudorandom generators do not exist, then Ω(n) random bits remain necessary for equilibria to exist.     

Quantum games and quaternionic strategies

It is well-known that the phenomenon of entanglement plays a fundamental role in quantum game theory. Occasionally, games constructed via maximally entangled initial states (MEIS) will have new Nash equilibria yielding to the players higher payoffs than the ones they receive in the classical version of the game. When examining these new games for Nash equilibrium payoffs, a fundamental question arises; does a suitable choice of an MEIS improve the lot of the players? In this paper, we show that the answer to this question is yes for at least the case of a variant of the well-known two player, two strategy game of Chicken. To that end, we generalize Landsburg’s quaternionic representation of the payoff function of two player, two strategy maximally entangled states to games where the initial state is chosen arbitrarily from a circle of maximally entangled initial states and for the corresponding quantized games show the existence of superior Nash equilibrium payoffs when an MEIS is appropriately chosen.     

Cooperative games with multiple attributes

ABSTRACT

In this paper, we introduce the notion of a cooperative game with multiple attributes where players can provide partial participations in multiple attributes and form coalitions. The power or influence of the players due to their multiple attributes is evaluated based on their memberships in the coalitions. Our game therefore, extends the notion of cooperative games with fuzzy coalitions. The Shapley function for this class of games is proposed as a rational and fair solution concept. Every fuzzy game stems out of a specific crisp game under the assumption that the players provide partial memberships in forming multiple coalitions simultaneously. We adopt similar techniques to obtain the cooperative games with multiple attributes from their crisp counterparts and subsequently determine their Shapley functions.     

Nash Play Strings of Symmetric Games and Their Language Classes

Abstract

It is an interesting point of view to consider N-person games as models of human behavior and their decision making processes in the society. Bryzgalov et al. [1] have proposed a kind of N-person game in which all players are equivalent, i.e., homogeneous games. In this paper, considering one of the homogeneous games, i.e., symmetric games, and assuming the patterns of Nash play strings as a language, we determine the language classes of them.     

Graphical Congestion Games

We consider congestion games with linear latency functions in which each player is aware only of a subset of all the other players. This is modeled by means of a social knowledge graph G in which nodes represent players and there is an edge from i to j if i knows j. Under the assumption that the payoff of each player is affected only by the strategies of the adjacent ones, we first give a complete characterization of the games possessing pure Nash equilibria. Namely, if the social graph G is undirected, the game is an exact potential game and thus isomorphic to a classical congestion game. As a consequence, it always converges and possesses Nash equilibria. On the other hand, if G is directed an equilibrium is not guaranteed to exist, but the game is always convergent and an equilibrium can be found in polynomial time if G is acyclic, even if finding the best equilibrium remains an intractable problem.     

A note on decisive symmetric games

Binary voting systems, usually represented by simple games, constitute a main DSS topic. A crucial feature of such a system is the easiness with which a proposal can be collectively accepted, which is measured by the “decisiveness index” of the corresponding game. We study here several functions related to the decisiveness of any simple game. The analysis, including the asymptotic behavior as the number n of players increases, is restricted to decisive symmetric games and their compositions, and it is assumed that all players have a common probability p to vote for the proposal. We show that, for n large enough, a small variation, either positive or negative, in p when p = 1/2 takes the decisiveness to quickly approach, respectively, 1 or 0. Moreover, we analyze the speed of the decisiveness convergence.