Large Number Of Players Research Articles

Equilibria problems on games: Complexity versus succinctness

We study the computational complexity of problems involving equilibria in strategic games and in perfect information extensive games when the number of players is large. We consider, among others, the problems of deciding the existence of a pure Nash equilibrium in strategic games or deciding the existence of a pure Nash or a subgame perfect Nash equilibrium with a given payoff in finite perfect information extensive games. We address the fundamental question of how can we represent a game with a large number of players? We propose three ways of representing a game with different degrees of succinctness for the components of the game. For perfect information extensive games we show that when the number of moves of each player is large and the input game is represented succinctly these problems are PSPACE-complete. In contraposition, when the game is described explicitly by means of its associated tree all these problems are decidable in polynomial time. For strategic games we show that the complexity of deciding the existence of a pure Nash equilibrium depends on the succinctness of the game representation and then on the size of the action sets. In particular we show that it is NP-complete, when the number of players is large and the number of actions for each player is constant, and that the problem is Σ 2 p -complete when the number of players is a constant and the size of the action sets is exponential in the size of the game representation. Again when the game is described explicitly the problem is decidable in polynomial time.

A decision-support methodology for priority allocation among road users at signalized junctions

Changing traffic signal programs due to traffic dynamics is an essential step to improve the quality of the city's traffic management. But the large number of players, who are competing for the same resources, complicates the selection of new signal programs. The cars, Public Transport (PT) and pedestrians all coming from different directions create a complex right of way allocation problem. The selection of a new program becomes an especially complex task when PT priority logic is integrated into the signal program planning. This paper suggests a methodology for performing the selection process. The methodology described in this article for selecting an alternative signal program is based on a definition of Standard Planning Attributes (SPA), which serve as a “data dictionary”. The selection criteria, called Integrated Components, takes into account the interdependencies linking the various Signal Groups (SGs) and Standard Planning Attributes and the directivity of the relationship between Planning Attributes (PA) and the performance level of each road user.

Study on Risk Assessment of Network Security Based on Game Theory

to strengthen the network security and to enhance the accuracy of the network security risk assessment, the essay conducts game analysis to the security system of protective mechanisms. Using the basic theory of games and the analytical and comparative method, and raising the network security and physical model for the security system, this process will protect and improve the network security. At the aspect of setting the model, we did not rely on the traditional game theory, but creatively set behavior of the game for a large number of players for the limit logos of groups in the model, and paid more attention to the detection system to reach a state of stability. Analysis shows that the proposed models and the method are feasible and effective.

Halonix Limited – the product portfolio dilemma

Subject area Strategy, strategic management, market and product analysis. Study level/applicability The case is intended for a business strategy course in management. The target participants are MBA students specializing in strategy area as well as middle level and senior level managers from the industry, who come for an executive programme in management science. Case overview Year 2009, Mr Pawan Kumar (General Manager, Halonix Limited) was facing a decision-making situation in the organization. Being one of the most experienced and oldest employees of Halonix (incorporated as Phoenix Lamps Ltd in 1991), he had witnessed the tremendous growth of the company since its inception in 1991. The company was having a global brand image in automotive halogen lamps and became a dominant player in compact fluorescent lamp (CFL) market in India by 2007. With the increasing competition and change in market dynamics, the company needed to decide upon the future product portfolio mix and strategy to be adopted to gain the maximum benefit and win over the competition in both the product segments. The automotive halogen product segment was generating higher margins but having relatively slow growth. The CFL product segment was a growing market but was generating low margins due to increasing competition from entry of large number of players. Expected learning outcomes The theoretical concepts, which will be explored in this case, involve the following: the importance of industry structure analysis in understanding the basis of competition. The importance of value-chain analysis in strategic planning. The importance of Boston Consulting Group growth-share matrix in evaluating the product portfolio mix having different growth drivers and target segments? Supplementary materials Teaching notes.

Some Recent Aspects of Differential Game Theory

This survey paper presents some new advances in theoretical aspects of differential game theory. We particular focus on three topics: differential games with state constraints; backward stochastic differential equations approach to stochastic differential games; differential games with incomplete information. We also address some recent development in nonzero-sum differential games (analysis of systems of Hamilton–Jacobi equations by conservation laws methods; differential games with a large number of players, i.e., mean-field games) and long-time average of zero-sum differential games.

‘You May Say What You Like to the Professional and Dismiss Them When You Want’: The Rise and Fall of Professional Chess Players in Victorian Britain

From the 1840s chess was a popular game among the middle classes in Britain, commanding great respect because it was regarded as being an ‘improving’ recreation. In 1851 London staged the world's first international chess tournament, and from then until the 1880s large numbers of players, both British and foreign, endeavoured to earn their living from the game. These ‘professionals’ were gradually undermined by two attacks on the game's respectability. Foreign players were attacked on simple xenophobic lines, but more broadly all professional chess players were also undermined by a disapproval of the financial element of the game. The paper pays particular attention to two professionals, Staunton and Steinitz, who embodied the transformation in attitudes towards professional chess.

Imitation in Large Games

In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation types: that of players who imitate choice of other (optimizing) types. Game theorists typically study the evolution of such games in dynamical systems with imitation rules. In the setting of games of infinite duration on finite graphs with preference orderings on outcomes for player types, we explore the possibility of imitation as a viable strategy. In our setup, the optimising players play bounded memory strategies and the imitators play according to specifications given by automata. We present algorithmic results on the eventual survival of types.

DISTRIBUTED LEARNING OF EQUILIBRIA IN A ROUTING GAME

We focus on the problem of learning equilibria in a particular routing game similar to the Wardrop traffic model. We describe a routing game played by a large number of players and present a distributed learning algorithm that we prove to converge weakly to equilibria for the system. The proof of convergence is based on a differential equation governing the global evolution of the system that is inferred from all the local evolutions of the agents in play. We prove that the differential equation converges with the help of Lyapunov techniques.

Evolution of Seeds Commerce: Deregulation, Technology, and Local Practices

This paper captures the evolution of seeds commerce in India, a traditionally agrarian economy. It also captures some exciting aspects of industry evolution of one of the top seeds market in the world (given its size). Following a review of the industry in India over the last few decades one observes that the deregulation of seeds commerce has been influenced not only by the progressive liberalization of the Indian economy but also by the development of science and technology in the private sector, both locally and globally. This has resulted in the seeds market in India becoming highly competitive by attracting a large number of players. The discussion also captures another interesting facet – that the norms and regulations of the industry and the way it develops can be severely influenced not only by the (large) private business players but also by the dispersed (and seemingly) powerless farming community! The existing farmer’s rights gives a free hand to farmers to multiply, exchange, sell and use any proprietary (seed) variety. The local practices especially of seed organizers also make the life of the rules setter (i.e., the state) very difficult. Perhaps, one can observe that seeds commerce in India has grown beyond the control of the state and its bureaucracy.

Democracy in the European Union

Many observers take it for granted that the European Union suffers from a lack of democracy: in the dual sense that common policies have diverged from voters’ preferences (output legitimacy) and that decision-making mechanisms appear to lack the basic requirements of transparency, accountability and democratic involvement (input legitimacy). Stefano Micossi, Director General of Assonime, argues in this paper that once the Union is recognised for what it is – an innovative polity, where power is shared by a large number of players with many participation and influence-wielding mechanisms, – it becomes apparent that on the whole it complies with democratic legitimisation standards no less than do member states, even if multiple, and potentially conflicting legitimisation channels and principles may confuse observers. The member states and EU citizens continue to turn to the Union to seek solutions to problems that cannot be solved nationally, and there is an extraordinary proliferation of subjects and channels providing participation in European debates and decisions, in new and ever-changing ways. Through this continuous adjustment process, the Union has designed new legitimisation solutions that may well represent the future of democracy in a world of diverse but increasingly interconnected communities. CEPS Working Documents are intended to give an indication of work being conducted within CEPS research programmes and to stimulate reactions from other experts in the field. Unless otherwise indicated, the views expressed are attributable only to the author in a personal capacity and not to any institution with which s/he is associated.

Distributed consensus in noncooperative inventory games

This paper deals with repeated nonsymmetric congestion games in which the players cannot observe their payoffs at each stage. Examples of applications come from sharing facilities by multiple users. We show that these games present a unique Pareto optimal Nash equilibrium that dominates all other Nash equilibria and consequently it is also the social optimum among all equilibria, as it minimizes the sum of all the players’ costs. We assume that the players adopt a best response strategy. At each stage, they construct their belief concerning others probable behavior, and then, simultaneously make a decision by optimizing their payoff based on their beliefs. Within this context, we provide a consensus protocol that allows the convergence of the players’ strategies to the Pareto optimal Nash equilibrium. The protocol allows each player to construct its belief by exchanging only some aggregate but sufficient information with a restricted number of neighbor players. Such a networked information structure has the advantages of being scalable to systems with a large number of players and of reducing each player’s data exposure to the competitors.

Stochastic dynamics and Parrondo’s paradox

The Spanish physicist Juan Parrondo has provided two stochastic losing games such that for certain stochastic combinations one may obtain a winning game. If a large number of players are involved and if they try to play such that their gain in the next round is maximized one arrives at the problem of investigating a random walk on a certain space of measures. The appropriate abstract setting is as follows. There is given a compact metric space ( M , d ) , and M is written as the union of certain closed subsets A 1 , … , A r . For every ρ = 1 , … , r there is prescribed a strict contraction Γ ρ : A ρ → M . A random walk ( X m ) m ∈ N 0 on M is then defined as follows. The starting position is X 0 = x 0 , where x 0 ∈ M is fixed, and if the walk at the m ’th step is at position X m ∈ M , then one chooses a ρ among the ρ with X m ∈ A ρ (with equal probability, say) and defines X m + 1 as Γ ρ ( X m ) . Associated with the walk is a gain φ ( X m ) in every round, where φ : M → R is a continuous function. The aim of the present investigations is the study of the expectation G m of φ ( X m ) as a function of m . Our main result states that the sequence ( G m ) is “eventually approximately periodic” provided that all A ρ are not only closed but also open in M : for every ε there is an l 0 ∈ N such that ( G m ) is l 0 -periodic up to an error of at most ε for sufficiently large m . In fact it turns out that the behaviour of our process can be described well with a finite Markov chain. In the general case, however, the process might behave rather chaotically. We give an example where M is the unit interval. M is written as the union of two closed subsets A 1 , A 2 , the contractions Γ 1 , Γ 2 are rather simple, but the expectations of the gains are not even Cesáro convergent.

Jeux à champ moyen. I – Le cas stationnaire

We introduce here a general approach to model games with a large number of players. More precisely, we consider N players Nash equilibria for long term stochastic problems and establish rigorously the ‘mean field’ type equations as N goes to infinity. We also prove general uniqueness results and determine the deterministic limit. To cite this article: J.-M. Lasry, P.-L. Lions, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

Dynamics of multi-player games

We analyse the dynamics of competitions with a large number of players. In our model,n playerscompete against each other and the winner is decided based on the standings: in each competition,the mth ranked player wins. We solve for the long time limit of the distribution of the number of wins for alln and m using scaling analysis of the nonlinear evolution equations, and find three differentscenarios. When the best player wins, the standings are most competitive as there is onetier with a clear differentiation between strong and weak players. When an intermediateplayer wins, the standings are two-tier with equally strong players in the top tier andclearly-separated players in the lower tier. Interestingly, the size and the strength of theupper tier are nontrivial. When the worst player wins, the standings are leastcompetitive as there is one tier in which all of the players are equal. We conclude thatcontrolling the rank of the winner provides a way of controlling social inequalities.

MMORPG에서의 부하 분산을 위한 가상 영역 정보 기반 동적 지역 분할

MMORPG(Massively Multiplayer Online Role-Playing Game)은 대규모의 인원들이 동일한 가상공간에서 동일한 시각에 상호작용하면서 활동하는 온라인 롤플레잉 게임이다. 대부분의 경우, 서버와 대역폭 등에서 상당한 수준의 하드웨어 사양과 지원 스태프를 필요로 한다. 수많은 개발자들의 노력에도 불구하고 사용자들은 여전히 플레이어의 과밀, 랙, 그리고 부족한 지원 등에 대해 불만을 가지는 경우가 많다. 본 논문에서는 MMORPG에서의 부하 분산을 위한 동적 지역 분할 방법을 제안한다. Field, sector group, sector, cell 등으로 구성되는 가상 영역 정보를 가진 VML(Virtual Map Layer)를 이용하여 지역을 분할함으로써 부하 분산을 시도한다. 실험 결과, 제안된 기법이 <TEX>$23^{\sim}67%$</TEX> 정도의 부하를 줄이는 효과를 가져왔다. 맵 데이터, 자원의 상태, 그리고 사용자들의 행동 패턴의 변화 등에 대해서는 VML에 대한 간단한 수정으로 유연하게 적응할 수 있다. A MMORPG(Massively Multiplayer Online Role-Playing Game) is an online role-playing game in which a large number of players can interact with each other in the same world at the same time. Most of them require significant hardware requirements(e.g., servers and bandwidth), and dedicated support staff. Despite the efforts of developers, users often cite overpopulation, lag, and poor support as problems of games. In this paper, a dynamic load balancing method for MMORPGS is proposed. It tries to adapt to dynamic change of population by using dynamic map-partition method with VML(Virtual Map Layer) which consists of fields, sector groups, sectors, and cells. From the experimental results, our approach achieves about <TEX>$23^{\sim}67%$</TEX> lower loads for each field server. By the modification to Virtual Area Layer, we can easily manage problems that come from changes of map data, resources' status, and users' behavior pattern.

Market Games in Large Economies with a Finite Number of Types

We study market games derived from an exchange economy with a con- tinuum of agents, each having one of finitely many possible types. The type of agent determines his initial endowment and utility function. It is shown that, unlike the well-known Shapley-Shubik theorem on market games (Shapley and Shubik in J Econ Theory 1:9-25, 1969), there might be a (fuzzy) game in which each of its sub-games has a non-empty core and, nevertheless, it is not a market game. It turns out that, in order to be a market game, a game needs also to be homogeneous. We also study investment games - which are fuzzy games obtained from an economy with a finite number of agents cooperating in one or more joint projects. It is argued that the usual definition of the core is inappropriate for such a model. We therefore introduce and analyze the new notion of comprehensive core .T his solution concept seems to be more suitable for such a scenario. We finally refer to the notion of feasibility of an allocation in games with a large number of players.

Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games

While there is an extensive literature on the theory of infinitely repeated games, empirical evidence on how “the shadow of the future” affects behavior is scarce and inconclusive. I simulate infinitely repeated prisoner's dilemma games in the lab with a random continuation rule. The experimental design represents an improvement over the existing literature by including sessions with finite repeated games as controls and a large number of players per session (which allows for learning without contagion effects). I find that the shadow of the future matters not only by significantly reducing opportunistic behavior, but also because its impact closely follows theoretical predictions.

Signal extraction for simulated games with a large number of players

A signal extraction problem in simulated games is studied. A modelling technique is proposed for deriving beliefs for players in simulated games. Since standard Bayesian games provide conditions for beliefs on the basis of the common prior assumption, they do not allow for non-uniform beliefs unless the game has some dynamic structure that allows for learning. The framework presented allows for deriving beliefs by characterizing the reliability of the signals, and the players’ degree of confidence in these signals. This makes it particularly suitable for games with a large number of heterogenous players.

Towards Global Information Society????

The idea for this lecture is Looking at a Complex Puzzle from different viewpoints, including changes resulting from the passage of time. The title gives anchor-positions to each single word and question mark - and offers the possibility of combining two, three or all four words. It is not only Technology Development, but also mankind's fantasy that is driving us. Most of the developments for our reality and environment have already been described years or even decades ago. We are moving towards an Information Society, but do we not already have more than one type of Society on this planet?The advantages of broadband communication with regard to education, knowledge formation and economical development are obvious, but not everyone has access to it or can use it. Last century during the 1950's, then United States' President. Dwight D. Eisenhower, initiated the Atoms for Peace Program. Worldwide networking was initiated with advanced information exchange. Is it now possible to set up a worldwide Read, Write, Calculate and Think Program?Assuming that information is important for mankind, we see a large number of players taking action, but we must understand that no individual player can do everything alone. It is together that they create a totally New World for legal and regulatory developments. The difficulties of harmonization are clearly shown by the lack of results from the Global Business Dialog: We are not ready! And although we are not able to look into future, we are certain of the following: The character of the information society under development is unknown, and the future information complex needs steady careful observation and improvement whenever and wherever possible.

A federated peer-to-peer network game architecture

A federated peer-to-peer game is one in which many small areas of interest within a game each supported using a peer-to-peer model are "knitted" together to form a game capable of supporting a very large number of players. Our work has involved determining whether such an architecture is a feasible alternative to the more common central server architecture for supporting large multiplayer network games.