Measuring skill in games: several approaches discussed

An aspect of casino games that in general leads to discussions among both participants and spectators, is the relative extent to which a player can positively influence his results by making appropriate strategic choices. This question is closely related to the issue of how to distinguish between games of skill and games of chance. This is an issue that is interesting from a juridical point of view too, since in many countries the legitimacy of exploiting a specific game depends on the category to which it belongs. This paper summarizes recent developments concerning the measurement of skill in games. It points out the elements in the definitions that need closer attention, it illustrates the analysis with examples and it discusses further possibilities.     

On the role of chance moves and information in two-person games

The value of information has been the subject of many studies in a strategic context. The central question in these studies is how valuable the information hidden in the chance moves of a game is for one or more of the players. Generally speaking, only the extra possibilities that are beneficial for the players have been considered so far. In this note we study the value of information for a special class of two-person games. For these games we also investigate how “badly” the players can do, both with and without knowing the result of the chance move. In this way one can determine to what extent the players are restricted in their possibilities by the fact that some information is hidden in the chance moves of the games. This allows for a comparison of the influence of the chance move to the control that the players have over the game result.     

Different ways to represent weighted majority games

It is well known that every simple game is the intersection of weighted majority games. the aim of this paper is to gather together various ways of expressing weighted majority games and, for each game of this type, to give the simplest way to define it. Normalized representations, the parameters of a simple game and the characteristic invariants of a complete game merit special attention. Research partially supported by projects PR9509 of the Polytechnic University of Catalonia and PB96-0493 of DGES     

Using an Iterated Prisoner's Dilemma with Exit Option to Study Alliance Behavior: Results of a Tournament and Simulation

Nearly half of all strategic alliances fail (Park and Russo, 1996; Dyer et al., 2001), often because of opportunistic behavior by one party or the other. We use a tournament and simulation to study strategies in an iterated prisoner's dilemma game with exit option to shed light on how a firm should react to an opportunistic partner. Our results indicate that a firm should give an alliance partner a second chance following an opportunistic act but that subsequent behavior should be contingent on the value of the next best opportunity outside the alliance. Firms should be more forgiving if the potential benefits from the alliance exceed other opportunities. The strategies were also found to be robust across a wide range of game lengths. The implications of these results for alliance strategies are discussed. Steven E. Phelan received his PhD in economics from La Trobe University (Australia) in 1998. Following five years at the University of Texas at Dallas, he joined the faculty of the University of Nevada Las Vegas in 2003. Dr. Phelan's research interests include competitive dynamics, organizational efficiency, acquisition and alliance performance, and entrepreneurial competence. His methods of choice to study these phenomena include agent-based modelling, experimental game theory, and event studies. Prior to joining academia, Dr. Phelan held executive positions in the telecommunications and airline industries and was a principal partner in Bridges Management Group, a consultancy specializing in strategic investment decisions. Richard J. Arend is a graduate of the University of British Columbia's doctoral program in Policy Analysis and Strategy. He is on the Management faculty of the University of Nevada, Las Vegas, arriving most recently from the Management faculty of New York University's Stern School of Business. Dr. Arend's interests lie in the analysis of unusual modes of firm value creation and destruction, where he has published in several top journals. He is a professional engineer with work and consulting experience in aerospace and computing. Darryl A. Seale joined the faculty of UNLV in 1999, following three years at Kent State University and the University of Alabama in Huntsville. Prior to Alabama, he completed his Ph.D. and M.S. degrees in Business Administration at the University of Arizona, his M.B.A. from Penn State University, and spent over ten years in management and market planning positions in the health care industry. Professor Seale's research interests include strategic decision making, bargaining and negotiation, and behavioral game theory. His research has been funded by the National Science Foundation and has been published in top-tier journals including Management Science, OBHDP, Games and Economic Behavior, and Strategic Management Journal. His teaching interests include business policy/strategy, managerial decision making, and bargaining and negotiation.     

Bidders and dispenser: manipulative hypergames in a multinational context

The object of this paper is to present an introduction to the basic ideas of Hypergame Analysis, and to illustrate these by building some models of a particular type of situation.Hypergame Analysis is an extension of the Game-theoretic framework, the purpose of which is to enable one to model situations in which the various parties are not well-informed of each other's preferences and strategies. we take as a basic structure not a single game, but a linked set of ‘perceived’ games: this, in essence, is what constitutes a Hypergame. Misperceptions may arise accidentally or be deliberately induced. Thus, a player may be acting ‘rationally’ relative to the game he perceives, but this game itself may have been ‘set up’ to suit the interests of some other party.The technique is used to explore situations in which several parties (the ‘bidders’) negotiate competitively with another (the ‘dispenser’) who is able to accept whichever bidder's offer is most advantageous to him. In particular, the ability of the dispenser to ‘play off’ one bidder against another is examined. This is related to an account of the siting of new plant by a Multi-National Corporation. Some general implications are suggested: especially, it is argued that to have a reasonable chance of producing adequate forecasts in such difficult situations, modelling techniques must embody at least this degree of conceptual complexity.     

Slow joins of loopy games

This paper is concerned with two-person games of perfect information and no chance moves in which play may possibly never terminate. The slow join is a way of playing several such games simultaneously, so as to form a single compound game. Our analysis of the slow join is accomplished by extending the notion of the suspense function from games which satisfy the stopping condition to the onside of games which may continue indefinitely. The remoteness function is also employed in the analysis.     

The sequence method for finding solutions to infinite games: A first demonstrating example

A noncooperative infinite game can be approached by a sequence of discrete games. For each game in the sequence, a Nash solution can be found as well as their limit. This idea and procedure was used before as a theoretical device to prove existence of solutions to games with continuous payoffs and recently even for a class of games with discontinuous ones (Dasgupta and Maskin, 1981). No one, however, used the method for the actual solution of a game. Here, an example demonstrates the method's usefulness in finding a solution to a two-person game on the unit square with discontinuous payoff functions.The author wishes to thank D. McFadden for very useful discussions. Financial support was provided in part by NSF Grant No. SOC-72-05551A02 to the University of California, Berkeley, California.     

Information patterns and Nash equilibria in extensive games: 1

In this paper we explore the relation between information patterns and Nash Equilibria in extensive games. By information we mean what players know about moves made by others, as well as by chance. For the most part we confine ourselves to pure strategies. But in Section 2 behavioral strategies are also examined. It turns out that they can be modeled as pure strategies of an appropriately enlarged game. Our results, applied to the enlarged game, can then be reinterpreted in terms of the behavioral strategies of the original game.     

A multistage game with incomplete information requiring an infinite memory

This paper describes a zero-sum, discrete, multistage, time-lag game in which, for one player, there is no integerk such that an optimal strategy, for a new move during play, can always be determined as a function of the pastk state positions; that is, the player requires an infinite memory. The game is a pursuit-evasion game with the payoff to the maximizing player being the time to capture.This paper is the result of work carried out at the University of Adelaide, Adelaide, Australia, under an Australian Commonwealth Postgraduate Award.The author should like to thank the referee for his valued suggestions.     

Dynamically Consistent Cooperative Solution in a Differential Game of Transboundary Industrial Pollution

This paper presents a cooperative differential game of transboundary industrial pollution. A noted feature of the game model is that the industrial sectors remain competitive among themselves while the governments cooperate in pollution abatement. It is the first time that time consistent solutions are derived in a cooperative differential game on pollution control with industries and governments being separate entities. A stochastic version of the model is presented and a subgame-consistent cooperative solution is provided. This is the first study of pollution management in a stochastic differential game framework. This research was supported by the Research Grant Council of Hong Kong Grant HKBU2103/04H and Hong Kong Baptist University Grant FRG/05-06/II22.     

Evolutionary games

This paper deals with a mathematical game. As the name implies, the game concept is formulated with biological evolution in mind. An evolutionary game differs from the usual game concepts in that the players cannot choose their strategies. Rather, the strategies used by the players are handed down from generation to generation. It is the survival characteristics of a strategy that determine the outcome of the evolutionary game. Players interact and receive payoffs according to the strategies they are using. These interactions, in turn, determine the fitness of players using a given strategy. The survival characteristics of strategy are determined directly from the fitness functions. Necessary conditions for determining an evolutionarily stable strategy are developed here for a continuous game. Results are illustrated with an example.Dedicated to G. LeitmannThis work was supported by NSF Grant No. INT-82-10803 and The University of Western Australia (Visiting Fellowship, Department of Mathematics, 1983).     

A differential game with jump process observations

We introduce a stochastic differential game with jump process observations. Both players obtain common, noisy information of the state of the system only at random time instants. The solutions to this game and its continuous observations in noise counterpart are obtained. Some earlier results dealing with the effect of changes in system parameters on the optimal cost for the continuous observations case are extended to the game with jump process observations.This work was supported by a 1978 Summer Faculty Fellowship from the University of Maryland, Baltimore County.     

Algorithms for discounted stochastic games

In this paper, a two-person zero-sum discounted stochastic game with a finite state space is considered. The movement of the game from state to state is jointly controlled by the two players with a finite number of alternatives available to each player in each of the states. We present two convergent algorithms for arriving at minimax strategies for the players and the value of the game. The two algorithms are compared with respect to computational efficiency. Finally, a possible extension to nonzero sum stochastic game is suggested.This research was supported in part by funds allocated to the Department of Operations Research, School of Management, Case Western Reserve University under Contract No. DAHC 19-68-C-0007 (Project Themis) with the U.S. Army Research Office, Durham, North Carolina. The authors thank the referees for their valuable suggestions.     

Teraoka-type two-person nonzero-sum silent duel

The paper discusses a silent nonzero-sum duel between two players each of whom has a single bullet. The duel is terminated at a random time in [0, 1] given by a cumulative distribution function. It is shown that the game has a unique Nash equilibrium under a wide range of possible payoff values for simultaneous firing. This contrasts with a very similar game considered by Teraoka for which there are many Nash equilibria.This work was carried out while the second author was visiting the University of Southampton on a Postdoctoral Fellowship of The Royal Society of London.     

Results in the theory of linear differential games with an information time lag

The solution to a class of differential games in which one player has imperfect information in the form of a time lag on the availability of the state vector is presented. Open-loop and closed-loop strategies are obtained, and the results are shown to reduce to the well-known perfect-information results as the time lag vanishes. The effect of lag on the existence of the solutions to the game and other important qualitative aspects of the game are discussed.The author would like to acknowledge his gratitude to Professor Celso de Renna e Souza, Department of Electrical Engineering, University of Notre Dame, South Bend, Indiana, who advised and encouraged him during the initial research efforts which led to the work presented herein. This paper is based in part on a portion of the dissertation which the author submitted in partial fulfillment of the requirement for the Ph.D. degree at the University of Notre Dame.     

Complete inflation and perfect recall in extensive games

This paper considers the relation between complete inflation and perfect recall of information partitions in extensive games. It is proved that an information partition with perfect recall is completely inflated. This result, combined with Dalkey's theorem, shows that in the class of games (without chance moves) with perfect recall, a game is determinate if and only if every player has perfect information. A necessary and sufficient condition is provided for information partitions whose complete inflations have perfect recall.     

Two Game Models for Cooperation with Implicit Noncooperation

We propose two flexible game models to represent and analyze cases that cannot be modeled by current game models. One is called sharing creditability game (SCG) and the other is called bottomline game (BLG). The new models transform cooperative games into new games that incorporate auxiliary information (noncooperative in nature) usually neglected in previous theories. The new games will be solved only by traditional noncooperative game theory. When the new solutions are applied to the original games, the solutions can reflect the auxiliary information in addition to the original objectives of the decision makers or players. Generally, the new solutions are different from the cooperative and the noncooperative solutions of the original games. Existing transferable utility (TU) games and noncooperative games will coincide with special cases of the two new game models. Using SCG and BLG, the prisoner’s dilemma can be reformulated and a richer set of decisions can be considered for the players. The two new game models have potential applications in military and socioeconomic situations.This research was partly funded by the College Engineering, Ohio State University.     

Opportunistic timing and manipulation in Australian Federal Elections

In many parliamentary systems, election timing is an important decision made by governments in order to maximize their expected remaining life in power. Governments can also introduce policy or economic actions to enhance their popular standing and thus their chance of being re-elected. On the other hand, an oppositions’ natural objective is to gain power, and they will also apply controls through their own policies to reduce the governments’ chance of being re-elected. In this paper we employ a dynamic programming approach to determine the optimal timing for governments and oppositions to best utilize their limited resources. At each decision branch, the optimal control is interpreted as a Nash–Cournot equilibrium of a zero-sum political game which, in certain states, admits mixed strategy solutions. We perform a case study on the Australian Federal Election for House of Representatives.     

General sum games with joint chance constraints

We consider an $n$-player non-cooperative game with continuous strategy sets. The strategy set of each player contains a set of stochastic linear constraints. We model the stochastic linear constraints of each player as a joint chance constraint. We assume that the row vectors of a matrix defining the stochastic constraints of each player are independent and each row vector follows a multivariate normal distribution. Under certain conditions, we show the existence of a Nash equilibrium for this game.     

An agent-based investigation into the new product development capability

The capability to bring products to market which comply with quality, cost and development time goals is vital to the survival of firms in a competitve environment. New product development comprises knowledge creation and search and can be organized in different ways. In this paper, we study the performance of several alternative organizational models for new product development using a model of distributed, self-adapting (learning) agents. The agents (a marketing and a production agent) are modelled via neural networks. The artificial new product development process analyzed starts with learning on the basis of an initial set of production and marketing data about possible products and their evaluation. Subsequently, in each step of the process, the agents search for a better product with their current models of the environment and, then, refine their representations based on additional prototypes generated (new learning data). Within this framework, we investigate the influence of different types of new product search methods and generating prototypes/learning according to the performance of individual agents and the organization as a whole. In particular, sequential, team-based Trial & Error and House of Quality guided search are combined with prototype sampling methods of different intensity and breadth; also, the complexity of the agents (number of hidden units) is varied. It turns out that both the knowledge base and the search procedure have a significant impact on the agents' generalization ability and success in new product development. Andreas Mild was born in Vienna, Austria, in 1973. He studied business administration in Vienna, in 2000 he received his Ph.D. from the Vienna University of Economics and Business Administration (WU). Since 2003 he is associated professor at the WU. He has been guest professor in Frankfurt, Germany, Sydney, Australia and Bangkok, Thailand. Previous research appeared in Journals such as MIS Quarterly, Management Science and Marketing Science. His research interests currently include agent-based models, new product development and recommender systems. Alfred Taudes was born in Vienna, Austria, in 1959. He studied business administration and management information systems (MIS) in Vienna (doctorate 1984), in 1991 he received his Ph.D. from the Vienna University of Economics and Business Administration (WU). He was assistant professor at the WU (1986–1991) and professor for MIS at the German Universities of Augsburg (1991), Münster (1991/92) and Essen (1992/93). Since 1993, he has been professor for MIS at the WU and Head of the Department for Production Management. Since 2000, Dr. Taudes has been speaker for the Special Research Area SFB # 010 (Adaptive Information Systems and Modelling in Economics and Management Science). His research interests currently include agent-based models of industry structures, management of innovation, technology management and business strategy.