Choosing the Game to Play Using the Strategic Games Matrix – An Illustrative Business Application Eliezer Arantes da Costa, U. Estadual de Campinas – UNICAMP; elicosta@uol.com.br Celso Pascoli Bottura, U. Estadual de Campinas – UNICAMP; bottura@dmcsi.fee.unicamp.br João Mauricio Gama Boaventura, U. Paulista – UNIP; jm@boaventura.adm.br Adalberto Américo Fischmann, U. de São Paulo - FEA-USP; aafischm@usp.br ABSTRACT – Many concepts in business strategy came from game theory and several papers present the use of classic games in business situations. However, as there are distinct mathematical models for classic games, in one hand – as Minimax, Nash, Pareto and Stackelberg–, and, there are different real conflict of interest business situation to deal with, in the other hand, managers intending to apply game theory to real business situation always face a problem: what is the right game to play? For helping managers to choose the right game to play, the Strategic Games Matrix –SGM– was proposed. It indicates what games should be played at each particular business situation. In this paper, the SGM is applied to the Intel Corporation’s case study presented in Ghemawat (1999). 1 – INTRODUCTION Many concepts in business strategy came from game theory, and several academic papers presenting the use of classic games in business situations were published (Parkhe, 1993; Smit & Ankun, 1993; Ghemawat, 1999; Arend & Seale, 2005). As the perspective of this strategic management study is grounded in game theory, for better distinguishing it from other perspectives, short overviews of different concepts of strategy, as well as of the concepts and structure of Strategic Games Matrix –SGM– are here presented. When using game theory in business, an essential question arises: what is the right game to play? This problem was previously studied by Brandenburger & Nalebuff (1995), where they proposed the co-opetition concept, and by Costa & Bottura (2004), where they proposed the SGM concept. This study applies the Strategic Games Matrix to an interesting case about Intel Corporation, as described by Collins & Pisano (1997), in Ghemawat (1999). 2 – GENERAL CONCEPTS OF THE STRATEGY CONTENT First of all it is important to clarify that the concepts discussed below regard the strategy content and not the strategy process. In this way, we follow Hax & Majluf (1996: 1) understanding that, for analysis purposes, the strategy content should be separated from the strategy process. Through the analysis of how distinct authors define strategy, an interesting overview of the different concepts of strategy can be made. An analysis of the strategy content is presented, grouping, by similarity, the different ways the investigated authors define strategy. It is possible to recognize four categories for the strategy content, as follows: (1) Strategy as means to attain goals; (2) Strategy oriented to competitive advantage; (3) Strategy focused in core competencies; and (4) Strategy based in the interaction with opponents. Some authors made definitions using more than one category and in these cases they were classified in more than one identified categories. The four types of strategy concepts chosen by the authors are briefly described below: (1) Strategy as means to attain goals. There is a group of authors that perceives strategy as a way to attain goals. Such as, in a causal relation, where the cause is a way to using the organization resources and the effects are goals achievement. Chandler (1962: 13), for example, states that strategy can be defined as determination of the basic long-term goals and objectives of an enterprise, and the adoption of courses of action and the allocation of resources necessary for carrying out these goals. Other authors with the same approach are Learned, Christensen, Andrews & Guth (1965), Andrews (1971), Ackoff (1973), Rhenman (1973), Rumelt (1974), Drucker (1977), Lorange & Vancil (1977), Hofer & Schendel (1978), Miles & Snow (1978), Christensen, Andrews & Bower (1978), Steiner (1979), Henderson (1979), Fahey & Randall (1998) and Johnson & Scholes (1989). (2) Strategy oriented to competitive advantage. The literature shows a group of definitions linking strategy to competitive advantage. The basic assumption is that the strategy should be oriented to achieve and maintain a competitive advantage. Porter introduced this new concept in 1985 and after that several other authors adopted it, like Andrews (1987), Hax & Majluf (1991), Henderson (1991), Pfeffer (1998) and Fahey & Randal (1998). Both Andrews (1971) and Henderson (1979), who initially defined strategy as the means to achieve goals, renewed their definitions, and later on, 1987 and 1991 respectively, reformulated it including the competitive advantage concept. (3) Strategy focused in core competencies: Another group of researchers emphasized the core competencies Choosing the Game to Play Using the Strategic Games Matrix – An Illustrative Business Application 2 issue, proposing that the competitive advantage or the advantage in the interaction within opponents would be the result of the core competencies of the organization. This concept was initially proposed by Hofer & Schendel (1978: 27) when they stated that the distinctive competencies were the most important part of the strategy. But, for sure, were Hamel & Prahalad (1994: 23) who made this idea widely known and pointed out the need of a strategic architecture that provides a blueprint for building the competencies needed to dominate future markets. (4) Strategy based in the interaction with opponents. There is also a fourth group of definitions linking strategy and the interactions with opponents. These authors gave priority to the actions and reactions between the organization and its opponents. In other words, they believe that it is not possible to conceive a strategy without considering the actions and reactions of the opponents. The route of this concept leads to Von Neumann and Morgenstern who in 1944 published the book The Theory of Games and Economic Behavior. Von Neumann and Morgenstern (1947) defined strategy as a complex plan which specifies what choices the player will make in every possible situation, for every possible actual information which the player may possesses at that moment, in conformity with the pattern of information which rules the game provided for him or her. Some authors who followed this concept were Simon (1947), Newman (1950), Schelling (1960), Dixit & Nalebuff (1991), Brandenburger & Nalebuff (1996) and Ghemawat (1999). 3 – GAME THEORY APPLIED TO BUSINESS STRATEGY This work is grounded in the fourth strategy content concept approach cited in 2 (4) – strategy based in the interaction with opponents –We choose this approach for being that one that, as we see, more adapts to the competitive strategies analysis, considering that the competitors are always present in any business and their actions and decisions can interact with the company’s decisions and results. Some attempts to apply game theory concepts and results to business environments were reported by some authors. Dixit describes the competitive movements of the companies, as moves in a board game, and make considerations regarding the possible reactions by opponents upon experiencing the adversary moves (Dixit & Nalebuff, 1991, Dixit & Skeath, 1999). Porter mentions the application of the classical theories of equilibrium strategies from game theory to interpret situations of strategic confrontation and the choices of moves by each competitor (Porter, 1980). Smit & Ankun describe the application of game theory to decision making in investment strategies under competitive conditions (Smit & Ankun, 1993). Oster (1994) develops the concepts of competitive rivalry, applying game theory concepts to analysis and interpretation for the rationales of company strategic decisions. Costa & Bottura (2004) proposed the Strategic Games Matrix concept. The concepts of game, player, objective function, equilibrium point, equilibrium strategy, saddle-point, zero-sum games, variable-sum games, strategy, used in this paper are the same concepts as defined and used in game theory. Başar & Olsder (1999), classic authors on game theory, describe cooperative and competitive game theory classic situations, and indicate forms of obtaining ‘equilibrium strategies’ for several types of games. Among these typical game situations, in this paper the following have been chosen: (1) Zero-sum games, where the saddle-point equilibrium and the Minimax strategy are applicable; (2) Non-cooperative variable-sum games, where the Nash equilibrium strategy is applicable; (3) Cooperative variable-sum games, where the Pareto equilibrium strategy is applicable; and (4) Hierarchical games, where the stronger player carries out its strategic move and announces it to the remaining players, to which the Stackelberg equilibrium strategy is applicable: leader strategy for the stronger player, and follower strategy for the weaker player. In this paper, inspired on the mentioned authors’ enlargement of the games concepts and their application to business environment, we apply the SGM, soon to be discussed, to a real business case situation. 4. STRATEGIC GAMES MATRIX (SGM) STRUCTURE DESCRIPTION The Strategic Games Matrix, described in this Section, intends to support the managers in diverse conflict management situations, helping them to identify the right game to play. The SGM is useful to alert each manager, explicitly, in each conflict of interests situation that, before deciding: “How should I compete?”, she or he should first decide: “What game should I play now?”. In addition, the SGM gives to managers an analytic perspective of the games to play. In the SGM structure description, two important dimensions of a game were considered, as resumed in the following topics: 4.1. The relevant dimensions for game analysis – There are various relevant dimensions that could be used for a conceptual mapping of the attitude or behavior a player may assume in explicit situations of conflict of interests. For the SGM concept, two dimensions, suggested by some distinguishing characteristics present in the classical games equilibrium strategies mentioned in topic 3 are adopted. In the application of this concepts to the business world, a player is seen as a decision-maker which, individually or as a team, considering the risks and opportunities involved, decides and implements its decision, even aware that such decisions imply in risks due to the results of the actions Choosing the Game to Play Using the Strategic Games Matrix – An Illustrative Business Application 3 influencing and being influenced, positively or negatively, by independent and unpredictable decisions by others decision makers, with others interests at stake. For different conflicts of interests situations between players, two strong conceptual conditioners that characterize and distinguish the classic games and strategies mentioned in topic 3 are the player typical attitude, or behavior, upon facing its competitors, and the power-ratio balance between the player being analyzed and the opponent with whom one understands there are conflicts of interests. These two conceptual conditions are the two axes of SGM. 4.1.1. The horizontal SGM axis: Players posture assumptions – A basic issue that involves situations of conflicts of interests between players is the manner by which a particular player faces ones opponent. For sake of simplicity, for this type of posture, three level or grades, mutually exclusive, typical types: (1) ‘rival posture’ (warrior attitude); (2) ‘individualistic posture’ (competitive attitude); and (3) ‘associative posture’ (cooperative attitude) are adopted. 4.1.2. The vertical SGM axis: Players power-ratio assumptions – In a second dimension, the power-ratio assumptions that a specific player adopts with regards to its main opponents are represented. For simplicity, three typical power-ratios: (1) ‘hegemonic power-ratio’; (2) ‘balanced power-ratio’; and (3) ‘weak power-ratio’ are considered. These three assumptions present in situations of conflicting interests should not add, so far, any connotation involving moral judgment of value associated to the position taken by the player in that specific confrontation. 4.2. The Strategic Games Matrix (SGM) structure – From the combination of the three players’ posture assumptions with the three players’ power-ratio assumptions, a matrix with nine cells representing nine typical strategic games, the Strategic Games Matrix resulted. The nine SGM cells are respectively entitled: Dominant, Leader, Paternalistic, Retaliatory, Competitive, Cooperative, Marginal, Follower, and Solidary, as shown in Figure 1. These names better represent mnemonically each one of the typical conflict of interests players may face. For each cell a strategic position name is indicated. Each one of the nine cells in the SGM represents a situation of a typical strategic game, and, to five of them, correspond classical games of game theory, as mentioned in topic 3.2. On the other hand, four specific game situations, corresponding to four SGM vertices cells, there is not a correspondent classical game. So, the SGM includes two new games added to the classical ones to fulfill all the cells of the SGM; these new games are described in section 6 (Costa & Bottura, 2004). 5 – CLASSICAL GAMES EQUILIBRIUM STRATEGIES ON SGM CELLS Four classical games are explained by the five central SGM cells, representing five typical game situations. These classical games are named: Cooperative Game, Competitive Game, Retaliatory Game and Leader/Follower Game and on the SGM are illustrated in Figure 1, and are described in the following topics. In this Section the classic game theory equilibrium structures mentioned in topic 3 corresponding to the five central cells of the SGM, as shown in Fig. 1, are briefly described: 5.1. Nash equilibrium strategies – Competitive games – The strategic position at the center-center SGM cell, named Competitive Game, describes situations of ‘perfect competition’, or ‘free market’, with many suppliers, where none of them is capable of dominating the remainders. In the non-cooperative variable-sum games, where a player decides to assume a competitive strategic position, it seeks to optimize its objective function ignoring what the other players are doing or intending to do. If this solution exists, it is characterized by the situation where none of the players is able to improve its result by changing only its own decision-control variables. Such set of decisions constitutes the Nash equilibrium point (Nash, 1950). 5.2. Pareto equilibrium strategy – Cooperative games – For variable-sum games – at the right-center SGM cell – the cooperation among players may lead to results – for all of them – that are better than those they would obtain if each one tried to optimize its objective function without an a priori knowledge of other’s decisions. These are the cooperative games: when players decide to share information on the respective constraints and conditions, alternative actions and objective functions, it is possible for them to find a point of equilibrium, called ‘Pareto optimum’, which is ‘the best’ possible for all players. This point, if it exists, is characterized by the fact that none of the players can improve its result without, with its action, harming the other’s results. These are the so called ‘winwin games’. The cooperative game environment implies, however, that there must be explicit or implied agreements between the players for them do not exacerbate their individual interests in detriment of others. This type of game requires good-faith and loyalty among all participants (Kuhn & Tucker, 1951). 5.3. Minimax equilibrium strategies – Retaliatory games – This strategic positioning applies to ‘lose-win type’ and ‘lose-lose type’ games – at the left-center SGM cell, where the players assume, explicit or implicitly, that a gain for one implies in losses to the remainder, characterizing a retaliatory competitive position. A zero-sum game is one for which the sum of all the individual objective functions is a constant, whatever are the strategies chosen by the players. For a zero-sum game, a solution, if it exists, for which each player acts towards what it understands as the Choosing the Game to Play Using the Strategic Games Matrix – An Illustrative Business Application 4 most favorable to optimize its objective function, considering all the possibilities the others could do, is called a saddle-point. This point has the peculiar characteristic that any deviation from it, by any of the players, makes its result worsen in relation to its objective function. A strategy that leads to a saddle-point is the Minimax strategy (Başar & Olsder, 1999: 26). 5.4. Stackelberg equilibrium strategies – Leader / Follower games – These strategies apply to hierarchical games where there is a stronger player, the leader, and another weaker player, the follower (Cruz Jr, 1978), both with individualistic posture, and are called Stackelberg strategies. They correspond to two opposed positions: centerupper and center-lower SGM cells. The Stackelberg game is treated and solved in Başar & Olsder (1999: 131-148). 6. LIMIT-CASE GAMES EQUILIBRIUM STRATEGIES MAPPED ON SGM CELLS Hegemonic Balanced Weak Players Power Ratio Assumptions The four situations described in the four SGM vertices corner cells describe other types of games, and are limitcase situations. Figure 1 illustrates the SGM indicating the mentioned limit-case situations. These situations really occur, in the business world. To explain and, formally, to describe their main characteristics, the two hierarchical games corresponding to the four corner situations on the SGM, are explained hereinafter. 6.1. Paternalistic/Solidary games – These limit-case games are characterized by having two opposed antagonist players, in Leader: Leader: different and opposed situations cells in the Paternalistic Dominant Stackelberg Despotic SGM, both with cooperative posture, as Equilibrium follows: (a) The paternalistic strategic position, at Cooperative: the upper-right SGM cell: It occurs in games Retaliatory: Predatory: Competitive: Competitive: Cooperative: Pareto where a more powerful player, by its own Saddle -point Nash Minimax Equilibrium Equilibrium decision, shapes its own actions and those of Equilibrium Equilibrium Equilibrium Equilibrium the remaining weaker players in the game, seeking preservation and development of its Follower: Follower: economic-business system as a whole. These Marginal Solidary Stackelberg games are similar to the situation of a family Marginal Solidary / Equilibrium father, supposed to have complete authority Equilibrium Solitary over the small children: he does all he comprehends to be necessary to promote the Rival Individualistic Associative development, growth and harmony within his Players Posture Assumptions family. A paternalistic equilibrium point limitFigure 1 – The Four Classical Games in SGM: Competitive, case game can be found as an optimization Cooperative, Retaliatory, and Leader / Follower games; problem with a multi-criteria objective and the Two Limit-case Games: Dominant / Marginal, function, encompassing all the objective and Paternalistic / Solidary games functions of all the N players, the new function to be minimized. A paternalistic equilibrium point for this limit-case game can be found as a solution to a multi-criteria optimization problem where the new objective function is a linear combination of all the objective functions for all players (Haimes & Li, 1988). (b) Solidary strategic positioning: In opposition to the paternalistic position described above is the Solidary position – at the right-lower SGM cell –, that represents the situation of a player, in a game, in a weaker, however associative posture which, without the power to impose its interests upon the others, seeks to follow the rules established by the ‘ruling power’, looking for some individual advantage. Otherwise it prefers to quit the game. A Solidary equilibrium solution for this limit-case game can be treated as a simple decision tree problem with only two branches, representing the alternative decisions: ‘join the collective’, or ‘work alone’ (Sage, 1991: 93-125). 6.2. Dominant/Marginal Games – These limit-case games are characterized as having two opposed antagonists players, in different and opposed strategic positioning cells in the SGM, both with rival postures, as follows: (a) A Dominant strategic position – at the left-upper SGM cell – characterizes the game where one player has all strength and has the intention to destroy the smaller competitors. Its attitude may be of intimidation, blackmail, price war, for instance, to try to bankrupt the small ones. It may pressure its clients not to purchase from the small ones. A Dominant equilibrium point limit-case for this game can be obtained through the solution of a mono-criterion optimization problem in which the player in Dominant position ignores all the objective functions of its ‘small’ opponents and simply minimizes its own objective function. The player at a Dominant position could treat the possible actions of ‘small’ competitors simply as random noises. (b) Marginal strategic position: Countering the Dominant position at the game described above, is the marginal Choosing the Game to Play Using the Strategic Games Matrix – An Illustrative Business Application 5 strategic position – at the left-lower SGM cell –, where a weaker however courageous and rival posture player in the game does everything it understands as necessary to survive, trying, as much as possible, to obtain some advantages upon causing losses to the major game dominator. A marginal equilibrium point limit-case for this game can be obtained through the solution of an optimization problem in which the Marginal position player tries to maximize the main and stronger competitor’s objective function with the purpose of infringing upon it the maximum possible damage. 7. AN APPLICATION OF THE SGM TO A BUSINESS CASE An application of the six SGM strategic games described in 5 and in 6, and represented in Figure 1, inspired on the value-network of Brandenburger & Nalebuff (1996), for a complex business environment in PC (personal computer) industry, is presented in Figure 2. For this purpose, we use the Collins & Pisano (1997) Intel Corporation’s case study. Although that case study covers a wide period of time about Intel Corporation story (1968 to 1997), the present application focuses on the business competitive strategies employed by Intel and by its counterparts on the 1990-1997 period. It involves PC makers –Apple, IBM, Compaq, Toshiba and others–, the production equipment suppliers, the software producers, as Microsoft for OS (operating systems), the Intel’s licensees, which produce microprocessors with Intel technology, the main Intel competitors, as AMD, and the Intel ‘clone’ producers. After a careful identification of these players involved in the various aspect and phases of PC industry, their relationships, their conflicts of interests, their relative power-ratios, and their objective functions, having the Intel Corporation as the central focus of this analysis, illustrated in Figure 2, two classes of games can be clearly characterized: (a) three types of balanced power-ratio games (1, 2 and 3), and (b) three types of hierarchical hegemonic / weak power-ratio games (4, 5 and 6), according to the concepts presented in 4.1.2. As balanced power-ratio games, we identified the following games, indicated Clients PC users market in Figure 2: (1) Since there are several PC makers companies disputing the same PC users 1 PC makers: market, the strategic game they play Apple, AST, Compaq, among themselves is a typical Nash Competitors Dell, Fujitsu, Gateway, game; IBM, NEC, Toshiba, etc (2) The strategic game between Intel Complementors and Microsoft is a typical Pareto game Clone AMD makers 5 Microprocessors because they have to work in cooperation and boards Microsoft and to add more value to the PC final 3 other software 2 product, with hardware and software producers adequately matched to the users needs; Intel 6 and Corporation Legend: (3) The strategic game played Microprocessors 5 1 – Nash strategy between Intel and AMD is a typical producers 2 – Pareto strategy 4 licensees Minimax game since they compete for 3 – Minimax strategy 4 – Stackelberg strategy 5 – Paternalistic-Solidary strategy 6 – Dominant-Marginal strategy market share in a supposed fixed size market. As hierarchical hegemonic / weak Suppliers power-ratios games we identified other three strategic games, also indicated in Figure 2 – SGM application to Collins & Pisano (1997) Intel Corporation’s case study Figure 2: (4) The strategic games played among Intel (the stronger) and its several equipment supplier producers (the weaker players) are typical Stackelberg games, where Intel acts as the leader and the suppliers as followers; (5) Intel proposed to its several clients, the PC makers, a participation in the “Intel inside” campaign to increase the visibility of Intel from a point of view of the final PC buyers. The strategic games played among Intel (the stronger) and the PC makers (the weaker playes), mainly in relation to their market strategy called “Intel Inside”, are typical Paternalistic – Solidary games; (6) The strategic games played among Intel (the stronger) and its ‘clone’ makers are typically Dominant – Marginal games, as Intel identified the existence of this weaker but warrior competitors and introduced pricing and continuous technology advancement policies to keep them in a convenient and non-threatening limited size. Equipments for production suppliers Choosing the Game to Play Using the Strategic Games Matrix – An Illustrative Business Application 6 8. CONCLUSIONS AND COMMENTS Although the problem of deciding which of the games a manager should play in each conflict of interest situation was already discussed by other authors, for example, Lado, Boyd & Hanlon (1977) and Brandenburger & Nalebuff (1995), the adequate use of the Strategic Games Matrix (SGM) concept, as shown in 7, can enhance the vision of the problem and help the managers to have a better understanding of the whole competitive strategic environment they are involved in. This way, managers can add, to their management tools repertory, the following specific skills: (a) being able to recognize that each particular conflict of interests situation is ‘unique’ and that there is no standard solution that can be applied to all of them equally; (b) knowing how to evaluate the situation and the correlation of forces in particular and selecting the best applicable power-ratio balance to assume in each case; (c) being able to examine the real situation, and deciding if he or she shell trust in the good-faith and the fidelity of the opponents, choosing the adequate attitude, in each case, to cooperate or not with its counterparts, and (d) being able to identify, in the SGM, the game to be played and choosing the most adequate strategy. 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