In game theory, the strategic form (or normal form) is a way of describing a game using a matrix. The game is defined by exhibiting on each side of the matrix the different players (here players 1 and 2), each strategy or choice they can make (here strategies A and B) and sets of payoffs they will each receive for a given strategy (p_1A,p_2A ; p_1A,p_2B ; p_1B,p_2A ; p_1B,p_2B).

In game theory, the extensive form is away of describing a game using a game tree. It’s simply a diagram that shows that choices are made at different points in time (corresponding to each node). The payoffs are represented at the end of each branch. Since the extensive form represents decisions at different moments, it’s usually used to describe sequential games, while simultaneous games are described using the strategic form. Since sequential games imply making decisions at different moments for each player, information is perfect since each player can see the decision taken by the previous player, complete and the rules of the game and each player’s payoffs are common knowledge.

In the first game tree we can see how player 1 is the first to decide, while player 2 will make a decision after observing what player 1 has decided. The payoffs represented at the end of each brand represent all possible outcomes. For instance, if player 1 chooses strategy A and player 2 chooses strategy B, the set of payoffs will be p_1A,p_2B.

A good example of a sequential game described with the extensive form is when considering collusion agreements, as depicted in the second game tree.

Two firms share the market, colluding and maintaining high prices. Each firm can decide to stop colluding and start a price war, in order to increase their market share, even force the other to quit the market. Firm 1 can either keep colluding with firm 2, or start a price war. If firm 1 decides to keep colluding, firm 2 will need to make a decision. If they both agree to collude, they will get 5,5. However, if one of them decides to start a price war, the set of payoffs will be either 4,3 or 3,4, depending on which one starts the war (and therefore acquires a greater market share). It’s easy to see that collude-collude is both the Nash equilibrium and a Pareto optimum situation. This result may change when considering repeated games.

It’s worth mentioning that the extensive form can be used also to describe simultaneous games, by using information sets, as shown in the third game tree. These information sets, usually represented by a dashed line uniting two nodes or by encircling them, mean that the player does not know in which node he is, which implies imperfect information, like when using the strategic form.

The perfection of information is an important notion in game theory when considering sequential and simultaneous games. It is a key concept when analysing the possibility of punishment strategies in collusion agreements.

Perfect information refers to the fact that each player has the same information that would be available at the end of the game. This is, each player knows or can see other player’s moves. A good example would be chess, where ech player sees the other player’s pieces on the board.

Imperfect information appears when decisions have to be made simultaneously, and players need to balance all possible outcomes when making a decision. A good example of imperfect information games is a card game where each player’s card are hidden from the rest of the players.

Common knowledge is a condition usually required in game theory, so the model is completely specified and its analysis is coherently undertaken. It completes the notion of complete information, which requires all players to know the rules of the game and each other’s utility function. Indeed, all players should also be required to be aware of this fact; this is, all players must be aware of the awareness of the other players regarding the rules and each other’s utility functions. Furthermore, each player must be aware that each player is aware that each player is aware, and so on. To sum up, the awareness of the description of a given game must be part of that description.

This condition implies that each player will be fully rational (understood as rational agents, that form and adapt their expectations as rational expectations). It also implies that each player will have to take into consideration how other players face their maximisation problems, in order to make rational choices. Therefore, common knowledge is the starting point of Nash equilibriums.

Complete information and incomplete information are terms widely used in economics, especially game theory and behavioural economics. We say that there is complete information when each agent knows the other agent’s utility function and the rules of the game. As Luce and Raiffa put it in their “Games and Decisions: Introduction and Critical Survey“, 1957, complete information, understood as the situation where “each player is fully aware of the rules of the game and the utility functions of each of the players”, is a central assumption of game theory. However, this situation and its definition does not consider the awareness of each player, which is covered by the term “common knowledge“, which means that each player is aware that the other players know the rules and every utility function.

Incomplete information, also known as asymmetric information, refers to the contrary, where not all players know each other’s utility functions. John Harsanyi developed the theory of incomplete information in his “Games with Incomplete Information Played by ‘Bayesian’ Players”, 1967.

Game theory is the science of strategic reasoning, in such a way that it studies the behaviour of rational game players who are trying to maximise their utility, profits, gains, etc., in interaction with other players, and therefore in a context of strategic interdependence.

Historical Framework

The initial game theory discussions and analysis can be traced back a long time before the 20^th century, with works from authors such as James Waldegrave and his minimax mixed strategy solution for a two-person game in 1713, James Madison and his theoretical analysis of what would the effect of different tax systems be, or Antoine Cournot’s solution to a duopoly that resembles to what would later be known as Nash equilibria. However, it is not until the 20^th century, that game theory is broadly developed. We can differentiate several periods in the game theory evolution through the 20^th century. However, many concepts were continuously developed through the years.

During the earliest years of the century, from 1910 to 1930, the main focus of game theory was on  strictly competitive games commonly referred to as two-person zero-sum games. In this kind of games, the preferences (and payoffs) of a player will always be opposite to the other player’s and therefore cooperation between both players will be pointless. This kind of games has been extremely productive, as they have set the bases for future development of game theory, becoming its first main milestones. During these years, John von Neumann’s contribution was especially important, and thus, he is considered as one of the fathers of game theory.  In his “On the Theory of Parlor Games”, 1928, he introduced concepts such as the extensive (or tree) form for the description of sequential games and the minimax theorem, providing empirical support to everything he wrote. Another important contribution during these years is the introduction of the strategic form (game matrix) of a game that represents each player’s profile in a matrix form.

The following 20 years were heavily influenced by von Neumann and Oskar Morgenstern’s work, which would culminate in the joint publication of their book “Theory of Games and Economic Behaviour”, 1944.  With this book, game theory gained the status of an independent scientific discipline. One of the major contributions of this book is the application of strategy game concepts instead of random ones, the introduction of a notion of a cooperative game, its coalitional form, and the ‘Neumann-Morgenstern stable sets’. They were the first to extensively apply game theory for practical reasons, especially for analysing economic behaviour. It is also important to stress that the impact of this book has gone beyond its own time.  Many future developments emerged from it, such as the notion of core and transferable utility, and the further development of expected utility theory. Other developments from this period include games with continuum of pure strategies, the computation of minimax strategies and advances in mathematical methods that would be instrumental to later work.

The 1950s were a key period for game theory. The initial phase of incubation had reached its end and the economic perspective and application took the lead, overtaking other perspectives such as the military one. It was during this period when John Nash laid the essential groundwork that would result in the general non-cooperative theory and for cooperative bargaining theory; Lloyd Shapley was another key figure as he defined the value for coalitional games (cooperative games), he initiated the theory of stochastic games, co-invented the core with D.B. Gillies, and, along with John Milnor, developed the first game models with a continuum of players; Harold Kuhn worked on behaviour strategies and perfect recall. The prisoner’s dilemma, which is probably the best known game, was formalized by Al Tucker also during this period. It was also during these years, when the Folk theorem appeared as a result of the interest and study of repeated games, used to analyse punishment strategies in collusion agreements.

The period from 1960 to 1970 was also important in the development of game theory. The discipline expanded, not only theoretically, but also geographically. With the extension of games such as those with incomplete information and non-transferable utility coalitional games, game theory became more widely applicable, and new research centres were established outside the U. S.

From 1970 on, game theory acquired maturity. Up till then, most of game theory concepts and discoveries had been spread word to mouth. However, during this period economic theory journals published many articles related with game theory and even, new journals entirely dedicated to game theory became popular. The interest and study in politics and political economic models grew. The use of non-cooperative game theory to a large variety of economic models brought also the study and refinement of the equilibrium concept. Other advances were made in other areas of research such as complete and incomplete information repeated games, stochastic games, value, core, nucleolus bargaining theory, games with many players and etc. The use of game theory proved to be useful in a wide diversity of areas that include biology, computer science, moral philosophy and cost allocation, to name a few.

It is worth to note, that game theory should be regarded as a tool to find where incentives will lead, but it makes no moral recommendation to what choices should be taken. This science could be pictured as the study of selfishness, but without recommending it.  Welfare economics and its main tools (such as Pareto optimality and compensation criteria) study these problems outside the selfishness condition.

X-inefficiency is known as the result of inputs not producing their maximum output as a consequence of an “X” factor. This translates into both cost minimisation and production maximisation failure and, hence, implies a loss of efficiency. This term was first introduced by Harvey Leibenstein in his “Allocative efficiency vs “X-efficiency”, 1966, since concepts such as organisation inefficiency or motivational inefficiency were not yet available. Therefore X-inefficiency makes reference to all non-allocative inefficiencies.

There are four main identified reasons that try to answer for X-inefficiencies:

• Relaxing maximisation behaviour: as the psychological Yerkes-Dodson Law postulates, individuals who are exposed to low pressure will not put much effort in their actions. As pressure builds up, maximising behaviours are reached until a point where too much pressure will again result in inefficiency. Other non-maximising decision making processes include habits, conventions, moral imperatives, etc.
• Incomplete contracts: employment contracts define workers economic compensation but other concerns such as the effort, the work load or specific tasks may remain undefined, which creates an incompleteness in contracts.
• Inertia: forces that are external to the company may exert pressure to make the firm become more competitive. Only with this external force efforts will increase.
• Discretion: it is assumed that workers will not show their “full potential” or maximize their efforts, and at the same time, that employers will not pay the maximum wages they could offer.

However empirical tests and models about X-inefficiency relevance have mixed results so no final transcendence can be assured. However, is interesting to realise the debate it has created, specially regarding incomplete contracts and managerial inefficiency, both also studied in the field of business management.

As a contribution to industrial organization, George Stigler developed his “own” theory on cost analysis in his article “Production and Distribution in the Short Run”, 1939, which moved slightly away from neoclassical cost analysis.

This theory arises as many economist started to criticize the traditional U-shaped representation of a firm’s average costs. George Stigler used empirical data to question the traditional theory. His cost theory can be divided into the analysis of both the short-term and long-term average costs:

Average Costs in the short-term

According to classical economics, each plant ensured only a specific level of output could be produced in the short-run because of production inflexibility. However, Stigler introduced the notion that firms could adapt to changes in demand and be flexible even in the short-run. His main argument in favour of this idea is that whenever a firms built a plant they would have what is known as a reserve capacity.

The existence of this reserve capacity is justified by economic and technical reasons. From the former we include possible changes in the good’s demand due to cyclical reasons, favourable changes in consumers’ tastes or as a preventive method to avoid a production stop in case there is a breakdown or a repair. The latter can arise as there are some basic installations that are indivisible or as managers and workers are hired in excess to allow future expansions.

-before X₁  : marginal costs < decreasing average costs (increasing returns to scale)

-X₁ to  X₂: marginal costs = average costs (constant returns to scale, maximum efficiency)

-after X₂  :  marginal costs > average costs (both increase, therefore decreasing returns to scale)

It must be noted that this theory allows for maximum efficiency to exist for a while, which completely differs from the neoclassical view, which viewed maximum efficiency as a point of inflection, rather than a straight line.

Average Cost in the long-term

Taking into account production costs and managerial costs, Stigler argued that in the long-run average costs will decrease until a point where they cannot longer do so and from which they will become constant.

Production costs will decrease due to economies of scale until the optimum size is reached and then remain constant. Further average production cost reduction could come along with technological or skills increase. As for managerial cost, he considers, they will start to increase after a certain size is reached. However, managerial diseconomies of scale would be compensated by technical economies of scale, with a zero sum net effect and therefore would remain constant as a result.

George Joseph Stigler, 1911-1991, was an American economist and Professor at Brown University, Columbia and University of Chicago.  Furthermore, and regarding the University of Chicago, he stands out as one of the most prominent members of the School of Chicago. Stigler was awarded the Nobel Prize in Economic Sciences in 1982 for his researches regarding industrial structures, functioning of markets and causes and effects of public regulations.

From Stigler’s contribution to the microeconomic theory and industrial organization we can highlight his work of enhancement and adaptation of microeconomics in such a way, that it allows its use and analysis in a great range of real phenomena. In this field we find Stigler’s cost analysis theory, which changed the way we understand economies of scale. Amongst his top works we can find “The Economics of Information”, 1961 and “The Theory of Economic Regulation”, 1971.

Stigler also produced a great amount of work as a historian of the economic thought. His merit does not related to the amount he covered, but the depth and originality of his analysis, and how clarifying they were. We can highlight his first economic history book “Production and Distribution Theories” 1941, that studies the formative period of neoclassical economics.

Industrial Organization is the economic field that studies the strategic behaviour of firms, and their interaction to determine the structure of markets. Knowing their evolution helps to understand them. The traditional neoclassical theory made the relation between “industrial” and “manufacturing”, making the manufacturing market the main target of studies focusing in the technological result. It left aside aspects, such as organization, management and property. This perspective was criticized for using unrealistic assumptions and because it failed to explain a series of phenomena such as imperfect competition and asymmetric information amongst others.

During the 1930s, a new perspective started to take shape, especially from ideas coming from the Harvard school, and theory began to focus in the behaviour of agents in the industry and in the structure of both firms and industry. In his book “The Theory of Monopolistic Competition”, 1933, Edward H. Chamberlin wrote about imperfect competition and found that many markets were differentiated, thus turning markets into unique. There were many works and papers produced on how markets were arranged in terms of the concentration of suppliers, describing how some markets were dominated by a relatively small number of firms.

In his book “Industrial Organization”, 1959, Joe S. Bain Jr. provided the Structure, Conduct and Performance paradigm (SCP), which is used as an analytical framework, to make relations amongst market structure, market conduct and market performance. The market structure will determine its conduct and thereby its performance.

As implications of all this, regarding economic policies, Harvard School recognizes market power as being dangerous, and establishes a relation between, the concentration ratio, and the harmful effects on social welfare. The dynamic behaviour of buyers and sellers have an effect on the markets, making it harder to predict and establish fixed market structures. Difficulties arise when trying to explain the paradigm and this is due to data shortage, and the multiple definitions and extension of markets.

The Chicago school criticized the “empiricism without theory” of the SCP paradigm, and so returned to the Neoclassical pricing theory, having a more benign view of the market’s results, and having a theoretical (rather than empirical) approach. They start from the framework of perfect competition, and consider interventionism as being the source of monopolies. From Chicago’s point of view, the market’s efficiency guarantees the achievement of social welfare, and therefore firms are encouraged to seek efficiency in their production and distribution. As to the implications regarding economic policies, government intervention is considered undesirable, as the market’s forces should be left to act, and the cost of the intervention is believed to be higher than the social benefit, producing a deadweight loss.

The Austrian school also contributed to the development of the Industrial Organization theory, breaking with the Neoclassical approach. From the same school we can distinguish two main views: von Mises and his disciples’ view and Schumpeter‘s.

Mises describes the structure of the market as a dynamic process of exploration of new methods and opportunities to improve the use of resources, and thus competition is beneficial, as it encourages efficiency and innovations. Therefore, markets have to be free, and it dismays government intervention, although some regulation is praised when innovation is promoted.

From Schumpeter’s point of view, technical progress comes from a process of creative destruction, in which innovations make prior technology out-dated and originate from the innovative entrepreneur. Monopolies have a positive consideration, as they carry out the function of promoting innovation and investments, and government intervention should guarantee both of these.

Contestable markets came up as an alternative approach to the problems concerning market power. These ideas were first introduced by William J. Baumol in his “Contestable Markets: An Uprising in the Theory of Industry Structure”, 1982. In contestable markets there are no entry or exit barriers, no sunk costs and firms have access to the same level of technology. All this makes the number of firms irrelevant, as many will access it and then leave, following different strategies. This view has important limitations: for instance, its starting assumptions are quite restrictive; the definition of cost is not fully suitable; and that, in the real world, a market with such characteristics, is unconceivable.

Between the 1970s and 1980s, a series of theoretical models formulated using game theory in a framework of imperfect competition, made obsolete previous models, such as the SCP paradigm. As a result, there is more emphasis in imperfect information, in firms’ behaviour and, also, in mathematical tools used to calculate social or optimal equilibrium and market equilibrium. In general, there is a shift towards analysing the internal structure of firms, and different views of the firm arose.

Ronald H. Coase, described businesses as being a series of contracts amongst its workers, and explains that it is more beneficial to form firms, since there are a number of transaction costs that can be reduced or even eliminated.

When a business grows in size, there will normally be a distinction between managers and owners. Olivier E. Williamson took notice of the internal boundaries that firms have, and distinguished between decision-making, management and business ownership. The agency theory describes and explains the issues that arise between business managers and owners, as their respective objectives differ.

George Stigler’s contributions to industrial organization must also be mentioned, even though they were more focused on the economical aspect of the theory, rather than opening a debate on how firms interact with each other. Stigler stressed the importance of economies of scale, since it would make a big difference when concentration in the market and firms’ size increased. Furthermore, Stigler developed his “own” theory on cost analysis in his article “Production and Distribution in the Short Run”, 1939 (see Stigler’s cost analysis theory), which moved slightly away from neoclassical cost analysis. When considering the size of firms, economies of scope are also a possibility, as Baumol pointed out in his co-authored book “Contestable Markets: An Uprising in the Theory of Industry Structure”, 1982.

To conclude, it is necessary to clarify that, nowadays, the industrial organization theory accepts multiple perspectives. This theory has not only grown within its field, but also in others, such as applied microeconomics and business management, and, as we have seen during the last years, the boundaries of business and markets have become less clear, and many new definitions and shapes are appearing. This explains the flexibility and the relevance of the industrial organization theory.