A game consists of a playing space, pieces, and rules. It embodies and is equivalent to a formal system. The space and the pieces may be literal and physical, or metaphorical and conceptual. The rules may be unstated or explicit. The space may be playfully explored or negotiated in earnest. If other players are involved, the game may have cooperative or competitive aspects. There may be levels of challenge and competence. Information concerning the structure of the game and the status of play in progress may be revealed or partially concealed-- as in poker where one does not show one's cards. The game may be a social event involving direct or indirect contact with other players, or may be a solitary discovery of the game space-- as in some computer adventure games. The game may involve strategy and/or chance. Game theory may be applied to the strategies of opponents.
The player occupies a higher logical level than the game-- her world is larger. A game could involve self-reference, logical levels, paradox. The elements meta to a game are everything about it that is not formally defined within it: strategy, communications and coalitions between players, bluffing and deception, the personal stakes of the players, actions between turns, etc. These could be incorporated as formal elements of a meta-game-- for instance, one which modeled the process of gaming.
A key to the universal fascination of games is their nature as structured but gratuitous creations. As such they have an appeal akin to that of music, art and mathematics, deriving from the interest of form. Mind, so to speak, needs a place to hang its hat. It seeks out and creates structured spaces within which it can operate competently. It likes ordered situations in which it can "learn the ropes". The rules and kinds of moves allowable must be clear; the playing space and pieces, the goals and payoffs, the criteria for win or lose, must be well-defined. Playing games is what the mind does well, ordering experience and behavior in rule-governed game-like structures. A game is a behavioral schema imposed in the domain of action, just as a cognitive model is imposed in the domain of perception or thought.
Such schemata, considered as informal systems, can either be "interpreted" or not. That is, they may either serve a metaphorizing function, pointing to the world and mediating our relationship to it, or they may gratuitously be indulged for their own sake or to satisfy an internal need. A model or theory could be considered a serious application of a game structure toward representing the real world. Conversely, games played for fun can be considered gratuitous versions of theories about the world (consider Monopoly as a model of capitalism).
A game is an individual as well as a species (a game of chess rather than the game of chess). A game tree is a simultaneous representation of the possible moves at every stage of an individual game-- a branching of branchings of branchings... It shows the actual development of play, among all such possible developments, as a timeless system of logical interrelationships.
As well as the formal aspect of games, there is the dimension of competition-- what Huizinga called the agonistic character of play. Games serve as a test or contest, the outcome of which is an increase or decrease of wealth or status. A game not only organizes activity but defines value. It has an outcome: the payoff. In game theory, a player is called rational who plays in earnest to win the defined payoff (who plays, in other words, for keeps!)
Roles may be differentiated within what is nominally the same game. Psychiatrist and patient have different positions within the game of therapy. But whatever asymmetries exist, it is certain that there is some reward for loser as well as victor, for otherwise the course of play would not continue. While the ostensible goal of therapy is to "cure" the patient, meta-payoffs in the game of psychiatry include the fees of the doctor, the prestige of having a "shrink" and that of being a professional in a superior position with regard to clients, the human contact involved, etc.
To the extent that playing is its own proper reward, winning can actually be counterproductive-- for then the game ends. The explicit payoff nullifies the meta-payoff, and the winner is a spoilsport for stopping the game. When the meta-payoff has priority, winning may be indefinitely postponed. This can have insidious results, for instance, in a therapeutic context.
A game must be finite, well-defined, graspable-- in short, playable. An activity is perceivable as a game when one can stand outside of it, detached from its premises and goal. Until then one is caught within it, hypnotized by it, believing it real, serious, unlimited. One is then grasped by it, carried away in its apparent reality.
A game is eminently a problem to solve, something for the mind to engage, figure out, enter into, possibly win. The problem-solving mentality eagerly accepts the premises of a game as found. Convergent thinking, as it is called, finds the preordained unique solution in a well-defined problem space by applying known algorithms. But even so-called divergent thinking, as measured by test problems that are ill-defined or have multiple solutions, calls for a response that is structured by a fixed problem space given by the creators of the test. The true alternative to convergent thinking is autonomous creativity, in which individuals define their own problem situations and rewards according to their own visions and goals. The fact that a game is a limited, structured activity makes it playable, but also guarantees eventual dissatisfaction with its limits. Disillusionment is seeing the limitedness, the finiteness and smallness of a game from which one feels oneself disengaging. Engagement means moving within a game which is not seen as such, since one is identified with it, lost within its parameters. The difference is more a matter of how than whether one continues to play the game.
Mind is prominently a game player, a problem solver. Every form of mental activity that has a content, a structure, a goal, is a limiting game. This includes all forms of cognition and thought. What is not such is just being-- a state of repose, like a radio that is "on" but tuned to no station. It does not depend on doing, on the outcome of any game-- even the game of "enlightenment".
Every game generates a world. A world is a game space, generated by a set of premises and rules, and projected as real. The game is crystallized as a world by the intentional act of taking it seriously (coupled with the equally intentional act of forgetting that one has done so). The world of Monopoly consists of every thing and action that is defined and allowable in the game. To the degree that human activities in the real world can be formalized, they are game-like. To the degree we intend an interpretation, the worlds generated by these games are the reality we actually inhabit. Consider the worlds of the office, the factory, the schoolroom, the home; worlds of high finance, backroom politics, medicine, the Pentagon; worlds of science fiction, TV commercials, soap operas; personal worlds of individual dramas. The entire human environment (the world), being an intentionally structured informal system, is a vast game imposed upon the substrate of Nature. Machines as embodiments of formal systems are games. Even physical reality itself, as accessed through game-like knowledge systems, is a hierarchy of games within games. The limit of the game is the limit of the world. We literally live in the world defined by our game-- the conceptual space within which action is possible and legal, and outside of which nothing is defined or even thinkable. While the notion of game may extend to include any serious activity-- business, war, love, career, etc.-- there exist recreational games that simulate (and trivialize) just about anything serious. Each constitutes a world in this diminutive sense. What the problem-solving mind does best is to endorse and embellish the existing order, or to pursue recreation for its own sake. True creativity transcends the status quo and the confines of the local metaphor to point to a larger reality beyond the game.
Experience must not be too boring (redundant) nor too novel (chaotic), but must fall within a middle zone in which stimuli can be comfortably assimilated to existing models. This is what problem solving is all about. It must take place within the cognitive limits of a well-structured game of assigning meanings to inputs. These limits are not absolute, but stretchable bounds of a preferred or habitual domain. Problems, questions, or areas of inquiry may be too large or vague for attack by the problem-solving mind, leaving it confused or unengaged, or producing solutions that are too general, facile, ambiguous or glib. At the other extreme, problem areas can be too circumscribed, leaving the mind uninspired and producing answers that are trivial, parochial, or irrelevant in their specificity. To be interesting, the problem space must be structured but not overgrown with its own workings. It must remain transparent and open to the larger world.
The further a game has progressed, the more restricted the possible moves, the more defined the problem space. There is a natural rhythm to a game. From the nearly arbitrary opening moves, interest deepens and focuses as we become involved in the convolutions of the game. Eventually options become so restricted that the outcome appears determined and interest wanes (as in chess, when one player no longer has enough or the right pieces to resist checkmate). The most engaging part of the game is the middle, in the excitement of problem-solving battle, in pursuit of solutions which are achievable but not fore-ordained. Some projects never get going because they do not reach a critical momentum of involvement. One must be able to see a certain distance into the game in order to be interested at all, to see that a goal can be reached before it is enquired how. Other projects fail near completion because all that remains are clerical tasks that no one wants to do. Problem solving seduces the aspect of mind that clings to the relative comfort of the middle zone. Problems must not be too difficult or complex, nor too easy or simple, but must present challenge and sport without exasperating or boring the mind.
There are as many worlds as there are world-creating gestures of the mind. The basic positive activity of the mind is creating worlds-- which are fleshed in through its need to operate in structures it experiences as independent of itself. This (pre-subjective) mode of the mind does not recognize such creations as worlds in the diminutive sense, but as constituting reality. Only after the fact, so to speak, does subjective consciousness reframe the mind's steps as a process of world creation.
One advantage of living in an apparently solid, real world is that decisions and beliefs are authorized as consequences of forces perceived to lie beyond one's control or responsibility. Reality provides a non-arbitrary basis for the priorities of the organism, and raises them to the status of necessity. A creature accepts the premises of its world, orienting its behavior toward winning in the game of survival. A world makes goal-oriented "rationality" possible and necessary. Its downside is that play is restricted to such activity, to the pursuit of such values as defined within it. The mind becomes mired in the labyrinth of its own cleverness. This is why people become disillusioned with a "rat race" they once pursued with enthusiasm.
The overhead of maintaining a world can interfere with its avowed purpose-- the perennial complaint about bureaucracies. The mind can be shipwrecked by its own sirens. The game is then played more for its own sake than as a mediator of reality; the rules assume more importance than the outcome. Much of modern western philosophy, for example, is every bit as scholastic as that of the middle ages-- a dance of technical angels on the heads of linguistic pins. The esthetic or play value of the game, appreciated by only a few, then supersedes its truth value, and so becomes irrelevant to life at large. Distracted by the intrinsic satisfactions of problem solving, the mind allows the problems of the larger world to go unheeded. Thus, personal games and private dramas take up so much of the collective energy that there is a kind of global brain drain away from the large-scale issues affecting human destiny. Evolution gives way to convolution.
The formal qualities of an activity or situation come to attention when we consider it as play rather than as serious. These functions compete as well as complement each other. Sometimes the serious intent of an activity (such as scientific research or charitable fundraising) is obstructed by its formal organization. The world of an activity has its own momentum that can divert its ostensible purpose. An activity may be aimed at the world, but covertly satisfy the need of the mind to play within formally structured bounds.
Cognitive activities have their formal game-like structure, and many activities considered gratuitous perform a mediating cognitive role. Sports and hobbies, like children's play, are reality-testing grounds for evolving basic attitudes and skills, while physical reality itself is a cognitive game whose tokens are various entities, and whose operations are laws or processes that amount to transformations performed upon initial states.
All intellectual disciplines have their formal qualities. Results must be reached by certain methods, the game must be played according to the rules. This is as true in law or medicine as it is in mathematics. Art, esthetic appreciation, and the concept of quality in general, involve games of evaluation and skill. In all creative fields there are esthetic sports of conception and imagination, of execution and technical mastery, of marketing, of showmanship and of one-upmanship, of satisfying particular tastes, etc. Ironically, originality itself can be a game in which the right move is determined by what others have done and are doing.