M.remondino and a ppellini: minority game possibilities somewhat. absolutely rational behaviour is more predictable than irrational behaviour. second, it provides a criterion for evaluation of the efficiency of an economic system. if the system leads to a reduction in the rewards coming to some people, without producing more than compensating rewards to others costs greater than benefits, broadly ; then something is wrong. pollution, the overexploitation of fisheries, and inadequate resources committed to research can all be examples of this. in neoclassical economics, the rational individual faces a specific system of institutions, including property rights, money, and highly competitive markets. these are among the "circumstances" that the person takes into account in maximizing rewards. the implications of property rights, a money economy and ideally competitive markets is that the individual needs not consider her or his interactions with other individuals. she or he needs consider only his or her own situation and the "conditions of the market." but this leads to two problems. first, it limits the range of the theory. where-ever competition is restricted but there is no monopoly ; , or property rights are not fully defined, consensus neoclassical economic theory is inapplicable, and neoclassical economics has never produced a generally accepted extension of the theory to cover these cases. decisions taken outside the money economy were also problematic for neoclassical economics. game theory was intended to confront just this problem: to provide a theory of economic and strategic behaviour when people interact directly, rather than through the market. in game theory, "games" have always been a metaphor for more serious interactions in human society. game theory may be aboutonline play and baseball, but it is not about chess, and it is about such serious interactions as market competition, arms races and environmental pollution. but game theory addresses the serious interactions using the metaphor of a game: in these serious interactions, as in games, the individual's choice is essentially a choice of a strategy, and the outcome of the interaction depends on the strategies chosen by each of the participants. on this interpretation, a study of games may indeed tell us something about serious interactions. in neoclassical economic theory, to choose rationally is to maximize one's rewards. from one point of view, this is a problem in mathematics: choose the activity that maximizes rewards in given circumstances. thus we may think of rational economic choices as the "solution" to a problem of mathematics. in game theory, the case is more complex, since the outcome depends not only on my own strategies and the "market conditions, " but also directly on the strategies chosen by others, but we may still think of the rational choice of strategies as a mathematical problem - maximize the rewards of a group of interacting decision makers - and so we again speak of the rational outcome as the "solution" to the game. the minority game the minority game mg ; is a simple, generalized framework, belonging to the game theory field, which represents the collective behaviour of agents in an idealized situation where they have to compete through adaptation for some finite resource. while the mg is born as the mathematical formulation of "el farol bar" problem considered by arthur, 1994 ; , it goes way beyond this one, since it generalizes the study of how many individuals may reach a collective solution to a problem under adaptation of each one's expectations about the future. in arthur, 1994 ; the "el farol bar" problem was posed as an example of inductive reasoning in scenarios of bounded rationality. the kind of rationality which is usually assumed in economics perfect, logical, deductive rationality is extremely useful in generating solutions to theoretical problems, but it fails to account for situations in which our rationality is bounded because agents can not cope with the complexity of the situation ; or when ignorance about other agents ability and willingness to apply perfect rationally lead to subjective beliefs about the situation. even in those situations, agents are not completely irrational: they adjust their behaviour based on what they think other agents are going to do, and these expectations are generated endogenously by information about what other agents have done in the past. on the basis of these expectations, the agent takes an action, which in turn becomes a precedent that influences the behaviour of future agents. this creates a feedback loop: expectations arise from precedents and then create the actions which, in turn, constitute the precedents for the next step. the original formulation of "el farol bar" problem is as follows: n people, at every step, take an individual decision among two possibilities. number one is to stay at home; number two is to go bar. since the space in the bar is limited finite resource ; , the time there is enjoyable if and only if the number of the people there is less than a fixed threshold an, where a 1 ; . every agent has his own expectation on the number of people in the bar, and according to his forecast decides whether to go or not. the only information available to the agents is the number of people attending the bar in the recent past; this means that there is no deductively rational solution to this problem, but there can be plenty of models. 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