Statistical and institutional foundations of economics



Economic General Equilibrium Theory aims to link un-coerced individual decision making to optimal price formation and resource allocation across entire economies.  It is a mathematical formalization of Adam Smith's concept of the invisible hand, and it is the only domain within modern economic thought that explicitly tries for theoretical unification to supersede case-by-case modeling or phenomenological descriptive rules.  Yet its core concepts of equilibrium, rationality, and complete and costless contracts are not empirically grounded, and it omits many features of institutions, dynamics, and uncertainty that are fundamental to real economic life.

Statistical definitions of core concepts such as equilibrium or social welfare.

The equilibrium concept of Arrow and Debreu might be called "mechanical", in that it assumes precisely specified prices and allocations of all goods, tied to each other by arbitrarily long-range foresight and coordinated by perfect markets.  The stability of such equilibria -- which does not imply either uniqueness or discoverability -- results from a balance of bargaining pressures among competitors.  Uncertainty may exist in the world, but idealized markets are supposed to pass it through the economy to be handled by the rationality of agents, who fairly price insurance contracts to cover all eventualities.

Many of these assumptions can be relaxed to arrive at more natural, and empirically better-grounded, economic equilibrium concepts defined in terms of distributions of outcomes.  Statistical equilibria result when incomplete markets or irrational agents cannot compensate for external or strategic uncertainty, leaving the consequences to be absorbed within the economy.  Stable distributions can reflect competitive pressures, but generally they result from convergence under significant degrees of random choice.  They are the kind of attracting distributions seen in the wealth and income of most nations.  Many existing economic concepts of optimization, aggregation, or social welfare already resemble constructions in statistical mechanics, and these may find a stronger foundation in a more statistical economic theory.

The mechanics and endogenous emergence of economic institutions.

The increasing use of game theory to frame equilibrium problems reflects a need to treat the structure of economic institutions, which overwhelmingly determine what is possible in economic life and what is impossible (or inordinately costly and difficult).  Institutions range from money systems, legal codes, and market designs, to entrained social norms or standards of conduct, or even habits.  They mediate signals, provide substitutes for costly acquired reputation and trust, and implement distributed algorithms for price determination.  To some (unknown) degree they probably influence which choices are ever considered.  Institutions can be represented in game theory as the definers of agent identities, the creators of strategy choices, and the arbiters of possible paths of play.  Yet real institutions have evolved historically, and like many historical phenomena, are likely to reflect contingencies and accidents which become "frozen" constraints.  Economists from Menger and Hayek to Schumpeter have recognized the importance of the interaction of human behavior and social institutions, and the difficulties their complexity and history dependence create for either predictive or prescriptive economic theory.

The importance of institutional detail to the outcome of fundamental processes such as price formation or trade completion (captured in measures of liquidity and price impact) can be readily studied in finance, where paradigms such as zero-intelligence modeling show that market mechanics can not only displace but obviate most strategic roles for agents as determiners of price and allocation.  More formally, the emergence and selection of institutions can be made part of the resource-allocation problem in a society, which was the original goal of equilibrium analysis.  Benefits of institutions, which must balance the costs to provide them if they are to survive, may be defined through their impact on stability and social welfare, within either General Equilibrium or statistical equilibrium concepts.

Stochastic play, game neutrality, and links to evolution.

Formal representations of strategic agency were first meant to capture forward-looking and goal-oriented behavior.  However, the formalism of game theory can also apply to unplanned action with reward or penalty after the fact, and in this usage games fall within the broader class of models of evolving systems.  Game structure may actually be a more universal characteristic, and one more reliably inferred from data, than the presence (or absence) or form of strategic motivation behind agents' actions.  The taxonomy of games offers one framework within which to systematically study some aspects of the dynamics of replication and selection.  In the context of stochastic play, which draws extensively from stochastic processes and non-equilibrium systems, games may provide useful formal models of the emergence of distinct kinds of strategically independent agents or levels of selection.  Conversely, concepts such as neutrality under mutation in the genotype-phenotype map, whose importance is well understood in evolutionary theory, take on new forms and applications when studied in the context of strategic independence among agents.



Duncan Foley

Martin Shubik

J. Doyne Farmer

Jessica Flack