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General Social Equilibrium and its Dynamics. Herbert Gintis Santa Fe Institute December 2015. The Social Division of Labor. The social division of labor is a network of interacting social roles (Mead, Linton, Parsons).
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General Social Equilibriumand its Dynamics Herbert Gintis Santa Fe Institute December 2015
The Social Division of Labor The social division of labor is a network of interacting social roles (Mead, Linton, Parsons). The content of a social role is a set of rights, duties, material and symbolic rewards, and behavioral norms. In equilibrium, the content of all social roles is public information shared by all members of society. In periods of social change, role content is contested and re-established through dialog, collective action, cultural conflict, and the exercise of political power.
The Social Division of Labor Role-occupants are actors who fill many different and contrasting roles (e.g., spouse,parent,sales manager,church member, and voter.). We model actors as rational decisions-makers who maximize an objective function subject to the content of the social roles they occupy, and a belief system (factual and moral). For instance, when one engages a taxi, both driver and client know what is expected of each, so there is no need to adjudicate mutually acceptable behavior.
General Social Equilibrium We model the articulation of social roles and social actors by enriching the Walrasian general equilibrium model . In general social equilibrium, we add families, political institutions, and private associations (e.g., religious). • Firm ----> Organization (network of social roles) • Family ----> Family as social institution • Labor ----> Actor • Price system ----> Price system
General Social Equilibrium While the price system is usually seen as the key element in adjudicating among the interests of economic actors, in fact, the complete network of social roles and actor choices adjust when out of equilibrium. The same is true for the general social equilibrium model.
General Social Equilibrium General social equilibrium is a network of Nash and correlated equilibria. • For the importance of correlated equilibria, see my book The Bounds of Reason (Princeton, 2009).
General Social Equilibrium Sociologists have traditionally held that a major difference between social and economic roles is that social roles function properly only by virtue of the moral commitments of role-occupants, whereas economic roles are based purely on material self-interest. In fact, we know that a market economy is as much based on morality as any other sphere of social life (Gintis, Individuality and Entanglement: The Moral and Material Bases of Social Life, Princeton 2016).
The Quest for Stability ofthe Walrasian Model The question of stability of the Walrasian economy was a central research focus in the years immediately following the existence proofs in the early 1950’s. The models of Arrow et al. assumed that out of equilibrium • there is a system of common prices shared by all agents, • the time rate of change of prices being a function of aggregate excess demand.
The Quest for Stability Even if this project had been successful, the result would have been of doubtful value, as the tâtonnement process is purely fanciful. However, it was not successful. General equilibrium theorists in the early 1970's speculated that plausible restrictions on the shape of the excess demand functions might entail stability, but Sonnenschein (1973), Mantel (1974, 1976), and Debreu (1974) showed that aggregate excess demand functions can have virtually any shape at all. It follows that the tâtonnement process cannot generally be stable.
The Quest for Stability It remains the case that the current literature offers us nothing systematic about the dynamics of decentralized competitive market economies! This explains why we have a field called Macroeconomics and why it is not very successful.
Rethinking Macroeconomics My work with Antoine Mandel (La Sorbonne) returns to the fully decentralized Walrasian model, but this time with the understanding that the market economy is a complex dynamical system that must be modeled using the modern analytical tools of complexity theory.
Private Prices We replace public prices with private prices. Each agent in the economy has a personal price vector ranging over all goods he produces or consumes, indicating the price ratios at which the agent is willing to trade. These price vectors are private information, but with positive probability an agent learns the price vector of another agent, as well as that agent’s trading success. The newly-informed agent can adopt this price vector, and may do so if the other agent has been more successful in past trades.
The Market Economy as a Game This gives rise to a replicator dynamic. The resulting economic system is a gamein which individual strategies are private price vectors. We can show that the Nash equilibria of this game are strict, and each is a stable critical point of the dynamical system. Thus, using standard results from evolutionary game theory, we can prove the stability of a decentralized market economy.
Main Theorem • Theorem: Given the above assumptions on the exchange mechanism , a strategy profile is a strict Nash equilibrium of the game if and only if it is p-uniform for some market equilibrium price vector p. • In multi-population games, strict Nash equilibria are the only asymptotically stable points of the replicator dynamic, and more generally of any monotone dynamic. • Corollary: Every market equilibrium satisfying the above assumptions is stable in the replicator dynamic.
A Decentralized Market System with Individual Production • Consider the stochastic process that obtains when finite populations of agents repeatedly play a finite game. • We can model this as a Markov process. • There is a close relationship between this discrete model and its deterministic approximation as a set of differential equations implementing the replicator dynamic (Benaim and Weibull, 2003). • The dynamics of the two systems are the same for sufficiently large numbers of agents. • Such Markov models cannot be solved analytically, but can be computer simulated.
A Decentralized Market System with Individual Production Starting the Markov economy with a random assignment of private prices to each agent, the economy moves quickly to what I term quasi-public prices, i.e., private prices with low relative standard error across agents. In the long run, quasi-public prices move to what I term general Walrasian quasi-equilibrium, i.e., a stationary distribution of the Markov process with near-market-clearing prices in almost all periods.
Fragility vs. Stability There is little doubt but that the above stability properties will extend to more complex decentralized market economies. However a system can be stable, yet extremely robust or, by contrast, extremely fragile in reaction to shocks. I find that in a fairly realistic model of a contemporary advanced economy, price bubbles occur rather frequently, although in the absence of a sophisticated financial sector, they do not produce large aggregate dislocations in labor and product markets.
Basic Assumptions My more realistic agent-based model (The Economic Journal, 2007) assumes that consumers must engage in price searches in each period; workers have a subjective reservation wage that they use to determine whether to accept a job offer; firms know their production costs, but not their demand curves, and hence must experiment and learn. There is a central bank and a tax-collecting authority, as well as a government sector that services unemployment insurance.
Basic Assumptions Workers periodically search for alternative job opportunities; firms maximize profits by experimentally varying their operating characteristics and copying the behavior of other firms that are more successful than themselves; both prices and quantities respond to conditions of excess supply or demand; all adjustment parameters are agent- and firm-specific, and evolve endogenously.
Main Results The dynamical system satisfies the complex systems counterpart to stability and uniqueness: excess supply in each sector; excess labor demand, as well as excess labor supply in each period; labor demand differs fromlabor supply by only a few percent; Prices are approximately equal to production costs; The wage rate in each sector is fairly stable, and wages are approximately equal across sectors. There is a considerable level of fluctuation in price and quantity series, even though there are no aggregate stochastic shocks to the system.
Stability percent • The vertical axis shows percentage efficiency.
Conclusion Simple market exchange is robust to shocks, whereas economies with sophisticated institutions can exhibit considerable fragility. The fragility of sophisticated market competition exchange is based on endogenous random shocks and does not require exogenous shocks. Markov process models provide insights into the dynamic performance of market economies.
