Resultados de Infraestructura

Herbert Gintis has developed and brought together two areas of work relevant to my research. The first is his agent-based modelling work, which is quite basic, though does ask interesting economic questions. The second is his theoretical work which attempts among other objectives to unify the behaviour sciences(!)

In Gintis [2006, 2007a] the dynamical properties of variants of classical mod- els of economies are examined using an agent-based modelling approach. The key innovation of this work is the proposal of a decentralised mechanism which leads to convergence of pricing from a far from equilibrium situation. How convincing and substantial Gintis’ framework really is will be examined, but his approach is very relevant to this thesis and some of the work is in some sense parallel to that of chapter 3.

The first of his papers Gintis [2006] focuses on a barter29 _{economy. This}

provides a simple setting in which to examine and compare approaches. Gintis’ basic barter economy consists ofngoods andN >> nagents each of whom produces one of the goods and consumes all of the goods. The utility function of an agent

i who consumes goods xi = (xi₁, . . . , xi_n) is ui = minj

xi

j

oj where o = (o1, . . . , on) is

constant for all agents. That is, with respect to utility agents are homogeneous. Each agent has a “private” price vector, giving his relative evaluation of each good,

pi = (pi₁, . . . , pi_n) which he uses to make and accept or decline offers of trade made

by other agents. In each period each agent producesnunits of his production good. Given this specification, bartering takes place in a series of periods in a process quite different to the major bartering formulations such as Rubenstein bar- gaining which introduces the notion of time and a penalty for delaying agreement. However, an alternative approach is demanded by the modelling approach Gintis adopts. His bargaining process is basically to randomly order each good, then each agent; in this order agents visit producers of a good attempting to carry out trades until some limit on offers has been reached. The agent consumes or holds onto the good he has obtained, and a score is calculated using the utility function given above. This is repeated for every agent.

29_{A barter economy is an economy where exchanges of goods or services take place simultaneously,}

without using money. The key consideration here is the relative evaluation agents, or some central coordinating body places on goods. Bartering is generally divided into axiomatic and strategic theory: the former is a more general set of results, the later focusing on more specific kinds of scenarios.

The key question here is how trades are made. If offers are made in terms of the agent’s “private” price vector (its strategy) then the change in goods held must meet the constraint M0 = pi ·xi(0) =pi·xi (where xi(0) is the amount of

each good an agent holds before trading). So the agents should attempt to trade for the quantities that would optimise their utility given this constraint. The optimal amount to attempt to trade for will be

xi_j =λ∗oj where λ∗ = M 0 P jpijoj .

Given the above, the agent producing goodaand trading forbwill make an offer of quantitiesxa, xb of his good and good to trade for via the ratio obtained by setting

pi_axa=pi_bxb. This offer will either be rejected, partially fulfilled or entirely fulfilled

- which occur respectively when it fails to meet the evaluation of the receiver, when the receiver does not have the requested quantity and when he does. Offers are repeatedly made as outlined previously and the success of the trading is evaluated via the utility function. The economy which has been describe above does not remain static. The ‘private’ prices evolve via a mutation-imitation evolutionary dynamic. After a fixed number of periods a fraction of low scoring agents copy the strategies of high scoring agents with a small mutation. For fuller details of the model see Gintis [2006].

There seems to be fundamental problems with Gintis’ proposed framework. The key idea is that of private prices, but on close inspection this notion is quite weak: the suggestion that they represent ‘private information’ is misleading. In formulating bids the prices must be revealed, but even more problematically they are copied by other weakly performing agents. Furthermore to be able to formulate bids the agents must ‘know’ enough to derive the equilibrium prices in any case (at least in the most basic form of the model). A better description would be ‘individual’s price’. The evolutionary framework is in some ways standard but it is not convincingly justified in the context of this work; in particular imitation conflicts with the notion of privacy of prices. It is difficult to see how one could approach Gintis’ framework in an analytic way. While one can derive the optimal pricing; this is only the case for the basic framework. It would be ideal if an alternative framework could be formulated that was more analytically tractable, though this is perhaps too ambitious a goal.

1. the claim that the results justify “the importance of the Walrasian model in contemporary economic theory”

2. “models which allow [agents] to imitate successful others lead to an economy with a reasonable level of stability and efficiency.”

One objection – the possibility of multiplicity of equilibria – is noted, but a more fundamental objection, namely that Gintis does not really include capital goods (but rather some “indestructible, non-produced factor”), forms the focus of Bilancini and Petri [2008]. That Gintis’ results are not generalisable to models including capital goods – something which for all their problems, Walrasian models are, moreover it is in these generalisations we are typically interested in – means that claim (1) doesn’t really hold. It is argued claim (2) will hold, but only in economies without capital. Furthermore the difficulty of introducing investment decisions to a Gintis- style model is pointed out.

Using the notion of stochastic stability Young [2008] Mandel and Botta Man- del and Botta [2009] explore equilibrium selection in a simplified form of Gintis’ model. As in Gintis’ formulation each agent is homogeneous (at least in terms of utility function). Noting that in this economy any price is an equilibrium price (no excess demand), they propose aminimal trading equilibrium. They consider instead of price pricing a selection of market institutions within which to perform exchange. Gintis [2010] is a refined version of his two previous work in Gintis [2006, 2007a], though many of the same weaknesses are still present.

In his text Gintis [2009a] (see also the abridged form in paper Gintis [2007b]) Gintis develops a five fold framework to unify the behavioural sciences: gene-culture coevolution, sociopsychological theory of norms, game theory, rational actor model (or Beliefs, Preferences, Constraints model) and complexity theory. The book is very much an economist’s take on offering a unified framework for the social sciences, it would most likely not be accepted by other disciplines, much fully less understood. Together with Samuel Bowles he has produced another text Bowles and Gintis [2010] which approaches things from a more biological/sociological angle.