Ülo Ennuste Economics

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Meta-Synthesis Approach to Hybrid Economic System Implementation Mechanisms*

 

    11. 05 2006

                                                 

                                                       Ülo Ennuste

                 Faculty of Economics and Business Administration, Tallinn University of Technology                               

                                                                  

                                                                      Abstract

This note is discussing heuristically compiled mechanism design process for general complex economic systems. Proposed for discussion meta-synthesis concept (Gu and Tang 2005) emphasizes for our case compiling of quantitative implementation methods with the imitation of the real world evolutionary mechanisms by intuition and informal information, and suggests almost surely robust hybrid (adding moral intuitional characteristics) sub-optimal implementing mechanisms designs for very general types of socio-economic social choice functions.

The main idea of the proposed design is to sequentially and adaptively coordinate learning of the agents with the help of stimulating their credibility and respectability behaviour by the coordinator with relevant moral side-payments and consultations.

In this game, the social planner will first of all take the role of implementor and will design the rules of the game, and then will take a role of coordinator of the game, mainly trying to correct the incompleteness of the design and use moral side-influences. In this note, however, in the underlying model of acquisition of additional informal information by agents is left un-modelled, and coordination procedures are modelled schematically.

 

JEL Classification Numbers: C72, D71, D78, H41.

 

Acknowledgements. The author has benefited from comments by Stefano Solari and many other participants of the EAEPE 2005 Conference in Bremen. Financial support from the Estonian Ministry of Education and Research (Project 0142086s02) is gratefully acknowledged. The remaining errors are my own.

 

1. Introduction

 

This Note tries to discuss semi-formalized optimality issues of the types of economic system implementing mechanisms that are synthesising and imitating characteristics of evolutionary emergent mechanisms (North 1990). In other words, it tries to analyse heuristically optimal reform possibilities of socio-economic institutional systems (Vanberg 2005).

The mainly narrative/heuristic discussion is heavily based on the framework of recent theoretic concepts of Descartes-Bayes-Nash transferred utility implementation as the most precise and rigorous tools in the field of New Institutional Economics (e.g. d’Aspremont, Crémer and Gerard-Varet 2004). Although, so far these tools are still quite stylised for a complex analysis of the empirical mechanisms’ clusters and constructivist design. The main missing link in a standard implementation theory by now is that at construction of the implementing mechanisms some moral social dimensions such as credibility/respectability of agents (Matsushima 1993, 2003 and Baliga 1999), bounded rationality (Eliaz 2002 and) and learning by doing and information trade-offs (Koessler 2004 and Kaminski 2004) and intuitional capacities of agents are not sufficiently exploited and the costs connected with transferring utilities are not taken into consideration, also the implementation variants of economic institutional structures are not explicitly formalized (Ennuste 2003) etc.

The evolutionary emergent institutional systems generally may be functioning (e.g. North 1990) sequentially, gradually, repetitively, adaptively and may be active in updating information in this process of communication, and the coordination fields of these systems are not only limited with primal socio-economic activities but also with constitutional activities (institutional design, organisational engineering and construction, reforms etc). In these processes, the social planners with their private information have had parallel roles as implementers of the game and also as players in the game in the role of coordinators and utility transferors. In these mechanisms, agents’ reports may be indirectly aggregated indicators; agents are worried about their consequential credibility status, depending on their behaviour (respect to others) in the process. They are in parallel consulted and multiply coordinated horizontally by other agents in market rules and vertically by the coordinator in their activity variant choices; they may have side payments and said constraints from the coordinator based on their credibility, the may be ostracised, they may use informal communication, they learn and create new knowledge in the coordination process, etc.

And more importantly, the imitations of empirical designs show that socio-economic mechanisms should be dealt with in complementary or co-varying clusters.

Our heuristic model findings, based on the assumption of separability of the social choice function by agents, containing institutional variables with complementarities and combined institutional influences, are that the synthesized models of emergent types of mechanisms have probably robust sub-optimal implementation permissiveness for a very general class of socio-economic systems choice functions.

 

2. Basic Framework of the General Institutional Social Choice Model

 

Let N = {1, n} denote the set of agents i who participate in the public decision-making process as representatives of all individuals in the society. We have to keep in mind that here implicitly N is taken to model a dynamic set (to avoid difficulties with too many indexes we are not explicitly giving time-period indexes of sets and variables). We regard social planner in the role of coordinator (not any more in the role of implementor) also as an agent denoted here as i=1, and assume that the coordinator is interested in the implementation and sharing its private information.

 

Let A denote the dynamic set of variants of the available activities (to avoid measure theoretical problems we take all sets to be finite). The taxonomy of activities is like that: socio-economic activities and policies (to change the socio-economic situation such as consumption, investments into physical as well into informational wealth etc) and reforming activities (political activities to change the institutional structure such as monetary system, budget code, business code, tax system, accession to the economic unions etc). We assume here that this set is decomposable according to the agents A=×Ai, iÎN and the variants may be contingent (depend on the states of nature).

Let  Mi denote the dynamic set of messages for each agent iÎN. Let M=×Mi, iÎN. Let miÎMi denote the set of message profiles and m=(mi) iÎN. For the agents iÎN-1 we assume Mi=A and for the coordinator M1 = {A,C} where C is the set of central (vertical) coordination parameters.

We study the following incomplete information environment. Formulating the announcement message, each agent will use her subjective private beliefs ωi, which have evolved in the course of the stream of private signals received by her formally and informally (small talk). We model ωi as follows: let Ωi denote the set of dynamic private beliefs for agent iÎN, let ω=(ωi) iÎN denote a social belief profile. We assume that the sets of private beliefs may change in correlation with the earlier activity profiles and are agent-wise overlapping. Let Ω=×Ωi iÎN denote the set of social belief profiles. Let pi: P → [0,1] denote a probability of Ω, according to which the signal profile is randomly determined, where P denotes the set of probability measures and pi(ω /ωi).

An important departure made here from the standard implementation literature is the explicit assumption that the prior private belief ωi is a subjective and not necessarily entirely rational model of stochastic objective state variable denoted μi.

Thus, the agent’s subjective beliefs may be different from the true objective picture of the environment that can be achieved by “rationally” bounded rationality informativeness. The agent may principally never have the exact knowledge about the stochastic state of her environment and the private information may be modelling excessively biased understanding of the true environment for the agent. We assume that it is possible for the agent to try to improve the objectivity of her current beliefs in repeated information exchanges (Kalai and Ledyard 1998 and Foster and Young 2003).

Thus, even in the case of undistorted informing by the agents they may not give objective information about the real situation. As we have stated already, in the standard literature it is generally taken that ωi is a deterministic variable that is easy to document in the direct messages. In a more adequate approach, we take here that ωi is a dynamic model of the stochastic variable, and the messages are not direct and are the elements of the activity sets. And we assume that the individual message sets are much smaller (aggregated, not direct, Ennuste and Matin 1989) than the individual information sets.

Another important departure we make here is that the social planner has also her private prior beliefs about the initial social choice function, about agents’ reputations etc.

 

Our initial general social choice function (operator, e.g. containing constraints) is defined as a dynamic stochastic mapping from the imaginary dynamic objective belief set to dynamic adaptive (contingent) activity variant set. For modelling simplifications we approximate this by the relaxed (Lagrangean combined with Geoffrion, i.e. by coordinating endogenous resource prices combined with endogenous resource directives, Geoffrion 1970 and Ennuste 1978) general social choice function f: Ω→ A, which is defined as a mapping operator from the initial bounded rationality belief profile set, as this signal set is the only information that can be practically used. We take the endogenous coordinated recourse equilibrium problems as standard in this hybrid approach and concentrate in the following mainly to the exogenous cohesive (from the point of the model) moral coordination side-transfers and side-constraint problems as these are not direct deductibles from the initial model.

We assume that this mapping may in a sliding way fix deterministic plans for the next planning period (year), as well as adaptive contingent plans for the succeeding periods (depending on the realisation of belief profile evolvements). We assume that the social choice function may be approximately decomposable by characteristics of agents iÎN and there exists (fi) iÎN such that

 

fi: Ωi→ Ai for all iÎN,

and

f(ω)=(fii)) iÎN for all ω.

 

Note that A1 of the social planner may be interpreted as a set of variants of the structure of the centre.

 

3. Basic Framework of a Moral Mechanism

 

A dynamic social moral mechanism is defined by

G=(x,c),

where

x(a)=(aii) iÎN, the report variant of  aii will be chosen by agent i in the sequences of agents, gradually by a -i =fixed and in the repetitive coordination process. In the coordination process, aij is denoting the horizontal coordinating consulting proposal of agent jÎN-i to agent i, where aii ,a ij ÎAi.

Coordinating agent (centre) will choose the side-coordination profile c(a,ω1)=(ci) iÎN-1and ci =(cti , cci)  where cti: A×Ω →R is the side payment (transfer) and cci is the side constraint cci: A×Ω →Ai. We assume that A is smaller than Ω, meaning that the centre is partially detail-free (Matsushima, 2003) in coordination. We assume that ω1 implicitly contains information about components of credibilty characteristics of the agents. We take credibility of agents as an aggregate={morality{honesty, respect to others, effort}, competence{rationality, informativeness, learning}, etc}.

We assume that transfers satisfy budgetary constraints in the sense that ∑cti(a,ω)=0 iÎN-1 for all (a,ω) Î (A×Ω), and the constraint components satisfy the balance condition for all system constraints b (implicitly in f) in the sense that ∑ cci(a,ω)=b iÎN-1. The coordination by the centre takes into consideration the credibility quality (aggregate of truth telling, respect to others and competence) characteristics of the agents.  

The coordination of the centre is dealing mainly with the problems belonging to the competence of the centre (e.g. long-term planning, social system’s external constraints, convex technologies, harmonisation of individual and social risk aversions etc). In the correction of coordination the centre is using among other information moral characteristics assessments of the agents and her own intuition We assume that in different periods the centre may change the structure of the coordination profiles (e.g. go over to smaller constraint profiles etc), meaning that the mechanism may be dynamic.

 

We assume the expected utility hypothesis and define a utility function for each agent iÎN by ui: →R. We allow interdependent values so that each agent’s utility can depend on the other agents’ activity variants. Let u=(ui) iÎN denote a utility function profile.

The utility function profile u is common knowledge among the agents:

 ui=vi (aii, a -ii)+ cti + hiΔξi

where vi: (A, Ωi) → R, and is called direct utility, ctis central side transfer to i, and

Δξi=∑ξijInd(aii=aij)-∑ ξijInd(aii≠aij), where Ind(aii=aij)=1 if aii=aij and 0 otherwise, and Ind(aii≠aij)=1 if aii≠aij and 0 if aii= aij, and ξij is subjective intuitional private credibility probability of the agent j for the agent i (may be a value of the Bayesian probit function) and hi is the subjective respect weight of agent i, this towards all the other agents. The latter values are more or less transparent and we may assume, e.g. that if hi=0 fixed by i, then the common expectation of other agents will be at the next iteration that i has no credibility (reputation) at all.

 

Given the set of message profiles M, a general social mechanism is defined by a Bayesian iterative process with the combination (G, Ω,p,u).

 

A stylized strategy for each agent iÎN-1 is defined as a function at each coordination step as:

si: A×Ci×Ωi→Ai

                

                  aii, if ui=vi(aii, a-i, ωi)+cti+ hiΔξi>>0,  aii>cci

                  ai if otherwise,

 

where ai is the status quo and a-i   for jÎN-I is fixed by i  and >> means better of ai.

 

A strategy for each agent jÎN-i for recommendation of a socially desirable aii is defined at each coordination step as:

sj: A×C j ×Ωj →Ai

                

                 aii  if uj=vj(aii, a-i j, ωj)+ctj+hjΔξj >>0, 

 ai if otherwise.

 

If  hiΔξi   is significant agent i  will repeat the step with refreshed information.

The general social choice function f is said to be implemented in iterative Bayesian component-wise sub-gradient movement if there exists a unique iteratively undominated activity plan profile a*, and this profile satisfies the condition /f (ω) -a*/ <ε, where ε is almost certainly rationally small or the condition that the planned activity profile is not worse than status quo.

 

4. Schematic Permissiveness Possibility Argument

 

Statement: An initial general social choice function with prior rationally objective knowledge profile μi is approximately optimally  (ε-best or not worse as status quo) implemented in the gradual (component-wise campaigns) iterative (repeated refreshed messages) sub-gradient movement by the real-like social choice mechanism.

 

Indeed: The above statement is almost surely true by the assumption of separability of the social choice function and combined institutional influences. E.g., the utility transfers for truth-telling and environmental externalities may be applied in parallel, e.g. the summary credibility of the fiscal-monetary system may be modelled as the sum or multiplication of the credibility indexes of both institutions. Thus, the combined implementation results may be applied to overcome difficulties of strategic behaviours of the agents and enhance their rationalities and intuition, to overcome market failures due to externalities etc. 

The necessary incentive compatibility condition fulfilment may be demonstrated in relation to the characteristics of the proposed hybrid mechanism (side payments, consequential credibility levels, partially based on moral characteristics of agents  etc). Combined coordination (parallel vertical coordination plus horizontal coordination) may probably be the basis for proving the sufficiency lemmas. 

The condition of additional learning about the objective nature by agents may be demonstrated by the virtue of overlapping (correlated) and changing private information sets and correlation of agents’ credibility levels with the objectivity of the agents’ reports etc.

 

References

 

Aoyagi, M. 1998. Correlated Types and Bayesian Incentive Compatible Mechanisms with Budget Balance. – Journal of Economic theory, 79, 142-151.

 

Adam, K. 2004. On the Relation between Robust and Bayesian Decision Making. – Journal of Economic Dynamics & Control, 28, 2105-2117.

 

d’Aspremont, C., Crémer, J. and Gerard-Varet, L.-A. 2004. Balanced Bayesian Mechanisms. – Journal of Economic Theory, 115, 2, 385-395.

 

Baliga, S. 1999. Interactive Implementation. – Games and Economic Behavior, 27, 38-63.

 

Eliaz, K. 2002. Fault Tolerant Implementation, – Review of Economic Studies, 69, 589-610.

 

Ennuste, Ü. 1978. A Theory of Decomposed Optimal Planning. “Valgus”, Tallinn.

 

Ennuste, Ü. 2003. A Linear Planning Analysis of Institutional Structure in the Economy. In: Ü. Ennuste and L. Wilder (Eds.), Essays in Estonian Transformation Economics. Tallinn Technical University, 265-279.

 

Foster, D. and Young, H. 2003. Learning, Hypothesis Testing, and Nash Equilibrium. – Games and Economic Behavior, 45, 73-96.

 

Geoffrion, A. 1970. Primal Resource-Directive Approach for Optimizing Nonlinear Decomposable Systems. Operations Research. 18, 375-403.

 

Gu, J. and Tang, X. 2005. Meta-Synthesis Approach to Complex System Modeling. – European Journal of Operational Research, 166, 597-614.

 

Kalai, E. and Ledyard, J. 1998. Repeated Implementation. – Journal of Economic Theory, 83, 308-317.

 

Kaminski, M. 2004. Social Choice and Information: The Informational Structure of Uniqueness Theorems in Axiomatic Social Theories. – Mathematical Social Sciences, 48, 121-138.

 

Koessler, F. 2004. Strategic Knowledge Sharing in Bayesian Games. – Games and Economic Behavior, 48, 292-320.

 

Matsushima, H. 1993. Bayesian Monotonicity with Side Payments, – Journal of

Economic Theory, 59, 107-121.

 

Matsushima, H. 2003. Universal Mechanisms and Moral Preferences in Implementation. Discussion Paper CIRJE-F-254, Faculty of Economics, University of Tokyo.

 

North, D. 1990. Institutions, Institutional Change and Economic Performance. Cambridge University Press.

 

Parreiras, S. 2005. Correlated Information, Mechanism Design and Informational Rents. Journal of Economic Theory, 123, 210-217.

 

Vanberg, V. 2005. Markets and States: The Perspective of Constitutional Political Economy. – Journal of Institutional Economy, 1, 23-49.

——————————————————————————

 * Ennuste, Ü. 2006. Meta-synthesis Approach to Economic System Implementation Mechanisms. In: Simulation and Optimisation in Business and Industry : International Conference on Operational Research, May 17-20, 2006, Tallinn, Estonia / Eds. H. Pranevicius [et al.]. Kaunas : Technologija, 2006, 9-12.

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October 30, 2008 - Posted by | Uncategorized

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