1.1. General Remarks

The political economy problems of the intra-regional or sub-regional cooperation problems have been by yet vastly discussed mainly verbally ( see e.g. Inotai, 1997 ). The modest objective of this note is to provide this gap with some more modern formalised instruments and conceptions. In other words, the note makes a modest attempt to provide for the research and design the intra-regional cooperation mechanisms and institutions with some mathematical tools and ideas developed in the latest economics papers on the mathematical implementation theory, especially in the field of mechanism issues. In this perspective we discuss mainly Aoyagi ( 1998 ) mechanism model with Bayesian incentive compatible report strategies and with budget balance monetary transfer rule and mutually payoff-relevant correlated types. We combine this mechanism with an optimisation model where the decision variables are interpreted as cooperation activities of the co-operating countries. Some relevant extensions and analyses, especially Lagrangian, of this model are given. We may additionally interpret the decision variables also as the involved countries social, educational systems etc. harmonisation levels.

The well-known problem in the institutional design of cooperation is that the incomplete information relevant for the cooperation decisions is dispersed among the agents involved. Thus for determining the satisfactory plan the cooperation institutions and mechanisms must provide incentives for the agents involved to report their information properly ( see e. g. Palfrey and Srivastava 1989 ). This note proposes a very simple incentive compatible report mechanism model ( Aoyagi 1998 ) for the intra-regional cooperation. This mechanism assumes the condition of the correlation among the countries involved, and achieves the incentive compatibility by the monetary transfers that depend on the reports and their correlations. The result may be also extended to inter-regional and global-local cooperation models.

The note is organised as follows. In the third section we describe the general framework of the initial model in the hypothetical situation of the existence of the intra-regional social planner institution. In the forth section we modify the initial model for the politically realistic situation where one country is in the role of the all regional planner, and analyse the optimal planning processes dependent on the financial assistance transfer budget limits, and make some remarks on the extensions of the model for the timing analyses. The paper concludes with some modest methodological and institutional policy proposals, but first of all a few methodological introductory remarks are still in order in the next section.


2. Methodological remarks

First, it is a widely recognised standpoint by now that the best institutional framework of economic and political intra-regional cooperation is a partnership ( Eatwell et al., 1997, p. 62 ). Following this paradigm of the partnership and financial transfers it seems that the most convenient mathematical tools to analyse these processes are first of all incentive mechanism planning models, and in some respects these models may have some advantages before the game theoretic non-cooperative negotiation models. E.g. Inotai ( 1997 September, p. 55 ) gives an example where some countries started to play "tough guys" in the financial transfers bargaining negotiations. We discuss these problems in some more details in what follows. Following the partnership and planning approach it is interesting from the theoretical economic point of view to assume as an ideal case the existence of the hypothetical intra-regional social planner institution and to build the initial decision model on this basis.

Second, since the cooperative counties are always engaged in an unique transformation and structural reform changes, the uncertainty about the economic structures of the countries involved is pervasive ( see also von Hagen, 1996, and Bertocchi and Spagat, 1997 ). Therefor the Bayesian approaches are here most adequate. Moreover, as the situations of the countries in the in the same region are correlated and the informational assumption of correlated cooperative country types is justified. This assumption is specially exploited in the Aoyagi ( 1998 ) model.

Third, this note assumes that uniting factor in the partnership are the financial transfers. These make clearly the cooperative processes economically effective not only in the sense of all region but also for each cooperative country.

Forth, in some discussions below the assumption is also made that all co-operating countries but one will be as net beneficiaries of the assistance monetary transfers, and the one "anchoring country" is the only net contributor to the budget. We also adopt here the point of view from Eatwell et al. ( 1997, p.64 ) about the political "trap" for the budget in a sense that in the contributor country politically acceptable transfers for the enlargement may be significantly less than economically optimal sums may be, and politically implementable admissible decision set may be much less than economically rational one.

Fifth. As to the specific informational problems, we have to add once more that the crucial problem in the planning under uncertainty of the large systems where the agents have private information is for the planner to collect true information from the agents. Bayesian mechanisms design problems have in this field attracted much attention in the recent literature ( see, for example, Ennuste, 1996 ). In this note we concentrate on the recent work by Aoyagi (1998). This work proves the existence of a centralised mechanism with the correlated agents which makes truth-telling a Bayes-Nash equilibrium with the help of the budget balance monetary side payment rule. The appeal of this result for our purposes lies among other mainly in the fact that the monetary transfers play anyway an important role in the intra-regional cooperation to help countries to overcome cooperation difficulties and neighbour countries are informationally correlated.

According to these methodological remarks the building and analysis of our planning model is carried out in the following, with the special emphasis on the cooperative partnership and asymmetric aspects.


3. Basic Model

3.1 Set-up

This section presents a simple initial economically first best model of the problem. The co-operating countries ( agents ) are presented by a set with elements i=1, … , n, n3, and let the set of all agents be denoted by I=( 1, … n ).

From here we follow the denotation from Aoyagi (1998). Each agent i has a type t_i as private information and T_i is the finite set of types profiles for i. We denote by T=T₁ …T_n the set of type profiles t=( t₁, …, t_n ) for all agents. For each t_i let p(t_-i/t_i ) be the vector of conditional probabilities for i about the other agents types.

Let aA be a intra-regional cooperation decision describing the harmonisation levels etc. of the economic systems of the members for the regional union.

For all agents the set of admissible decisions is denoted A, and let the convention be that higher value of a in that set denotes higher level of cooperation or harmonisation. Each agent i has the quasi-linear total utility ( cost and benefit ) function:

u_i(a,t)+y_i, (1)

where u_i(a,t) is the direct utility function and y_i is monetary transfer to agent i.

Note that the agents may be mutually payoff-relevant ( Aoyagi, 1998 ) in the sense that each agent's utility function contains types of all agents, t. That assumption may also have economically good interpretations.


3.2. The intra-regional social planner model (ISP)

Let there be a hypothetical intra-regional social planner who is in the position to make the decisions in behalf of all agents and arrange monetary transfers between all agents . For that ISP solicits private information from the agents. Let the report from the agent i be r_iT_i and a report profile is denoted by r=(r₁, …,r_n). The ISP selects a decision rule c: TA, and a transfer rule x: TRⁿ, the last has to fulfil required budget balance property x_i( r )=0 for any rT.

We assume that the types are correlated in the sense of Aoyagi (1998) Assumption 1. Loosely speaking that means the conditional probabilities about the other agents types change when the agent's own type is changing. Under the regional context this is a very natural assumption.

According to Aoyagi (1998) result under the assumption of correlated types for any c and u_i there exists a x such that truth-telling ( reported type is the true one ) is strict Bayes-Nash equilibrium ( strict Bayesian incentive compatibility ) for any agent. In other words, accordingly to this result the ISP is able by the help of the specific transfer rule collect the true information from all agents and to realise the optimal social choice in this system.

On above discussion let us define a compact optimisation problem for the ISP. Here we assume that the transfers depend on a: y=y(a,r). Using this rule in mind we formulate the following optimal decision rule for the ISP where A is expressed by the constraint:

a=arg(optu_i(a,r), s.t. y_i(a,r)=0, iI ). (2)

Note, that from the agent's i point of view, after he learns his type he will make a report r_i to the centre for the quantification of (2). The last contains also transfer rule, and so does agent's expected payoff at the time of choosing the best report strategy. According to Theorem 1 in Aoyagi (1997) the best reporting strategy for each agent is the truth-telling.

The intuition behind Theorem 1 now is now is very easily seen: in the condition of correlated types it is possible to construct transfer rules that will make for an agent in the case of distorted reporting the expected transfers and utilities less than in the case of truth-telling. Namely, because of the correlation the distorted reporting will in the same way distort the information about other agents conditions and so, in the situation of constrained transfer budget, be harmful for the distorted ( on the basis of Caushy-Schwartz inequality ). On the basis of the Theorem 1 is also possible to construct explicitly the transfer rules, and the intuition there is that the transfers for the agent are better in case the agent's reports correlate better with the other agents reports.


4. The Contributor Country in the Role of the Intra-Regional Planner (CIP)

4.1 Pre-limited Transfer Budget

As the special social planner institution is not always politically possible to build, we here resort to the economically second best model where by assumption the only contributing country i=1is playing centres role, and the agents in this model are: i=2, … ,n.

A difficult economic issue in this model will be the amount of transfers. As there is now no economic institution to plan for the first agent economically optimal contributions to the cooperation, the level of these contributions in this model will be an endogenous political issue in this country. We assume here the politically agreed transfers in the CIP model are less than in the ISP model, and we probably have to deal with the effectively pre-limited transfers budget, and with the more restricted set of admissible decisions and with resulting economic inefficiencies.

The transfer rule in this model has to fulfil required budget limit property: q x_i( r )>0, x_i( r )>0, for i=2, … ,n , where q0 is in the first country the politically agreed transfer limit.

The problem now is, can this reduced budget still induce truth-telling? According to Aoyagi (1998) certain adjustments to y are not effecting the incentives of each agent, and thus the CIP model still realises the social objective in the pre-limited budget conditions.

4.2. Lagrangian comments on the budget limitation

On the basis of (2) and notes in 3.1 the following Lagrangian function may be formulated:

L(a,)=(u_i(a,r)+y_i(a,r)) - y_i(a,r), (3)

where i=2,…,n, and is the positive shadow price for the transfers. Here we also assume that the Lagrangian is mathematically "nice" ( the common convention that the utility functions have Neumann-Morgenstern characteristics and that shadow price will increase if the transferee budget will be more rigorous etc.).

As the first agent is missing we may now conceptually adequately assume that a is separable by agents and the applicants utilities depend only on their own decision parameters. Accordingly the Lagrangians for the agents are:

L_i(a_i,)=u_i(a_i,r)+y_i(a_i,r)(1 - ). (4)

From (4) we immediately see that the transfers to the agents are less if the shadow price for the transfer will be bigger, and consequently to our conventions the less will the cooperation processes be advanced.

It is important here to note that the more limited or rigorous financial assistance does not mean the exclusion of certain countries from the process, but for all the transfers are proportionally reduced compared to the economically first-best optimal transfers.

It can also readily seen that then the value of the shadow price approaches to 1, that means the values of transfers will be insignificant and the incentive mechanism will vanish. In this case the mechanism type model is not adequate any more ( Abreu and Matsushima, 1994 ), and these situations should be dealt with the extremely complicated direct incomplete information implementation models or with the Bayesian game theoretic tools.


Conclusions

Methodological Conclusions

Following the Eatwell et al. (1997 ) paradigm of the partnership in the intra-regional decision making and relevant institutional design problems our model analyses demonstrate that a convenient mathematical tools to analyse these processes may be a Bayesian incentive mechanism optimal social planner models, and in some respects these models may have in this field some advantages before the non-cooperative game theoretic tools.

This note shows that the recent work by Aoyagi (1998) which proposes a Bayesian centralised mechanism with correlated types and budget balanced side payments which makes truth-telling a Bayes-Nash equilibrium, has a great appeal for the study of an intra-regional cooperation decision making and relevant institution building. The appeal of this result for our purposes lies among other mainly in the fact that the intra-regionally cooperative countries are informationally correlated.

Policy advises

Our model concludes that in the case of certain reductions of the financial assistance to the cooperative countries above the economically optimal level it is rational policy to disseminate this limited financial assistance still to all countries and not to escape to exclusions of certain countries from the cooperation processes. Moreover, the model predicts that for all countries the economically sub-optimal transfers should be proportionally reduced compared to the economically first-best optimal transfers.

The institutional characteristics of this cooperative partnership, according to our model results, are best implemented in the institutions of incentive compatible planning mechanisms where the with help of side payments the counties have incentives to report truthfully all the thin and changing local information. This gives the economic right also to the one country to play the role of the all regional social planner as the economically second-best institution.

Our model analyses based on Aoyagi (1998) results demonstrate, consistent with intuition, that the intra-regional monetary cooperation transfers to create Bayesian incentive compatibility in the partner countries should depend on the level of the correlations of the information reports given by these countries.

It can be easily seen that the results of this note may be extended to the inter-regional and global-local cooperation models.


References

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