Three-person games: an attempt at theorizing a game-theoretic model of social change from authoritarianism in the Soviet Union and the Philippines, Part II

Posted: May 6, 2018 in Game theoretic model, Game theory, Mikhail Gorbachev, Philippine politics, Philippines, socialist reform, Soviet Union

A Filipino Marxist, Ricardo Ferrer (1990) attempted to construct a formal mathematical model of Marxist political economy.  We use his model to illuminate and understand better the essence of the reform process in the Soviet Union and its ultimate outcome in late 1991.  After doing so, we explore the fitness of the same model in the analysis of the transit from authoritarianism in the Philippines since 1983 and beyond.


Ferrer’s model devoted attention to the Marxist propositions regarding the correspondence between so-called ‘forces of production’ and ‘relations of production’ as well as the appropriate state and/or state form.  His key insight: non-correspondence invites both reform and/or revolution.


The appropriate model is reproduced below.


Let L be the vector (L1, L2, …, Ln-1, Ln) which measures the development of the forces of production in society.[1]


We define q as the level of operation of the economy so that 0 ≤ q ≤1,

and Z as the ratio of surplus labor to total labor .


(1)                             Z = Z (L, q)


In equation (1), Ferrer notes that Z may be thought of as the surplus product per worker divided by total product per worker, where the total includes, apart from the surplus, what is considered the necessary requirement (for consumption) of each worker on the average.  This is conceptually equivalent to the Marxian notion of surplus labor divided by total labor.


By definition, 0 ≤ Z < 1; meaning, necessary labor can never be equal to zero while surplus labor can.


At all levels of the economy, some amount of unproductive but socially necessary labor is needed.  For instance, trading firms facilitate the circulation of products while financial intermediaries expedite the flow of funds from surplus cash holders to borrowers-users.  In that case, Ferrer postulates a social cost function Cu:

(2)                Cu = Cu (L, R, RS, RS’, RI’, q)



L      =  (L1, L2, …, Ln-1, Ln)

R     =  (R1, R2, …, Rn-1, Rn)

RS   = (RS1, RS2, …, RSn-1, RSn)

RS’  = RSR

RI    = (RI1, RI2, …, RIn-1, RIn)

RI’  = RIR

q =    level of operation of the economy


The variables R1 to Rn index relations of production; RS1 to RSn are the corresponding laws applicable to production relations R1 to Rn.  We would imagine that under a given state, laws would correspond to relations such that RSi = Ri (where i = 1, 2, …, n-1, n).  Similarly, RI1 to RIn are the ideological representations of the relations of production variables.  Ideally, they should also correspond wholly.  RS’ and RI’ measure deviations between actual relations of production and their legal and ideological representations.  Intuitively, we see that the larger RS’ and RI’ are, the larger the total social costs will be.


We know the last point to be true by noting that when property arrangements tend to run afoul of the law and social beliefs, it would be more costly to impose worker discipline.  In addition, if property rights are questioned, greater transactions cost will attend normal economic exchanges.  Unproductive labor will tend to be higher at all operational levels of the economy.


An efficient economy is one which is able to attain the maximum net surplus.  In that case, the economic problem is to maximize net surplus NZ which is the difference between Z and Cu by choosing the appropriate values for q, R, RS’ and RI’ given the level of development of productive forces L.  In notation, this is equivalent to

(3)          Max [Z(L, q) – Cu (L, R, RS’, RI’, q)]

{R, RS’, RI’, q}


Ferrer also shows that maximizing net surplus NZ is the same as minimizing total cost at a given level of the economy’s operation, i.e., at a given q.  This means that the social goal could also be written as

(4)           Min Cu (L, R, RS’, RI’)

{R, RS’, RI’}


Equations (3) and (4) indicate that relations of production and superstructure, laws and state action and ideology, correspond to the level of development of productive forces if they maximize net surplus NZ in society.  The object of any social reform (or revolution) is to remedy non-correspondence whenever and wherever such is present.  In case of correspondence, the social goal is to optimize the levels of L and q.  A greater reform project tries to effect correspondence as well as advance L and q simultaneously, or at least, sequentially after securing correspondence.  This appears to be Gorbachev’s intent.


The struggle for reform (or the revolutionary struggle) will be a political contest.  In such a contest, politicians of all stripes, from reactionaries to reformists to revolutionaries will participate and contend.  In such a struggle, even the variable L will be part of the political programme offered for the (s)electorate’s consideration apart from R, RS, and RI.  As Ferrer puts it: “The assumption that the development of L is entirely autonomous must be discarded, insofar as self-interest seeking men running political parties can benefit from some intervention in L, as the results of such intervention satisfies some demand, and would tend to maximize political parties’ chances of getting the reins of power” (Ferrer 1990: 106).  In other words, competing parties will offer complete programs which have political, economic, and cultural components.


To be continued…


Next part:  The Political Contenders and the Games They Play












Bova, Russell (1991). “Political Dynamics of the Post-Communist Transition: A Comparative Perspective.” World Politics 44(1): 113-138.

Ferrer, Ricardo (1990). “A Mathematical Formalization of Marxian Political Economy.”  UP School of Economics Seminar Papers.

Mendoza, Amado Jr. (1992). “The Soviet Reform Process, 1956-1991: From Socialist Renewal to Liquidation.” MIS Thesis, University of the Philippines (ms.).

Mendoza, Amado Jr. (2009).  “’People Power’ in the Philippines, 1983–86.” In Civil Resistance and Power Politics: The Experience of Non-violent Action from Gandhi to the Present, pp. 179-196. Ed. Adam Roberts and Timothy Garton Ash. Oxford University Press. 

[1] In Ferrer’s model, there are eight (8) L variables which measure the degree of worker control over instruments of production (L1), raw materials (L2), the level of development of material instruments of production, or roughly, capital intensity (L3), level of development or processing of raw materials (L4), the level of development of labor power, which indicates the degree of substitutability between workers within enterprises (L5), within a particular economic sector (L6), within the entire economy (L7), and the level of development of economic space (L8).  Economic space, defined in Marxian terms, consists of total productive fixed capital stock (such as factory buildings, silos, roads, ports, etc.) in an economy.  All eight L variables have values between 0 and 1.  Thus, L is the vector (L1,…, L8).

  1. bongmallongamendoza says:

    Thanks, lemanshots!

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