WORKER SOLIDARITY AND STRIKES:"

YANIS VAROUFAKIS

University of Sydnr\!

I . INTRODUCTION

Strikes usually succeed o r fail depending on the degree of solidarity the Union can muster. And yet the strike literature continues to assume perfect participation by the workforce and to treat capital-labour bargaining as a two-person division game.' In contrast to other areas of economic analysis where egoistic behaviour by agents may inhibit the provision of public goods, the theory of industrial conflict has failed to articulate a sound explanation of why individuals may choose to co-operate in the pursuit of common objectives. Moreover, when wage determination is consistently examined as i f Union unity is never an issue, one wonders what aspects of wage setting remain hidden.

Recently, Varoufaltis (1986) and Naylor (1987)* adapted AltcrloF's social custom model in order to shed some light on how a strike coalition may come i n t o being. The common theme in these models has been a willingness to visualise t h e worker a s a social animal who has no access to a genuinely free ride. By assuming that those who cross picket lines incur socially as well as privately determined reputation costs, defcction loses much of the appeal it would have in a world inhabited by individuals who live in isolation from their social environment. Under certain circumstances, it is shown that rational agents will choose to sacrifice monetary gains in exchange for valuable reputation. The Union's public good, i.e. the strike, will therefore be at least partially provided.

This paper attempts to build on earlier results by endogenising wage and strike duration outcomes. Section 2 offers a version of the original social custom model and discusses the existence and nature of solidarity equilibria. The stability of worker coalitions is examined and it is shown that, in the face of multiple equilibria, the outcome depends on initial beliefs as well as on the heterogeneity of preferences. In Section 3 we introduce the two negotiating teams: Union leaders who are uncertain about the level of product demand and managers who are imperfectly informed on the Union's internal cohesion. In order to provide the firm with a n incentive to divulge privileged information, Union leaders offer wagelstrike duration combinations out of which the firm has to choose one. If the chosen bundle involves a positive strike duration then conflict occurs and its purpose is to

'"Lengthy discussions with Shaun Hargreaves-Heap and Jeff Sheen have been invaluable in formulating the main model. Thanks are also due to Peter Johnston for introducing me to catastrophy theory and to an anonymous referee for useful comments on earlier versions. Errors are mine.

'For example see Kennan's (1987) extensive survey of the strike literature in which there is not a single reference to a theory incorporating imperfect solidarity.

'1 am grateful to an anonymous referee for pointing out the similarity of the two approaches.

76

1989 WORKER SOLIDARITY A N D STRIKES 77

optimally convey information to the Union. Section 4 blends the models of Sections 2 and 3 and examines how variable worker solidarity can give rise to dynamic adjustments in employer offers. In Section 5 it is demonstrated that a n interesting three phase history of the Union-firm relation emerges once bounds are placed over the bargaining horizon. Not surprisingly, the model's main characteristic turns out to be the sensitivity of outcomes to the properties and timing of the strike coalition. Finally, Section 6 concludes.

11. THE EMERGENCE O F A STRIKE COALITION

As Union gains from a strike are reaped by those who make the short term sacrifices and those who free-ride alike, collective impotence rather than action should be taken as the starting point. One way of explaining why prisoner dilemmas are frequently defeated is to argue that defection carries its own legacy and ceases to be a ride free of all costs. Provided a social ethic is in place which prompts society to view defection as deplorable, all that is needed for rational cooperation is the assumption that individuals suffer disutility from being identified as disloyal to the common cause. In that case, workers may, in customary marginalist fashion, choose to strike if doing so enhances their utility. The following assumptions set the scene: Assumption Z - An individual worker decides on whether a strike is worth joining as part of an exercise in personal utility maximisation. Assumption IZ - Workers draw utility from two sources: expected income and the reputation they enjoy amongst their colleagues. Assumption IlZ - The degree of disutility associated with strike breaking depends on both personal and social factors.

The first two assumptions can be expressed in terms of the typical worker's utility function U(w, R ) with w the wage rate and R the level of reputation at any point in time where

Letting T be the length of the currently negotiated contract, s the expected strike duration, w the expected wage settlement, r the discount factor of all agents in the model, b the level of strike benefits per period payable by the Union we the firm's final pre-strike offer (>b),

0 and

our worker will join a strike beginning at time 0 and expected to last until time s if

The above decision rule is made more manageable without loss of generality by letting T-00 and adopting a simple separable utility function U(w,R)=a Iw+a2R. The following determines the decision.

78 AUSTRALIAN E C O N O M I C PAPERS J U N E

if y ~ > z STRIKE BREAK if yc,<z INDIFFERENT otherwise

Decision Rule

where y=a2/al is the worker’s relative valuation of reputation, e=R,-Rni the magnitude of reputation loss from not joining and

z=(we -b) ( l -e-rs) 0 The simple rule in (1) confirms the intuition that the probability of participation is

positively related to the relative weight one assigns to good reputation and the Union’s ability to compensate its members during the dispute, while inversely related to the firm’s final offer and the expected duration of the strike.’ Less obvious predictions can now be generated once the role of the proportion of the workforce wishing to strike (say a , 0<0<1) is recognised. Function z can be thought of as the rule’s component encapsulating the decision’s monetary considerations and will be therefore referred to as the objective part. It is clear that the average worker expects a shorter strike to be sufficient for the attainment of a given wage demand the greater the degree of mobilisation by the Union. Moreover, with more and more workers ready to join in, the employer will increase the pre-strike offer we 0 as a further inducement to strike breaking. Thus, both we and s are treated by workers as a function of the level of solidarity a. In particular, the rate of change in z with respect to changes in solidarity is given by

0

awe z‘ = 3 = 0 [ ~ - e x p [ - r s ( a ) ~ ~ + ~ w ~ ( a ) - b ~ r e - ~ ~ ( ~ ) W (3 )

The greater (a) the employer’s last offer and (b) the responsiveness of expected strike duration to levels of solidarity, the flatter the z-(r relation in Figure 1. The significance of this will become apparent when formulating Proposition I .

a0 aa d U

0 02 l U FIGURE 1

’It will be assumed throughout that strike breakers receive w: per period.

1989 WORKER SOLIDARITY A N D STRIKES 79

Having codified Assumptions I and I1 in rule ( l ) , we now seek to incorporate Assumption 111. This is straightforward in view of the logical dependence of the subjective part of (1) - i.e. y p - t o solidarity. Indeed, there is every reason to believe that a custom respected by very few is a weak custom with limited impact on our individuals. Following Akerlof (1980), we postulate that the larger the coalition of strikers the greater the stigma attached to crossing picket lines:

Defining Equilibrium Solidarity - A coalition of strikers is said to be in equilibrium if neither those workers who have decided to join it nor those who have chosen to continue working have an incentive to change their minds.

In the case of identical individuals, the condition for a coalition 8 to be in equilibrium is that z ( 6 ) = e(5) with intra-marginal strikers and strike-breakers alike being indifferent between changing sides or staying put. The same result applies when personal tastes differ between workers but are uniformly distributed over a continuous range. However, i f there exist different sub-groups within the Union holding diverse ideological positions with y values to match, an equilibrium may arise which involves no marginal workers. For a brief discussion see the Appendix.

Proposition I -A sufficient condition for an interior equilibrium 5 (i.e. 0<5<1) to be stable is that z’(8)>pf(8).

From Figure 1 it is clear that, when z cuts yp from below, any perturbation around interior equilibrium a2 will trigger rule (1)4 and return us to it. This is, however, not the case with u1. The above inequality of slopes would have been a necessary, in addition to sufficient, condition for stability if workers were either identical, or their differences were uniformly distributed. However, more unevenly distributed personal valuations of reputation could generate stable equilibria even if the condition in Proposition I is violated. To keep the analysis tractable, the discussion of the effect of the 7’s distribution on stability is placed in the Appendix. Here we proceed with a simplifying assumption.

where n is the size of the Union’s membership and y o , y 1 correspond to the valuations of reputation by the most egoistic and the most loyal members respectively.

Proposition /I - Thc Union’s preparation for the strike will result in an imperfect level of solidarity only if the employer is expected to ‘‘take” a strike irrespective of participation rates.

’

The above asserts that when perfect solidarity is expected to win the day for the Union, there will be n o dichotomy in the decisions of members: collective rationality will prevail as the workers either stand solidly behind the leadership or unanimously refuse to down

4An imperfect but stable coalition will be more likely the more responsive the employer’s last offer is to changes in u relative to Q, the lower the worth of reputation in relation to income 7 and the higher the anticipated strike length.

80 AUSTRALIAN E C O N O M I C PAPERS JUNE

tools. Free-riding will, therefore, only become a possibility if it is ltnown that absolute unity is not sufficient to force the employer into submission. Therefore, the contradiction between private and collective interest does not manifest itself unless sacrifices are called for.

Proof: The condition for a stable equilibrium at 3 can be written as

( l -exp(- rs (u) )~ + r(we - b ) a s 0 exp(-rs(u))> 7 W (5) d U dU

do 0

If expected strike duration vanishes as u increases ( i e . s-0 when u-1, or s=O when u hits

an upper bound), inequality (5) reduces to r(we -b) 6 > 7 at! , a condition that cannot be

fulfilled since I$ > 0, s’<O and we b. If on the other hand a positive strike length is thought 0 necessary even when u=l , the mixture of strikers and free-riders will be stable provided

0 a u au

The multiplicity of outcomes calls for a n interpretation of observed solidarity levels. A useful way of thinking about the actual realisation is in terms of an equilibrium of beliefs. Suppose in the context of Figure 1 that workers initially expect solidarity to be below o 1. In that case the dynamics of the model will ensure that n o worker will wish to strike. Conversely, if the typical expectation exceeds u1, equilibrium behaviour commends u2 as the dominant coalition size.

U’ ,? l a FIGURE 2

At time s=O strikers walk out (where the size of the coalition is 5 ) and the z-function rotates to position z‘ rendering 3 an unstable equilibrium.

19x9 WORKER SOLIDARITY AND STRIKES 8 1

The Strike The moment workers walk out, the preceding analysis is altered in two important ways.

First, we0 is disengaged from CJ as any further concessions by the employer will not be granted until agreement is reached. Second, workers may alter their valuation of reputation (7) when they gain first hand experience of the hardship as well as the cathartic properties of collective action.

The effect of the former is to instantaneously cause a rotation of the z function - see Figure 2 -as dwE/aa is set to zero and may lead to a destabilisation of the coalition if z‘ < e’. In that case, the effect of the strike on (i.e. average valuation of reputation) becomes central to the fortunes of the strike. If the new 7, say y’, exceeds the old, then y e moves upwards and a bandwagon effect takes CJ to unity. In the opposite case, when the strike adversely affects average valuation, solidarity will recede. A possible model for the dynamic adjustment which will occur is given by

(7) ; = A(@-2) ; L>O

where L represents the speed of adjustment.

111. A MODEL O F STRIKE CAUSATION

Strikes are usually perceived as either the manifestation of irrationality’ or the unavoidable cost of informational asymmetries. Although both could be employed in order to motivate the analysis, the more elegant view of conflict as a n information transmission mechanism is chosen. Union leaders are assumed to be less well informed than managers about the state of demand for the firm’s products and it is this assumption that allows conflict t o establish a foothold. Since it is always in the interest of employers to pretend that the market is depressed, “taking” a costly strike is the only credible way of convincing the Union that demand is truly low. Hayes (1984) has actually shown that when the Union is seeking a wage demand that maximises its expected utility subject to the firm’s optimal response, a perfect equilibrium strategy is to present a schedule of wage demands that is a decreasing function of strike duration and independent of the true state of product demand.6 It is worth noting that the crux of the model is the credibility of this schedule. Unless the Union can articulate a believable pledge that it will obstruct re-negotiation of the original locus of proposed outcomes, the model collapses. Although such a degree of commitment appears to be suspect, there is an impeccable logic behind it provided the Union and the firm expect to periodically bargain under similar circumstances in perpetuity. The effect of relaxing the stringent commitment requirements are discussed in Section V.

During pre-strike negotiations the Union presents the firm with a concession schedule (CS) representing the collection of outcomes out of which management has to select one.

cs: wu = f(0, yx, s) ; fv, fy>O, fs<O (8)’

’See Cross (1969) and Ashenfelter and Johnson (1969) for examples

%ee Fudenberg and Tirole (1983). The role of commitment will become apparent in the next Section.

’See Hayes (1984, p. 65) for a proof that a concession schedule of this type represents an equilibrium strategy for the Union. The role of this schedule is to offer the firm incentive compatibility.

82 AUSTRALIAN ECONOMIC PAPERS J U N E

where wu is the Union leaders' wage demand, their estimate of the firm's total revenue,

1 if y ' > v

-1 if y'<Y while < = { reflects their views on the direction of the

bandwagon effect once the pre-strike equilibrium is destabilised. Finally is the Union's estimate of the bandwagon effect's speed.* Having no other alternative, employers treat (8) as the constraint in the maximisation of the firm's objective function:

where V[.] is total revenue

and F are fixed production costs per period L is the fixed level of employment

The optimal outcome will signal a dispute only if V is less than a certain threshold level below which the firm is compelled to take the strike in an attempt to reduce long term wage costs.' Simp!ifying the firm's profit function during the strike as 1 rn(a){V-weL}e-rt where

O<m(a)<l is the average proportion of normal profits generated during the stoppage by strike breakers and evaluated a t we, letting T-tm, and imposing an exponentially declining function for the Union CS,"

S

0 0

0

wu = w:, + (w: - w$xp(-as) (10)

(where w, is the previous wage rate, zu' is the value of CS at s=O - i.e. the initial Union demand - and a the speed of Union concessions)

yields the final wage

0

which will be agreed upon after a strike lasting

U = In(wo - w:::) - In(w - w:::)

a

'The €2. term contains the leaders' expectations on how the coalition will fare during the strike. In the pre-strike period workers communicate to them the value of which is used as a basis for computing the concession schedule. The direction of change in u will thus depend on whether y ' exceeds ?or not. With 2 being the estimate of the speed of adjustment, t,l is a complete description of the Union's view of its future cohesion.

'This implies that if V [ . ] was known to both the firm and the Union, strikes would always be sub- optimal.

"'The adoption of an exponential functional form is, of course, ad hoc. Its purpose is to demonstrate how a solution can be derived given a particular CS. It also links the asymmetric information approach with that of Ashenfelter and Johnson (1969).

1989 WORKER SOLIDARITY AND STRIKES 83

Not surprisingly, the final wage will be higher the greater the actual level of the producer surplus, the better the reputation of the Union as a cohesive organisation and the higher the previous wage rate. Equations (1 1) and (12) depict the outcome as perceived by the employer side at s=O. If (12) reports a non-positive value, a corner solution averts the strike. Alternatively, the dispute goes ahead with uL worlters walking out. It is the evolution of this coalition that plays the major role in determining any deviations of the final outcomes from those predicted by the static model.

IV. SOLIDARITY A N D STRIKE DYNAMICS

Unlike the Union, employers can adjust their offers along the CS t o suit new information on the level of solidarity. Any deviation of m ( u ) from the anticipated level will overturn the optimality of (11). (12) and prompt managers to re-consider. There are three obvious parameters whose re-estimation may lead to revised offers. First, the employer will a t s=O be eager to observe whether the initial level of solidarity lives up to ex-ante predictions. Such alterations will lead to one-off discrete changes in the firm's offer. Second, in view of the likely destabilisation of equilibrium solidarity, employers will be wise to keep a wary eye on the direction of the bandwagon effect (<).'I If <=1, the firm's worst fears will have been realised as the strike will gather momentum. Suppose, for example, that re=-l while (=1 and te is the ex-ante expectation concerning (. In this case, the firm has got its predictions badly wrong with solidarity being strengthened monotonically while (1 1) was calculated on the assumption that the strike would decline in intensity. Major re- adjustments are, thus, essential. Third, even if teq=-l, there is still the matter of the speed with which the proportion of strikers is eroded ( A ) . For instance, suppose that the employer held over-optimistic expectations about 1. Coming to terms with the Union's higher than hoped for ability to impose strike costs will necessitate a shift in the firm's isovalue curves on the ( W J ) plane, the effect of which is a higher offer and a shorter strike. Let n(1) be the firm's prior otbelief concerning the value of l . When observed solidarity is a t level u and the conditional distribution of u given A is f (u /A), the posterior n(A1 u) is derived by the rule n(Alu) = fon(n) where p ( u ) is the Bayesian predictive distribution of u. It can be

P ( U )

shown'* that the Bayesian updating mechanism for the firm's point estimate of I after s periods of conflict is given by

"Recall the definition of 5 in (8).

"Proof of equation (13):

E [ p ( o ) ] = ( op(u)do = u( n ( l ) f ( o l i ) d i d o = ( n(i)j o f ( o ) i ) d i d o

Hence, E(1) = { i n ( i ) d i = 1 j if(. J i ) n ( i ) d u d A =

{ j i n ( l I u ) p ( a ) d o d i = E ( i I a)p(o)do. i .e. the expectation of the prior o f l is equal to the expectation of the posterior averaged by the Bayesian predictive distribution. Alternatively, 2 = E ( 1 ) = j 1 I f ( a i i ) n ( l ) d u d i

84 AUSTRALIAN ECONOMIC PAPERS JUNE

Consequently, when 1 is exposed as an over(under)estimate, managers will, provided {=-l, increase(decrease) their offer a ~ c o r d i n g l y . ’ ~ In geometric terms, the firm’s isovalue map defined on the (w,s) axis rotates and its new tangencypoints with the CS constitute thenew optimal solutions. Figure 3 depicts one possible scenario.

V. FINITE HORIZONS A N D CATASTROPHIC OFFER PATHS The sceptical reader will rightly remark that the whole model collapses the moment the

credibility of the CS is undermined. If there was no room for relaxing this requirement, then the generality of the analysis would be in jeopardy. The most obvious way of establishing the truth behind this suspicion is by removing the justification for the unwavering Union commitment to the CS, namely the infinite horizon. Recall that the Union is assumed to adhere to the CS even if during the dispute its solidarity predictions were found wanting. In the short run, Union leaders would wish to be able to alter the CS since the beliefs on which it was based proved erroneous. However, doing so would allow the firm to toy with the idea of ignoringa CS in a futurenegotiation and would inevitably be detrimental to labour’s long term bargaining power. Thus, a n infinite horizon fosters absolute commitment to the CS. What if, however, an upper bound, be it fixed or stochastic, were to be placed over the horizon? For instance, the current Union leader may be due to retire after, say, k further bargains are struck between the two sides.14 Will the analysis require major revisions? Consider the kth negotiation. Leaders who are solely interested in pursuing the Union’s objectives will have no hesitation in re-thinking the CS during the strike. Doing so will have

I3If the firm did not possess perfect information the shape and location of function Q, then an adaptive learning rule is as good as any:

@ = p ( n - 2 ) ; p>o ds

I4One could think of many other ways in which to introduce a finite horizon. Note that the bound could take a stochastic form with k representing the negotiation with unit probabilityof being the last. See Hargreaves-Heap and Varoufakis (1987) for a discussion.

1989 WORKER SOLIDARITY AND STRIKES 85

no long term effects since the opposite side knows that the current negotiation is the last which they conduct prior to retirement. Hence, the model of Section I11 is made redundant by the mere fact that employers are not convinced that during the kth negotiation the Union leader will remain faithful to the CS. Furthermore, if this break down is expected to occur ~ . i negotiation k , it will also be expected to characterise negotiation k-1. Backward induction unravels and it transpires that a t no time will our one-sided asymmetric information model represent a fair account of the bargaining process.15 Thankfully, all is not lost. The bulk of the analysis can be revived by injecting a small amount of uncertainty in the mind of the employer about the Union leader’s preferences.16 This is how: Backward induction unfolds only because its logic achieves a toehold during negotiation k . It is the conviction that the Union leader will certainly wish to drift away from the CS that leads to the model’s collapse. In an environment where the leader’s motives are transparent the Union loses its ability to bargain credibly. However, if there is some doubt about the leader’s behaviour a t time k , then this is not so. Suppose there is a small probability that the leader is averse to going back on a pledge ( i e . the CS) even if doing so were to increase the Union’s payoffs.’6 We call this type of person intransigent. The slightest of doubts as to whether the leader is a pragmatist or intransigent, suffices t o wreck the backward induction process and gives rise to a sequential equilibrium solution concept.”

Proposition 111 - After the election of the Union leader(s) to a fixed term in office, three distinct phases of stochastic length arise. Phase 1: Bargainers behave as they would have had the horizon been infinite. With the firm reluctant to contest the Union’s wagelstrike duration bundles, the analysis of the previous sections applies intact. Phase 2: The transition to this second phase occurs when the time comes for the firm to optimally challenge the Union’s offers. As long as the Union remains defiant, outcomes will remain on the concession schedule. Thus, the original analysis requires only minor adjustment to allow for the longer strike durations necessary to rebuff the employer’s challenge. Phase 3: Provided labour leaders would prefer to concede during the strike if it was not for the long term repercussions of such acquiescence, they will eventually do so as their term in office draws to an end. The period of credible commitment t o ex-ante offers is now over and a qualitatively different model of strikes is needed to guide us through the uncharted third phase that leads to fresh Union elections.

The firm’s dilemma brought on by the introduction of the finite horizon revolves around the wisdom of pressing for a settlement off the CS (e.g. combination w’-s in Figure 4). If it challenges the CS by insisting on such a bundle, there is a risk that the Union will wish to teach it a lesson by only accepting w’ after a n s‘ long strike. Of course this risk is only a problem if the firm is unsure about the leaders’ intransigence. If they were known to be pragmatic, backward induction would ensure the CS’ downfall. However, in the face of uncertainty, the leader who is pragmatic may wish to build, a t least in the early stages, a reputation for intransigence and commitment to the CS. This being common knowledge, the firm does not dare challenge for a number of early negotiations, say k’<k, as doing SO

”This is the so-called Chain Store Paradox

‘%reps and Wilson (1982) suggest this type of incomplete information as a means of defeating the Chain Store Paradox.

”See Kreps and Wilson (1982) for a full definition.

86 AUSTRALIAN E C O N O M I C PAPERS J U N E

S SI strike duration FIGURE 4

would allow the pragmatic leader to put on a display of intransigence. The higher the leader's initial reputation for intransigence the longer this first phase during which the finite and infinite horizon models are indistinguishable." At negotiation k '+ l , the firm will challenge with positive probability. Faced by this threat to the CS, leaders deliberate between meeting the challenge with a longer dispute than the one predicted by (12) and acquiescing. Their equilibrium randomisation decision rule will be such that in the event of a prolonged strike the leader's reputation for intransigence will follow an optimal growth path. In the event of acquiescence - i.e. a settlement off the CS - the second phase is complete and the final one begins which takes the two sides to the end of the horizon.

In summary, a second type of uncertainty was introduced in order to salvage the analysis from the claws of backward induction: uncertainty with regard t o the leader's intransigence. It is encouraging to note that the leader suddenly becomes central to the game, especially in view of the insight that even a pragmatic leader may wish to show signs of intransigence. Irrationality is, therefore, not necessary for the model t o explain strike activity. Unlike models which rely on irrational behaviour (see Ashenfelter and Johnson, 1969; Cross, 1969), all we really need is that not everyone assumes everyone else to be rational. It is this possibility of intransigence that makes intransigence optimal even for rational bargainers who have no natural inclination towards it. Good unionists creatively exploit the uncertainty surrounding their character and know how to pick their moment for switching from a defiant to a conciliatory strategy.

Conclusion: Proposition 111 suggests that in the first phase the original infinite horizon model is valid while in the second the CS based predictions will still hold although strikes will tend to be longer as the firm challenges for a bundle below the CS. In the third phase, however, the CS is discredited and the true concession schedule will only emerge ex-post. To avoid the complication and certain intractability of a two-sided information exchange, I will restrict the analysis to a tentative geometric description which serves well in evaluating the role of solidarity in determining wages.

"The analytical proofs are available from the author on request.

1989 WORKER SOLIDARITY AND STRIKES 87

wage' offers

The Geometry of the Third Phase The commencement of the third phase coincides with the first settlement off the Union

announced CS. Thereafter the leader is expected to re-adjust the CS and the firm embarks upon a search for the new CS. Figure 5a represents the set of possible candidates for a replacement of the initial CS. Depending on a given prior of belief, managers select one of the available candidates as the new constraint in the maximisation of (9). If a strike occurs there are two possible ways in which offers can be adjusted. First, equation (13) may be activated if solidarity diverges from its anticipated path. Second, the employer may begin to swap one CS for another if Union negotiators appear to follow a different CS to the expected.

FIGURE 5

Proposition IV - With a CS reflecting a non-monotonic relation between wage demands and strike duration, employer offer paths will be characterised by hysteresis.

Consider the first type of adjustment where the firm is continually being surprised by unexpected rates of change in the size of the strike coalition. In the case where u is growing, the firm's estimate of its average profitabilitym (see Section 111 for a definition) falls'and its isovalue map on the (w,s) plane becomes steeper. When expected average profitability falls below mo - see Figure 5b - the sequence of employer offers undergoes a catastrophic jump.

88 AUSTRALIAN E C O N O M I C PAPERS JUNE

wage offers

A

W l

w3 -

104

w2 . H

I I I ., m2 mo m i m

FIGURE 6

Conversely, if worker solidarity is rapidly dropping and mo exceeded, the firm will reduce its offer discretely. The nature of the discontinuity will clearly depend upon the employer’s ability to absorb information. If there is some delay between the reception of new information and the issuing of offers, Figure 6 takes over from Figure 3b and the discrete drop (rise) in the firm’s offer resulting from a continually increasing (decreasing) profit rate during the stoppage, will occur a t an anticipated average in excess (lower than) m,. When solidarity is growing, offers will follow path DEFA as opposed to ABCD when it declines; a case of hysteresis.

Interestingly, for a n average profit rate generated by strike breakers in the region of mo, the final settlement may be either w1 or w2 depending on solidarity dynamics. As the same number of lost working days may lead to drastically different wage settlements, there is little doubt that the study of wage determination is incomplete without a thorough understanding of solidarity and its determinants.

Let us now consider the second type of adjustment: if the firm is for the moment assumed to be well informed on m, offer fluctuations may still be forthcoming while managers search for the most likely CS. It is helpful to visualise the inter-play between the firm’s fluid views on (i) the level of participation/profits during the strike and (ii) the Union negotiators’ concession curve, in terms of a three dimensional diagram featuring two control and one state variables. The state variable is the firm’s wage offer which at any point in time is “contro1led”by the predicted level of average profits courtesy of strike breakers (ie. m) and the precise location of the CS which is denoted by a parameter l j i ~ (031). As the employer moves from CS1 to CS,, lji rises from zero to unity. Thorn’s classification theorem of elementary catastrophies‘’ applies in the case of an adjustment delay of the Figure 6 type suggesting that the Figure 7 relationship is the most complicated one that can possibly

“Thorn’s theorem shows that if adjustment is not instantaneous in a model governed by smooth functions and containing two parameters, there is essentially only one possible type of local geometric structure (see Poston and Stewart (1978) for a full exposition): the cusp of Figure 7 , where the two parameters in question are the anticipated avcragc profitability over the whole dispute ( m ) and a measure of the gradient of the Union’s CS ( c ) . F o r other economic applications of the cusp sec Harris (1978) and Dogson (1982).

1989 WORKER SOLIDARITY AND STRIKES 89

wage

FIGURE 7

emerge.20 Figure 6 is indeed contained within Figure 7 since freezing g at, say, g’and varying m yields the familiar paths DEFA or ABCD depending on the direction of solidarity changes. The additional insight provided by the complexity of Figure 7 becomes apparent when we consider the case of a relatively stable average profit level in the region of mo. If the firm takes as its constraint the CS with o=q”, the optimal offer will be near point M on the stationarity surface S. Supposing that the Union appears to be more conciliatory than g” initially implied, a gradual uEwa,rd revision of q from q” to g‘ may lead t o two qualitatively different offer paths 81,82. The Union will, thus be faced with the prospect of very different payoffs for more or less the same level of solidarity. The suspicion that the resolution of industrial conflict owes more to fortune than hitherto acknowledged may after all have a theoretical foundation.

Proposition V - During the third phase, bimodality in wage offers with respect to participation levels leads to a dichotomy between two qualitatively different types of settlements.

The slightest of perturbations around m, will decide the ultimate fate of the dispute.

The importance of solidarity cannot, therefore, be overstated. Proposition IV confirms that the direction of the solidarity process is instrumental in boosting wages while Proposition V suggests that labour’s success or failure can depend on the attitudes towards the common cause of a very small number of workers.

Note that although Figure 7 is topologically the most complicated structure, there is always the possibility of multiple cusps. I f , for example, we used the firm’s discounting rate ( r ) as an additional control variable, it would be possible to generate a second cusp for high values of r . However, this would not be particularly interesting since it is not very likely that r will change during the dispute.

20

90 AUSTRALIAN E C O N O M I C PAPERS J U N E

VI. SUMMARY

This paper calls for the restoration of solidarity as a central notion in the study of wage determination under Trade Unions. If the process from prisoner dilemma to common assurance preferences is of a dynamic nature and involves ideological externalities, the attitudes of workers during a dispute cannot be adequately summarised by a single time- invariant utility function. Section I1 offered a model of solidarity formation and discussed the conditions under which a stable coalition of striking workers may arise. Section 111 rationalised the Union’s strike call be means of an asymmetric information model which, suitably formulated, produces pre-strike estimates of the outcome. Section IV examined the effect of unanticipated solidarity changes on offers and outlined the firm’s optimal learning rule. Finally, Section V sought to relax the perfect commitment requirement by imposing bounds on the horizon and invoking a sequential equilibrium solution concept. The result was a rich history in the Union-firm relationship comprising three diverse phases. It was argued that the first two are either identical or qualitatively similar to the infinite horizon model, whereas the third phase requires a major departure from the standard anaysis. A tentative geometric investigation revealed some interesting features of the effect of mobilisation and solidarity which usually elude conventional models.

Apart from the theoretical importance of worker solidarity, there is a number of clear implications for empirical work. At least a t a disaggregated level, steps should be taken to account for the strike’s intensity preferably through the introduction of the average proportion of strikers as an endogenous explanatory variable. Whenever possible, a proxy for the direction of change in participation should also be enlisted since its absence might cause serious misspecification (see Proposition IV). Recalling that Section V predicted an increase in strike duration as we pass from the first to the second phase, it may be interesting to test for the hypothesis that strike duration is related to the lifecycle of the Union leader - management relation. Indeed, a number of institutional aspects related to the internal rules of the Union appear to be significant. In the asymmetric information framework of Section IV, compulsory pre-strike ballots are certainly beneficial to the employer as they provide her with a distinct informational advantage. The Union movement’s aversion to them may, therefore, not be solely due to an alleged dislike of democracy.

In conclusion, the ability of a Union to provide its members with an essentially public good is contrained by the extent to which individual workers see the subjective components of their utility function dominate their monetary considerations. In commending the dynamic properties of the coalition formation process as a crucial missing link in the strike literature, the analysis formalises the labour movement’s pre-occupation with Unity as a source of strength. It also points to the importance of ideology as a guarantor of the conventions which facilitate the convergence of common and private interest.

1989 WORKER SOLIDARITY AND STRIKES 91

APPENDIX Equilibrium Stability and Worker lfeierogeneity

Figure A1 shows why Proposition I does not argue that the z’lyc,’ condition is necessary in addition to being sufficient. The diagram portrays a situation where the Union is divided in three equal sub- groups each with its own ideology. The most militant members value reputation highly with y 1 being the relevant valuation parameter, the least ideological group is characterised by 73 while the “moderates” enjoy reputation according to 7 2 . I fz is downward sloping, the condition in Prbposition I can never be satisfied as c, will always be an increasing function of c. Thus, equilibria u1 and c2 are by nature unstable indicating that n o internal equilibrium coalition involving workers who take a decision on the margin will ever be sustainable. Howdver, a stable equilibrium does exist even though z’<yp’: it is the coalition with solidarity level 8. Here we have the simple case where the most ideological group of workers will strike while the members of the two other groups will continue working. Condition z’>yp’ will, therefore, become necessary only if ideology is uniformly distributed amongst all workers, in which case the discontinuities in )JQ disappear.

The effect of introducing sub-groups (each with different ideologies/valuations) o n Proposition 11 is that, although the predicted bandwagon effect will still go ahead, it may not take call the way to either 0 or 1. As Figure A2 shows, the rotation of z from z’ to z” caused by the strike will take c to one of the absorbing barriers u 1 or “ 2 .

t

I I I I I I I I

I # U

0 a, c=y, a2 Y 3 1

FIGURE A1

/ I I

1 I #l7

FIGURE A2

0 a,=!/, a A a]=% 1

92 AUSTRALIAN ECONOMIC PAPERS JUNE

REFERENCE s

Akerlof, G. A. (1980), “A Theory of Social Custom of which Unemployment may be one consequence”, Quarterly journal of Economics, vol. XCIV.

Ashenfelter, 0. and Johnson, G. E. (1969), “Bargaining Theory, Trade Unions and Industrial Strike Activity”, American Economics Review, vol. 59.

Cross, J. (1969), The Economics of Bargaining (New York: Basic Books)

Dogson, J . S. (1982), “Kinks and Catastrophies: A Note on the Relevance of Catastrophe Theory for Economics”, Australian Economics Papers, vol. 21.

Fudenberg, D. and Tirole, J. (1983), “Sequential Bargaining with Incomplete Information”, Review of Economic Studies, vol. 50.

Hayes, B. (1984), “Unions and Strikes with Asymmetric Information”, journal of Labour Economics, vol. 2.

Hargreaves-Heap, S. and Varoufakis, Y. (1987), “Multiple Reputations in Games with Uncertain Horizons”, Economics Research Centre, University of East Anglia, Disc. Paper No. 22.

Harris, L. (1978), “Catastrophy Theory, Utility Theory and Animal Spirit Expectations”, Australian Economic Papers, vol. 19.

Kennan, J. (1987), “The Economics of Strikes”, in 0. Ashenfelter and R. Layard (eds), Handbook of Labour Economics (Amsterdam: North Holland).

Kreps, D. and Wilson, R. (1982), “Reputation and Imperfect Information”, journal of Economic Theory, vol. 27.

Naylor, R. (1987), “Strikes, Free Riders and Social Customs”, mimeo, University of Warwick

Poston, T. and Stewart, I . (1978), Catastrophe Theory and its Applications (London: Pitman)

Varoufakis, Y. (1986), Optimisation and Strikes, Ph.D. Thesis University of Essex