Tuesday, April 5, 2016

Zero-Sum Foolery 4 of 4: Wage Prisoner's Dilemma

Soon after the wages-fund doctrine fell out of favor with economists, it was immediately attributed to trade unionists under the label of the "fixed work-fund fallacy" and then the "Theory of the lump of labour." In denunciations of the lump-of-labor fallacy, it has become fashionable recently to appeal to the notion of the "zero-sum game" in addition to the customary allegation of a "fixed amount of work to be done."

What follows is a brief sketch of the wage prisoner's dilemma that I modified from one posted last June. The outline can be elaborated by thinking of the dilemma in terms of Garrett Hardin's "Tragedy of the Commons" and Elinor Ostrom's analysis of common-pool resources. I have previously presented the perspective of labor power as a common-pool resource and a full treatment of wage prisoner's dilemma would incorporate those arguments. I've added a pay-off matrix at the end.

The principle of labor as private property is enshrined in the chapter, "Of Property," in John Locke's Second Treatise of Civil Government:
...every man has a property in his own person: this no body has any right to but himself. The labour of his body, and the work of his hands, we may say, are properly his.
Except for the most part we are not talking about just "the labour of his body, and the work of his hands." We are referring to a complex division of labor, co-operation and means of production that dwarfs the manual labor of a person. Regarding this augmented labor power as a common-pool resource recognizes the greatly-enhanced social productivity of labor. The wages system is calculated to siphon off the lion's share of that social productivity and award it to the owners of capital.

How does that happen?

Consider the wage prisoner's dilemma: given a choice between working long hours for more money and working short hours for less money, many will chose to work longer hours. But if a preponderance of workers choose (or are compelled) to work long hours, they will oversupply the labor market, depressing wages. They may end up working longer hours for less money.

This is not rocket science. It is elementary supply and demand: an observed regularity. And, no, it does not imply or assume "a fixed amount of work to be done." If I flood the market with bananas, it is likely the price of bananas will fall even if the demand for bananas increases in response to the lower price. It is conceivable that the temporarily lower price could instigate a banana craze that subsequently overwhelms the initial price decline. But as a rule...

Imagine the following scenario:

One hundred workers are fully employed for 40 hours a week. The current wage is $10 an hour. Due to some inscrutable technical feature of the production process, it is determined that optimal scheduling requires workweeks of either 36 hours or 44 hours. However, weekly output per worker is the same for a 36-hour worker and a 44-hour worker. Hourly output is correspondingly higher for the 36-hour worker. Pay is determined by averaging total output and aggregate hours of the workforce as a whole.

After adjustment to the new schedules, the uniform wage rate will be somewhere between $9.09 and $11.11 an hour, depending on the proportion of workers who choose each schedule. Weekly pay will thus range between $328 and $400 for those working a 36-hour week and between $400 and $488 for those working a 44-hour week.

If half the workers choose a 36-hour week and half choose a 44-hour week, hourly wage will remain at $10 and thus the weekly pay will be $360 and $440 respectively.

One payoff matrix – out of 99 – for each worker would look something like the following, with the worker's choice occupying the rows:

Assuming an individual was indifferent about the loss of leisure time, that individual would be "better off" choosing a 44-hour workweek whether all the other workers chose 36 hours or 44 hours. Aside from that assumption, the best option would depend on the relative strengths of the worker's preference for leisure, risk aversion and assumptions about other workers' preferences.

This is, of course, an extremely simple-minded example. It is meant only to suggest that "zero-sum thinking" is not the sole possible explanation for people's anxieties about unemployment – it is unlikely to be the most plausible.

Despite all the arrogant rhetoric about zero-sum fallacies committed by advocates of shorter working time, early retirement, trade protectionism or limiting immigration, there doesn't appear to have been any research to substantiate the claims empirically. There has, however, been empirical research on prisoner's dilemmas or social traps, as the tragedy of the commons model is also known. Elinor Ostrom was one of the authors of "Cooperation in PD games: Fear, greed and history of play" that references Rapoport's earlier studies. "Take-Some Games: The Commons Dilemma and a Land of Cockaigne," by Peter Mitter is included in Paradoxical Effects of Social Behavior: Essays in Honor of Anatol Rapoport.

Another kind of game has evolved with a primarily didactic rather than investigative purpose. Julian Edney's nuts game and Linda Booth Sweeney's harvest game exemplify the commons dilemma or social trap learning game. In principle, there is no obstacle (other than time and money) to incorporating a harvest-type game into a research design similar to the prisoner's dilemma research conducted by Rapoport, Ostrom and their respective colleagues.

Epilogue: Is the Road to Hell Paved with Pareto Improvements?


Random said...

One solution would be to offer a living wage job for any spare hours working for the public good and to put a floor in the labour market.

Described here

Random said...

Evidence from a different dilemma shows people value their time at about ~ £10 an hour

Magpie said...


A question for you, who are an expert in the LOL "fallacy".

Most economists -- including those who denounce the alleged LOL fallacy -- seem to believe supply and demand determine prices and quantities. Given a fixed demand, a higher supply -- they would add -- reduces prices. Vice versa, given a fixed supply, a higher demand increases prices.

Whether one believes that or not, is besides the point. They do believe it, and this is what matters.

Note that those explanations imply "lumps", at least temporarily: there is something fixed, constant. If we are talking about the widgets market, for example, then there are "lumps" in the demand and/or supply of widgets: in the first case -- see above -- a lump in the demand for widgets; in the second case, a lump in the supply of widgets.

My question is: is there a reason in those economists' views why lumps are perfectly legitimate in the case of the widgets market, but outrageously illegitimate in the case of labour market?

Or am I missing something?

Denis Drew said...

"Prisoner's Dilemma" would be a good concept to apply to the race-to-the-bottom for wages in a non-unionized labor market. To help people understand that it is not a truly free market just because you can go down the road to offer your labor elsewhere.

Sandwichman said...


"My question is: is there a reason in those economists' views why lumps are perfectly legitimate in the case of the widgets market, but outrageously illegitimate in the case of labour market?"

Excellent question! I can only speculate about the reason. I suspect it is because treating labour markets consistently with widgets market would expose the incongruities of the "supply" and "demand" metaphors. W.T. Thornton pointed out these difficulties long ago in his discussion of what he called the "higgling" of the market.

Let me see if I can simplify...

There is no "objective" demand, supply or price for a commodity. All of these terms only emerge from the bargaining situation in which the parties involved exchange guesses about each others' eagerness to trade. Thornton argued that, contrary to the "laws of supply and demand" most trades take place at disequilibrium positions, leaving unsold inventories and/or shortages.

Marginalist analysis gets around this embarrassment by simply DEFINING the quantity exchanged as the equilibrium point between supply and demand. What is sold at price P is equal to what is bought -- a tautology.

Andre Orlean's critique of value in The Empire of Value as not inherent in any substantive, quantifiable characteristic of the goods -- whether quantity or labor or of utility -- is also pertinent to the characteristics of so-called supply and demand.


"'Prisoner's Dilemma' would be a good concept to apply to the race-to-the-bottom for wages in a non-unionized labor market."

Exactly my point! And, in fact, Rapoport provided a template for doing so in chapter 4, "Cooperation and Exploitation" of Fights, Games and Debates. I am still in the process of absorbing the enormity of the implications of his analysis there and awaiting receipt of additional texts related to that demonstration.

Peter T said...


Bit O/T, but I'd add that most economists simply assume "price" equals "money paid" and "demand" as wanting some defined thing. But price can include time (queues/waiting periods), entry requirements, rationing and so on, and the thing demanded can be redefined. So the supermarket mostly does not raise the price of, say, a cereal in high demand. They post a notice saying "we reserve the right to limit purchases to reasonable quantities". And they sell the peanut butter under cost and sell the bread with a higher margin (they price baskets of consumption, not single items). Supply and demand is a rarified abstraction.

Magpie said...

Thanks, Sandwichman and Peter T.