Coordination Problems in the Work of William Faulkner
Wainwright, Michael, Papers on Language & Literature
Coordination problems, situations in which the actions of an individual depend on the behavior of others, constitute an important subject for game theorists, but their value to literary analysis remains undervalued. This article begins to redress the balance by applying a number of common gaming concepts to selections from the canon of William Faulkner. (1) Those works by Faulkner set in the opening three decades of the twentieth century are particularly apposite since their narratives unfold within a context of urbanization. Until this period, most Americans had lived in small communities, and the effects of individual actions on the wider populace had been imperceptible. Before the Civil War most Americans had been, in some manner or another, involved with agriculture, but by the turn of the century the number of farm dwellers had dropped to one third of the population. Many of these remaining agrarians lived in the South, but, as Faulkner's fictional county of Yoknapatawpha evinces, modernity was encroaching below the Mason-Dixon Line as well. Timber extraction and cotton farming changed the southern landscape while an improving infrastructure led to fervent land speculation. Urban centers--Faulkner's Mississippi hometown of Oxford, the blueprint for Yoknapatawpha's Jefferson, is a case in point--expanded rapidly. Henceforth, individuals were likely to encounter a greater number and range of people during the course of their daily lives. As a corollary, a person could affect countless other people in numerous ways to an extent heretofore unimagined. If each individual now did what would be better for himself, his family, and his loved-ones when faced with the exigencies of life, then resulting conditions would be worse, and sometimes much worse, for everyone. Faulkner was alert to this practical dilemma, and his literature offers political and moral solutions to the ramifications of human conduct exercised in a modern setting.
One case of interdependence, which came to the fore in the twentieth century, constitutes the Prisoner's Dilemma or PD: a behavior pattern fostered by genes. In its most recognizable two-participant form a PD simulates the separate questioning of a pair of suspects, A and B, about a crime they are suspected of having committed together. Each subject must enter one of two possible pleas before learning the other suspect's decision. In addition to the two subjects, an authority sets the tariffs applied to each outcome. Whether these tolls are penalties or, as in some scenarios, rewards, this authoritative figure is commonly known as the banker. A state's judicial system is an example of this arbitrator as is an individual who receives or pays out benefit for the collective choices made by the prisoners. Matrix 1 shows possible outcomes from an interrogation:
Matrix 1 Suspect B confesses Suspect B keeps silent Suspect A Outcome 1: Outcome 2: confesses Both get ten years. A goes free. B gets 12 years. Suspect A Outcome 3: Outcome 4: keeps silent A gets 12 years. Both get two years. B goes free. Matrix 1: Possible outcomes from an interrogation in a standard Prisoner's Dilemma.
No matter what the other suspect does in this dilemma, each individual achieves a better outcome if that individual confesses. By confessing, each suspect is certain to save himself two years of imprisonment. If both confess, however, that will be worse for each suspect than if both keep silent. Simply put, the outcome will be worse for both suspects if each rather than neither individual acts selfishly.
In gaming terms, a number of conditions have to be met before a situation conforms to a true PD. Matrix 1 adheres to these requirements because in the case of suspect A, and using the number of years of imprisonment as a measure of costing, this PD takes the form of Matrix 2:
Matrix 2 Suspect B confesses Suspect B keeps silent Suspect A confesses Outcome 1: 10. …