Peter Ramus often turned to a particular visual aid, the decision tree, to represent dialectic. This visualization is also suited to the representation of coordination problems. Thus, as an inheritor of Agricolan dialectic, on the one hand, and as a pioneer of eidetic techniques, on the other, Ramus remains central to an intellectual lineage that stretches from Plato, Aristotle, Lorenzo Valla, and Rudolph Agricola to Charles S. Peirce, Josiah Royce, Émile Borel, and John von Neumann.
Game theory, which is shorthand for “the theory of games of strategy” (John Davis Williams 3), represents von Neumann’s contribution to this history. The word strategy, “as used in its everyday sense, carries the connotation of a particularly skillful or adroit plan, whereas in Game Theory it designates any complete plan.” Put succinctly, “a strategy is a plan so complete that it cannot be upset by enemy action or Nature; for everything that the enemy or Nature may choose to do, together with a set of possible actions for yourself, is just part of the description of the strategy” (16; emphasis original). Each strategic participant in a coordination problem is a player. “Coordination games,” as Michael S. Alvard and David A. Nolin emphasize, “are characterized by common interest among players” (534), and “in some models,” as Paisley Livingston notes, “a single ‘player’ is comprised of a number of ‘agents’” (69).
Von Neumann established modern game theory in “Zur Theorie der Gesellschaftsspiele” (December 1928). In games of strategy, each logically minded player in a self-interested situation has to anticipate the other players’ choices and pick a strategy according to the prospects of preference-satisfaction. “The problem,” states von Neumann , “is well known, and there is hardly a situation in daily life into which this problem does not enter” (13). Von Neumann’s analysis of this common occurrence “demonstrated that any two rational beings who find their interests completely opposed can settle on a rational course of action in confidence that the other will do the same” (William Poundstone 97; emphasis original). Selection in such situations involves each player minimizing the maximum harm that can befall him. This minimax theorem underpins game theory.
Von Neumann would apply and extend his theorem in the seminal work he coauthored with Oskar Morgenstern: Theory of Games and Economic Behavior (1944). This volume opens by stressing the important distinction between the abstract concept of a strategic game and the discrete plays of that game. “The game is simply the totality of the rules which describe it. Every particular instance at which the game is played—in a particular way—from beginning to end, is a play” (49; emphasis original). The taxonomic distinction between games of perfect, complete, and incomplete information is of additional importance. If a game has sequential (or dynamic) rather than simultaneous (or concurrent) moves, then perfect information requires knowledge of all preceding moves. Complete information does not involve details of previous moves. Incomplete information involves neither details of previous moves nor absolute certainty over current options.
As with Ramus’s desire to establish a single, dialectical logic that abides by categorical (or attributive) and hypothetical (or conditional) propositions, coordination problems often present each player with two choices. These options concern cooperation or defection. Coordinative situations often present a wider range of choices, but game theory can translate these options into a series of paired decisions. Most game-theoretic modeling, therefore, deals with two-player dilemmas. If a situation involves three or more players, then the analysis breaks down their relations into a set of two-player dilemmas. Hence, modeling usually concerns two-choice, two-player scenarios, and the social dilemmas of Deadlock, the Prisoner’s Dilemma, the Assurance Game (or Stag Hunt), and Chicken are the most prevalent of these games.
A utility describes the preference-satisfaction score for each possible outcome. A banker (or umpire)—who is either detached from or embedded in the play, and who comprises an agency, authority, or a combination of the players themselves—sets the utilities. A player’s cost–benefit analysis considers the losses and gains associated with each combination of player choices. The outcome from mutual cooperation concerns remuneration (R), the outcome from unilateral defection concerns temptation (T), the outcome for mutual defection concerns punishment (P), and the outcome for unilateral cooperation confers the role of sucker (S).1 The seeming tautology of “mutual cooperation” designates the players’ simultaneous choice of collaboration.
Certain sets of player choices lead to what game theorists call a Nash equilibrium. John Nash’s (1928–2015) concept of equilibrium, explain Alvard and Nolin, “describes a combination of players’ strategies that are best against one another.” When a game reaches a “ Nash equilibrium, no player can do better by changing his or her decision unilaterally” (534). A Nash equilibrium is sometimes a Pareto optimum. Pareto optimality measures efficiency: a Pareto optimum arises when no other outcome makes at least one player better off and no player worse off.
A zero-sum dilemma occurs when acquisitions or losses derive from the players alone so that no gain or loss accrues in toto. An ordinal, a discrete, or a continuous scale ranks the outcomes of a game. Mathematical models often involve the second of these scales, a narrow utility (or payoff) that consists of material gain alone. A strategic move involves a player’s additional assumption of the banker’s role. This action enables that player to alter the options and payoffs for the game.
Theorists tabulate games of strategy using matrices and decision trees. Ramus’s contemporary Gerolamo Cardano introduced matrices to European mathematics, Ramus used decision trees, and Edward de Vere would have been aware of the latest trends in mathematics. “By the late years of the sixteenth century,” chronicles Ann E. Moyer, “such steps tended mainly in the same direction, away from the ‘theoretical’ arithmetic of Boethius and toward [the] computational, ‘practical’ arithmetic” (130) of Cardano and Ramus. Although Ramus’s Latin version of Euclid’s Elements made relatively little impact in England, both his friendship with John Dee and his wider influence on rational thought, to repeat Paul Lawrence Rose, helped to lay the institutional basis of “a new natively English mathematical tradition” (59). That tradition embraced Cardano’s innovation. In fine, matrices as well as decisions trees would have been familiar to the Seventeenth Earl of Oxford.
Game theorists employ the most convenient modeling option. “When there are more than two players, or two strategy choices at a move,” as Steven J. Brams explains, “the payoff matrix quickly becomes cumbersome and the game-tree analysis is easier” (41). Whenever there is a dominant strategy, however, matrices have a major advantage over tree diagrams. A dominant strategy, explains Anatol Rapoport, “leads to the most preferred outcome regardless of what else may happen or what others may do” (309). This “ dominating strategy principle” (311) governs both reflective and reflexive rationality: if a player has a dominant strategy, then he invariably chooses that course; if an opponent knows of this option, then he invariably assumes this course to be his counterpart’s inevitable choice. A dominant strategy precludes the need for the other player’s preference information. Whereas the matrix approach does not require backward rationality calculations to discern this possible preclusion, the game-tree method does.
The basal standard of human behavior for the game-theoretic assessment of utilities is self-interest. “The resolute application of the assumption of self-interest to social actions and institutions,” as Russell Hardin summarizes, “began with Hobbes and Machiavelli, who are sometimes therefore seen as the figures who divide modern from early political philosophy. Machiavelli commended the assumption of self interest to the prince; Hobbes applied it to everyone” (64). In The Prince (1532), Niccolò Machiavelli does not renounce the influence of God on human affairs, but unlike most Renaissance scholars, he charges individuals with significant responsibility for their personal circumstances. “I believe that it is probably true that fortune is the arbiter of half the things we do,” states Machiavelli, “leaving the other half or so to be controlled by ourselves” (105). Notwithstanding this division of responsibility, as his judgment of individual loyalty to an alliance attests, Machiavelli believes certain attitudes involve self-interest alone: the utility “for being a true friend” is “prestige”; loyalty in collaborative games “is always more advantageous than neutrality” (96).
Ramus’s mindset accommodated what Kendrick W. Prewitt calls its founder’s “willingness to apply methodical study to courses of military or political action” (22–23). These courses concern what game theorists call strategic imagery. “One can distinguish two levels or components of the image,” expound Glenn H. Snyder and Paul Diesing: “a background or long-term component, which is how the parties view each other in general, apart from the immediate crisis, and an immediate component, which comprises how they perceive each other in the crisis itself.” Before a definite crisis begins, “only the background component exists” (291). The Ramist accommodation of strategic imagery met the Machiavellian mindset in Sir William Cecil. That meeting was tangible. For some theoreticians, such as Poundstone, “game theory is about perfectly logical players interested only in winning” (44; emphasis original). An extreme judgment of the calculating Cecil casts him in this guise. “At the most abstract level,” avows Poundstone, “game theory is about tables with numbers in them—numbers that entities are efficiently acting to maximize or minimize” (61), and from this perspective, Cecil becomes a calculating machine.
This assessment of Edward de Vere’s father-in-law agrees with previous character studies. In William Cecil, the Power Behind Elizabeth (1934), Alan G. R. Smith describes Cecil as “planning, weighing, calculating” (25). Denver Ewing Baughan, whose document on “Sir Philip Sidney and the Matchmakers” appeared four years after Smith’s publication, calls Cecil “calculating” (509). More recently, in “Elizabeth I and the Politics of Gender” (2007), Jennifer Clement concurs, accepting John Banks’s portrayal of Cecil (as Lord Burleigh) in The Unhappy Favourite, or the Earl of Essex, a Tragedy (1682) as “a cold and calculating man” (15). Lastly, in Burghley: William Cecil at the Court of Elizabeth I (2008), Stephen Alford offers a similar assessment, casting his subject as forever “evaluating, calculating and planning” (106).
That profounder judgment, to repeat Walter J. Ong from Ramus, Method, and the Decay of Dialogue, “simply disappears” in Ramism, “and with it all rational interest in the psychological activities which such a term covers” (289; emphasis original) also fits Poundstone’s game-theoretic abstraction. A concession toward unconsciousness, however, opens a means of addressing the conundrum that faces theorists of competent cognition: why players with perfect strategic knowledge do not necessarily exploit that omniscience. “People,” as George Ainslie confirms, “often fail to maximize” (136), and “game theorists,” as Livingston avers, “do not contend that we should always assume that players adopt optimal strategies” (69). Even when prefect information identifies the most profitable strategy to adopt, players often choose another course of action for social, cultural, religious, or moral reasons, and most game theorists accept such influences.
A focal point can discourage a player to maximize. This lure results from a cultural predisposition. Humans embody an evolutionary receptiveness to protological structures that Ramus would have called correct reason. Their game-theoretic sense—what Ramus would have termed their natural reason—is inherent. “Worn pathways and synapses,” avers Arthur F. Kinney, “suggest that any cognitive response is in large part unconscious,” where Kinney’s reference to unconsciousness refers to nonconscious rather than subconscious motivation. Individual behavior draws “on the predispositions of a person’s past and a person’s culture” (130). That past and that culture have substrates determined by evolution, and those predispositions encourage the formation of focal points. In psychological terms, cultural norms often canalize a player’s desire, directing strategic behavior. The player either chooses a specific option or rejects closure. Denial occurs when the choices on offer fail to provide the answer...