The disciplines of science and engineering are complementary. Science comes from the Latin root scientia, or knowledge, and engineering comes from the Latin root ingenerare, which means to beget. While any one individual may fulfill multiple roles, a scientist qua seeker of knowledge is concerned with the analysis of observed natural phenomena, and an engineer qua creator of new entities is concerned with the synthesis of artificial phenomena. Scientists seek to develop models that explain past behavior and predict future behavior of the natural entities they observe. Engineers seek to develop models that characterize desired behavior for the artificial entities they construct. Science addresses the question of how things are; engineering addresses the question of how things might be.

Although of ancient origin, science as an organized academic discipline has a history spanning a few centuries. Engineering is also of ancient origin, but as an organized academic discipline the span of its history is more appropriately measured by a few decades. Science has refined its methods over the years to the point of great sophistication. It is not surprising that engineering has, to a large extent, appropriated and adapted for synthesis many of the principles and techniques originally developed to aid scientific analysis.

Localization concepts

Intrinsic rationality, as contrasted with substantive rationality, relies upon comparisons of attributes (gains versus losses) for each option rather then requiring the total ordering of preferences over all possible options. We may view intrinsic rationality as a local information concept, since only information pertaining to a particular option is involved in ordering the gain with respect to the loss. By contrast, we may view substantive rationality as a global information concept, since complete information regarding all options is required to form the rank ordering so that optimization can be performed.

One of the most successful concepts of science and engineering is the idea of localization. To localize a phenomenon is to delimit the extent of its influence. Some well-known examples of localization include: (i) model localization, such as lumped-parameter models that convert the partial differential equations of Maxwell's equations for modeling electromagnetic behavior into the ordinary differential equations of Kirchoff's laws; (ii) spatial localization, whereby a nonlinear dynamical system is constrained to operate near an equilibrium by confining inputs and initial conditions to be small enough to ensure that superposition approximately holds, thereby permitting the phenomenon to be characterized by a linear differential equation; (c) temporal localization, whereby a phenomenon is characterized over a small time interval, such as occurs with the design of a receding-horizon controller.

Unless a community is a total dictatorship or is given to complete anarchy, there will be some form of sociality that is conducive to at least a weak form of agreement-seeking, or congruency. Cooperative societies may be expected to agree to work together, competitive societies may be expected to agree to oppose each other, and mixed-motive societies may be expected to agree to compromises that balance their interests. The procedures used to arrive at these agreements, however, are not determined simply as a function of the preference structure of the decision makers, either for von Neumann–Morgenstern scenarios or for satisficing scenarios. Instead, the procedures often involve some form of negotiation. Negotiation is a deliberative process whereby multiple decision makers can evaluate and share information when they have incentives to strike a mutually acceptable compromise.

In this chapter we first review von Neumann–Morgenstern N-person game theory, which forms the basis of classical negotiation theory. We then describe a new approach to negotiation based on satisficing game theory.

Uncertainty and complexity are opposite sides of the nescience coin. One who suffers from uncertainty is frustrated by a lack of knowledge; one who suffers from complexity is frustrated by a lack of know-how. Knowing what to do is one thing, but knowing how to do it is quite another thing. Even if one knows of a way, in principle, to solve a problem, the computational burden of the solution may be impossible with existing technology. In such cases the solution must await the development of improved methods of computation.

Apparent complexity can often be reduced by eliminating irrelevant attributes of the decision problem, a procedure that Rasmusen terms “no-fat modeling.” This approach is as follows: “First, a broad and important problem is introduced. Second, it is reduced to a very special but tractable model that hopes to capture its essence. Finally, in the most perilous part of the process, the results are expanded to apply to the original problem” (Rasmusen, 1989). Once the problem has been reduced to its essence, game theory provides a way to compute solutions to be expanded to the original problem.

In this appendix we summarize the basic concepts of von Neumann–Morgenstern game theory that are relevant to our treatment of that topic in this book.

Definition B.1

An agent, or player, X, is a decision maker; that is, an entity that is capable of autonomously choosing from among a set of options.

Definition B.2

A decision problem for X is a triple, (U, π, C), consisting of an option space, U (also called the action space), to be applied by the players, a set of outcomes or consequences, C, to be realized by the players, and a mediation mechanism, or mapping function, π: U → C, that relates choices and outcomes.

Definition B.3

A joint decision problem, or game for a family of agents, {X1, …, XN}, where N ≥ 2, is a triple (U, π, C) where U = U1 × … × UN is the joint action space with Ui being Xi's individual action space, C = C1 × … × CN with Ci being Xi's individual consequence space, and π = (π1, …, πN) where πi: U → Ci is a vector of mapping functions, one for each player.

An option vector is an ordered set of options, u = {u1, …, uN}, one for each player, where ui ∈ Ui.

The implication that probability theory has a praxeic role to play may appear to be an arbitrary and perhaps dubious appeal to a convenient analogy simply for purposes of posturing for credibility or enhancing intuition. However, the purpose of this appendix is to establish that the praxeic characterization arises from exactly the same kind of assumptions that underly the construction of probability theory for dealing with epistemic issues. We establish the claim that the mathematics of probability theory is the appropriate mechanism with which to characterize preference relationships between members of a multi-agent system. To facilitate this development, we will form praxeic analogies to the various epistemic concepts and present the epistemic concepts in parallel with the praxeic ones.

Probability is based on two-valued logic, i.e., Aristotelian logic. In the epistemic context, this means that an event is either true or false. For any event set A, we will say that A is true if any member of the set is true. If probability theory is to apply to praxeic considerations, it must be based on two-valued logic in that context as well. The praxeic Aristotelian analog to truth is instantiation – an action is either performed or it is not. For any set A of actions, we will say that A is instantiated if any member of the set is instantiated.

The goal of an epistemic inquiry is to ascertain truth. Analogously, the goal of a praxeic endeavour is to ascertain how to act.

Bounded rationality deals with the problem of what to do when it is not possible or expedient to obtain a substantively rational solution owing to informational or computational limitations. Sims (1980) has characterized the situation as a research “wilderness.” There are several different notions of bounded rationality, but they tend to follow two distinct streams. The first stream deals with bounds on the resources, such as computational power or time, and the second deals with bounds on the information available to obtain a decision.

Resource-bounded problems deal with the problem of making decisions under severe computational or time constraints. Consideration of such problems has led to the development of procedures that fall under a category termed constrained optimization. Constraints, in this context, do not refer to functional restrictions on the behavior of the decision maker, such as energy limitations or performance requirements. Rather, the constraints of interest here are limitations in the ability of the decision maker to process information and arrive at a solution. Within this subclass of problems, there are multiple approaches.

Principles of rationality serve as normative models of behavior, but rationality can never be anything more than an ideal. Even the most determined adherent to a particular code of rationality must recognize that circumstances often prohibit the attainment of the ideal in practice. This realization, however, should not change the standard that is sought. Indeed, failure to achieve the standard should serve as motivation to improve the ability to perform, rather than a rationale for lowering the standards.

Perhaps the most salient criticism of satisficing à la Simon's aspiration levels (see, e.g., Levi (1997) and Zeleny (1982)) and other forms of ‘bounded rationality’ is that they condone the deliberate acceptance of a solution that is less than the ideal. In terms of human behavior, deliberately falling short of achieving the goal to which one has made a commitment may be disingenuous, but at least the decision maker can mount an explanation for his or her failure. One possible explanation for a decision maker who has apparently committed to optimality only to equivocate is that, after all, he or she is not really an optimizer, but is merely using the tools of optimization to find a solution that is good enough. If it happens to be optimal, so much the better, but that would be a bonus, not a necessity.

A dutiful decision maker may not be persuaded to adopt a satisficing solution just because the gains exceed the losses. The satisficing options should also conform to a sense of fairness or equanimity. There are three additional criteria that should govern the ultimate selection of a satisficing option. First, if time and resources permit, a decision maker should neither sacrifice quality needlessly nor pay more than is necessary. Second, a decision maker should be as certain as possible that the decision really is good enough, or adequate. Third, a decision maker should not foreclose against optimality; that is, the optimal decision, should it exist, ought to be satisficing.

Equilibria

Although the satisficing set Σq contains all possible options that satisfy the PLRT and, in that sense, are legitimate candidates for adoption, they generally will not be equal in overall quality. Consider the following example.

It is a platitude that decisions should be optimal; that is, that decision makers should make the best choice possible, given the available knowledge. But we cannot rationally choose an option, even if we do not know of anything better, unless we know that it is good enough. Satisficing, or being “good enough,” is the fundamental desideratum of rational decision makers – being optimal is a bonus.

Can a notion of being “good enough” be defined that is distinct from being best? If so, is it possible to formulate the concepts of being good enough for the group and good enough for the individuals that do not lead to the problems that exist with the notions of group optimality and individual optimality? This book explores these questions.

Decision makers are usually not hermits and do not function in isolation from others. They are usually influenced by the opinions (i.e., preferences) of other decision makers, and their problem is one of how to select a course of action, not only for themselves, but for the community. If each individual were to possess a notion of rationality for the group as well as a notion of rationality for itself, it might be in a position to improve its behavior.

Group rationality, however, is not a logical consequence of rationality based on individual self-interest. Under substantive rationality, where maximization of individual satisfaction is the operative notion, group behavior is not usually optimized by optimizing each individual's behavior, as is done in conventional game theory. Unfortunately, those who put their final confidence in exclusive self-interest may ultimately function disjunctively, and perhaps illogically, when participating in collective decisions.

The point of departure for conventional game theory is games of pure conflict, with the prototype being constant-sum games, where one player's loss is another player's gain. For a constant-sum game, any notion of group-interest is vacuous; individual self-interest is the only appropriate motive.