Wynn C. Stirling

A theory of satisficing decisions and control

The existence of an optimal control policy and the techniques for finding it are grounded fundamentally in a global perspective. These techniques can be of limited value when the global behaviour of the system is difficult to characterize, as it may be when the system is nonlinear, when the input is constrained, or when only partial information is available regarding system dynamics or the environment. Satisficing control theory is an alternative approach that is compatible with the limited rationality associated with such systems. This theory is extended by the introduction of the notion of strong satisficing to provide a systematic procedure for the design of satisficing controls. The power of the satisficing approach is illustrated by applications to representative control problems.

A cooperative multi-agent approach to free flight

The next generation of air traffic control will require automated decision support systems in order to meet safety, reliability, flexibility, and robustness demands in an environment of steadily increasing air traffic density. Automation is most readily implemented in free flight, the segment of flight between airports. In this environment, centralized control is impractical, and on-board distributed decision making is required. To be effective, such decision making must be cooperative. Satisficing game theory provides a theoretical framework in which autonomous decision makers may coordinate their decisions. The key feature of the theory is that, unlike conventional game theory which is purely egotistic in its structure, it provides a natural mechanism for decision makers to form their preferences by taking into consideration the preferences of others. In this way, a controlled form of conditional altruism is possible, such that agents are able to compromise so that every decision maker receives due consideration in a group environment. Simulations demonstrate that reliable performance can be achieved with densities on the order of 50 planes per ten thousand square miles.

Convex Bayes decision theory

The basic concepts of Levis epistemic utility theory and credal convexity are presented. Epistemic utility, in addition to penalizing error as is done with traditional Bayesian decision methodology, permits a unit of informational value to be distributed among the hypotheses of a decision problem. Convex Bayes decision theory retains the conditioning structure of probability-based inference, but addresses many of the objections to Bayesian inference through relaxation of the requirement for numerically definite probabilities. The result is a decision methodology that stresses avoiding errors and seeks decisions that are likely to be highly informative as well as true. By relaxing the mandatory requirement for unique decisions and point estimates in all cases, decision and estimation criteria that do not demand more than is possible to obtain from the data and permit a natural man-in-the-loop interface are obtained. Applications are provided to illustrate the theory. >

A Satisficing Approach to Aircraft Conflict Resolution

Future generations of air traffic management systems may give appropriately equipped aircraft the freedom to change flight paths in real time. This would require a conflict avoidance and resolution scheme that is both decentralized and cooperative. We describe a multiagent solution to aircraft conflict resolution based on satisficing game theory. A key feature of the theory is that satisficing decision makers form their preferences by taking into consideration the preferences of others, unlike conventional game theory that models agents that maximize self-interest metrics. This makes possible situational altruism, a sophisticated form of unselfish behavior in which the preferences of another agent are accommodated provided that the other agent will actually take advantage of the sacrifice. This approach also makes possible the creation of groups in which every decision maker receives due consideration. We present simulation results from a variety of scenarios in which the aircraft are limited to constant-speed heading-change maneuvers to avoid conflicts. We show that the satisficing approach results in behavior that is attractive both in terms of safety and performance. The results underscore the applicability of satisficing game theory to multiagent problems in which self-interested participants are inclined to cooperation.

Social utility Functions-part I: theory

The dominant approaches to utility-based multiagent decision theory rely on the premise of individual rationality-the doctrine that each individual is committed to achieving the best outcome for itself, regardless of the effect doing so has on others. This fundamentally asocial concept is the basis of conventional von Neumann-Morgenstern (vN-M) utilities but is inadequate to characterize truly cooperative artificial systems. Social utility functions differ from conventional vN-M utilities in that they are functions of multiple decision-maker preferences, rather than actions, and thus permit individuals to expand their spheres of interest beyond the self. A logical basis for coherent reasoning in multiagent environments must obey exactly the same desiderata as do multivariate probability functions. By taking a dual utilities approach (one to account for effectiveness and one to account for efficiency), a new game-theoretic structure, called satisficing games, provides a decision-making procedure that accounts for both individual and group interest and presents a framework for the design of sophisticated multiagent societies.

Satisficing Equilibria: A Non-Classical Theory of Games and Decisions

Satisficing, or being “good enough,” is the fundamental obligation of rational decision makers. We cannot rationally choose an option, even when we do not know of anything better, unless we know it is good enough. Unfortunately, we are not often in the position of knowing that there could be no better option, and hence that the option must be good enough. A complete search through all logical possibilities is often impractical, particularly in multi-agent contexts, due to excessive computational difficulty, modeling complexity, and uncertainty. It can be equally impractical, if it is even possible, to determine the cost of the additional required search to find an option that is good enough. In a departure from the traditional notion of satisficing as a species of bounded rationality, satisficing is here redefined in terms of a notion of intrinsic rationality. Epistemic utility theory serves as the philosophical foundation of a new praxeological decision-making paradigm of satisficing equilibria that is applicable to both single- and multiple-agent scenarios. All interagent relationships are modeled by an interdependence function that explicitly accommodates both self and group interest, from which multilateral and unilateral selectability and rejectability mass functions can be derived and compared via the praxeic likelihood ratio test.

Satisficing games

Optimization is a mathematical sophistication of the common sense view that decision makers ought to do the best they can, and leads to well known solution concepts for mathematical games. For multi-agent systems in naturalistic settings, however, uncertainty and complexity may subordinate optimal performance to the more moderate goals of functionality and robustness. Moderation is another common sense idea that can be made mathematically precise by defining a notion of comparative rationality, leading to a theory of satisficing games. Preferences in an m-agent satisficing game are characterized by a 2m-dimensional interdependence function, from which the joint m-dimensional gains and losses of the agent system can be derived and compared to determine the set of jointly satisficing decisions. This paradigm permits decision makers in the presence of uncertainty to consider multiple sets of possible actions and make decisions that are both robust and functional. Two well-known games, Prisoners Dilemma and Battle of the Sexes, are analyzed from this, point of view.

Satisficing negotiations

Negotiation procedures that are founded on the doctrine of individual rationality, where each participant is committed to maximizing its own satisfaction, are limited in their ability to accommodate the interests of others, and therefore, may unnecessarily constrain the negotiability of a decision maker, particularly in cooperative environments. Satisficing game theory provides a distinct alternative to the hyperrationality of conventional rational choice by waiving reliance on the individual rationality premise and offering an approach to negotiatory decision making that is based on a well-defined mathematical notion of satisficing, or being good enough, that permits the modeling of complex interrelationships between agents. This approach provides a mechanism to compute the attitude, or degree of conflict or contentedness, of the negotiators. Examples illustrate both single-round and multiround satisficing negotiation protocols

Model predictive satisficing fuzzy logic control

Model-predictive control, which is an alternative to conventional optimal control, provides controller solutions to many constrained and nonlinear control problems. However, even when a good model is available, it may be necessary for an expert to specify the relationship between local model predictions and global system performance. We present a satisficing fuzzy logic controller that is based on a receding control horizon, but which employs a fuzzy description of system consequences via model predictions. This controller considers the gains and losses associated with each control action, is compatible with robust design objectives, and permits flexible defuzzifier design. We demonstrate the controllers application to representative problems from the control of uncertain nonlinear systems.

Social utility Functions-part II: applications

Social utilities account for agent preferences and, thus, can characterize complex interrelationships, such as cooperation, compromise, negotiation, and altruism, that can exist between agents. Satisficing game theory, which is based on social utilities, offers a framework within which to design sophisticated multiagent systems. Key features of this approach are: a) an N-agent system may be represented by a 2N-dimensional Bayesian network, called a praxeic network; b) the theory accommodates a notion of situational altruism (a willingness to defer to others in a controlled way if so doing would actually benefit others under the condition that others wish to take advantage of such largesse); and c) satisficing games admits a protocol for effective negotiation between agents who, though interested in their own welfare, are also willing to give some deference to others. Three applications are presented. The first two involve well-known two-person games: the Prisoners Dilemma and the Battle of the Sexes, and the third is a simulated uninhabited aerial vehicle scenario.