Solution concepts in two-person multicriteria games

In this paper, we propose new solution concepts for multicriteria games and compare them with existing ones. The general setting is that of two-person finite games in normal form (matrix games) with pure and mixed strategy sets for the players. The notions of efficiency (Pareto optimality), security levels, and response strategies have all been used in defining solutions ranging from equilibrium points to Pareto saddle points. Methods for obtaining strategies that yield Pareto security levels to the players or Pareto saddle points to the game, when they exist, are presented. Finally, we study games with more than two qualitative outcomes such as combat games. Using the notion of guaranteed outcomes, we obtain saddle-point solutions in mixed strategies for a number of cases. Examples illustrating the concepts, methods, and solutions are included.

Stochastic differential games with multiple modes

We have studied two person stochastic differential games with multiple modes. For the zero-sum game we have established the existence of optimal strategies for both players. For the nonzero-sum case we have proved the existence of a Nash equilibrium.

Evolution of cooperation by reciprocation within structured demes

The iterative two-person Prisoners’ Dilemma game has been generalised to theN-person case. The evolution of cooperation is explored by matching the Tit For Tat (TFT) strategy (Axelrod and Hamilton 1981) against the selfish strategy. Extension of TFT toN-person situations yields a graded set of strategies from the softest TFT, which continues cooperation even if only one of the opponents reciprocates it, to the hardest, which would do so only when all the remaining opponents cooperate. The hardest TFT can go to fixation against the selfish strategy provided it crosses a threshold frequencypc. All the other TFT are invadable by the selfish (D) or the pure defector strategy, while none can invadeD. Yet, provided a thresholdpc is crossed, they can coexist stably withD. AsN, the size of the group increases, the threshold pc also increases, indicating that the evolution of cooperation is more difficult for larger groups. Under certain conditions, only the soft TFT can coexist stably against the selfish strategyD, while the harder ones cannot. An interesting possibility of a complete takeover of the selfish population by successive invasions by harder and harder TFT strategies is also presented.

Electrophysiological correlates of hanseniasis

Sensory nerve action potentials (SNAPs) and compound nerve action potentials (CNAPs) were recorded from 25 normal subjects and 21 hanseniasis patients following electrical stimulation of the median nerve at the wrist. The various nerve conduction parameters from the affected nerves of the patients were compared with those from the clinically normal nerves of patients as well as data from healthy individuals. Analysis of the data and clinical correlation studies indicate the suitability of amplitudes of the SNAPs and CNAPs rather than the nerve conduction velocities in better characterizing the neuropathy of the patients. Significantly reduced amplitudes of responses from clinically unaffected nerves of patients indicate an early stage of neuropathy, thus being of predictive value. Further, a discriminant classifier, trained on data from clinically affected nerves of patients, classified most of the data from clinically unaffected nerves of patients as abnormal. This indicates that clinical neurophysiological studies can reveal leprous neuropathy much before it becomes clinically evident by means of sensory or motor loss. A discriminant score involving only the parameters of motor threshold, amplitude of digit potential and palm nerve conduction velocity is able to classify almost all of the normal and abnormal responses. The authors hope that further confirmative studies might ultimately lead to the use of the study of distal sensory conduction in the upper limbs in possible screening of a population exposed to Mycobacterium leprae. On the other hand, misclassification of a normal person occurred and suggests that further refinement of the methods is necessary in order to facilitate wider use of the methods under held conditions.