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.

Glycodelin A, an immunomodulatory protein in the endometrium, inhibits proliferation and induces apoptosis in monocytic cells

Glycodelin A (GdA), is a lipocalin with an immunomodulatory role, secreted by the endometrium under progesterone regulation and proposed to play a role in protecting the fetus from maternal immune attack. Glycodelin A has an inhibitory effect on the proliferation of T cells and B cells and also on the activity of natural killer cells. We have earlier demonstrated that the inhibitory effect of glycodelin A on T cell proliferation is due to apoptosis induced in these cells through the caspase-dependent intrinsic mitochondrial pathway. Studies reported until now have shown that glycodelin modulates the adaptive immune responses. We, therefore, decided to look at its effect, if any, on the innate immune system. The effect of glycodelin on monocytes was studied using human monocytic cell lines, THP1 and U937, and primary human monocytes as model systems. We demonstrated that glycodelin inhibited the proliferation of THP1 and U937 and induced apoptosis in these cells as well as in primary monocytes. We found that this signaling was caspase-independent but followed the intrinsic mitochondrial pathway of apoptosis. No effect of glycodelin was seen on the phagocytic ability of monocytes post-differentiation into macrophages. These observations suggest that, at the fetomaternal interface, glycodelin plays a protective role by deleting the monocytes that could become pro-inflammatory. Importantly, leaving the macrophages untouched to carry on with efficient clearance of the apoptotic cells.

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.