Equilibria in Finite Games

This thesis studies various equilibrium concepts in the context of finite games of infinite duration and in the context of bi-matrix games. We considered the game settings where a special player - the leader - assigns the strategy profile to herself and to every other player in the game alike. The leader is given the leeway to benefit from deviation in a strategy profile whereas no other player is allowed to do so. These leader strategy profiles are asymmetric but stable as the stability of strategy profiles is considered w.r.t. all other players. The leader can further incentivise the strategy choices of other players by transferring a share of her own payoff to them that results in incentive strategy profiles. Among these class of strategy profiles, an 'optimal' leader resp. incentive strategy profile would give maximal reward to the leader and is a leader resp. incentive equilibrium. We note that computing leader and incentive equilibrium is no more expensive than computing Nash equilibrium. For multi-player non-terminating games, their complexity is NP complete in general and equals the complexity of computing two-player games when the number of players is kept fixed. We establish the use of memory and study the effect of increasing the memory size in leader strategy profiles in the context of discounted sum games. We discuss various follower behavioural models in bi-matrix games assuming both friendly follower and an adversarial follower. This leads to friendly incentive equilibrium and secure incentive equilibrium for the resp. follower behaviour. While the construction of friendly incentive equilibrium is tractable and straight forward the secure incentive equilibrium needs a constructive approach to establish their existence and tractability. Our overall observation is that the leader return in an incentive equilibrium is always higher (or equal to) her return in a leader equilibrium that in turn would provide higher or equal leader return than from a Nash equilibrium. Optimal strategy profiles assigned this way therefore prove beneficial for the leader