Recognise that people have many, possibly conflicting, aspects to their personality. We hypothesise that each separate characteristic of a personality may be treated as an independent player in a non-zero sum many player game. This idea is applied to the two person Prisoners’ Dilemma as an introductory example. We assume each prisoner has a “mercenary” characteristic as well as an “altruistic” ...

This paper studies a nonzero-sum Dynkin game in discrete time under non-exponential discounting. For both players, there are two intertwined levels of game-theoretic reasoning. First, each player looks for an intra-personal equilibrium among her current and future selves, so as to resolve inconsistency triggered by Next, given the other player’s chosen stopping policy, selects best response equ...

In this paper Boolean games are introduced as a class of two-player zero-sum games along with a number of operations on them. We argue that Boolean games can be interpreted as modelling the information structures of two-person zero-sum games. As such they comprise games of imperfect information. The algebra of Boolean games modulo strategic equivalence is then proven to be isomorphic to the Lin...

A substantial effort has been devoted to various incentive Stackelberg solution concepts. Most of these concepts work well in the sense that the leader can get his desired solution in the end. Yet, most incentive strategies developed thus far include either the follower’s control, which may not be realistic in practice, or delays in the state, which makes stabilization more difficult to achieve...

In this paper we consider a dynamic nonzero-sum game between the polluting firms and the authorities. Although the proposed game is not easily solvable for the feedback case, i.e., it is not the linear quadratic case of game and not a degenerated case, we calculate explicitly a stationary feedback equilibrium. In the proposed game the regulator has the ability to turn the optimal allocation of ...

We consider in this paper a class of risk-sensitive stochastic nonzero-sum differential games with parameterized nonlinear dynamics and parameterized cost functions. The parametrization is such that if all or some of the parameters are set equal to some nominal values, then the differential game either becomes equivalent to a risk-sensitive stochastic control (RSSC) problem, or decouples into s...

We study new classes of games, called zero-sum equivalent games and zero-sum equivalent potential games, and prove decomposition theorems involving these classes of games. We say that two games are “strategically equivalent” if, for every player, the payoff differences between two strategies (holding other players’ strategies fixed) are identical. A zero-sum equivalent game is a game that is st...

We introduce generous, even-matched, and greedy strategies as concepts for analyzing games. A two person prisoner's dilemma game is described by the four outcomes (C,D), (C,C), (D,C), and (D,D). In a generous strategy the proportion of (C,D) is larger than that of (D,C), i.e. the probability of facing a defecting agent is larger than the probability of defecting. An even-matched strategy has th...