This paper is a self-contained survey of algorithms for computing Nash equilibria of two-person games. The games may be given in strategic form or extensive form. The classical Lemke-Howson algorithm finds one equilibrium of a bimatrix game, and provides an elementary proof that a Nash...

For choice with deterministic consequences, the standard rationality hypothesis is ordinality, i.e., maximization of a weak preference ordering. For choice under risk (resp. uncertainty), preferences are assumed to be represented by the objectively (resp. subjectively) expected value of a von...

Epistemic game theory formalizes assumptions about rationality and mutual beliefs in a formal language, then studies their behavioral implications in games. Specifically, it asks: what do different notions of rationality and different assumptions about what players believe about…what others...

This chapter reviews developments in the theory of decision making under risk and uncertainty, focusing on models that, over the last 40 years, dominated the theoretical discussions. It also surveys some implications of the departures from the “linearity in the probabilities” aspect of...

We provide an axiomatic approach to a belief formation process in an informational environment characterized by limited, heterogenous and differently precise information. For a list of previously observed cases an agent needs to express her belief by assigning probabilities to possible outcomes....