Equilibria in Non‐cooperative Games I: Perturbations Based Refinements of Nash Equilibrium

Abstract

The concept of Nash equilibrium is widely used to analyse noncooperative games. However, one of the problems with that concept is that many games have multiple equilibria. Recent work has concentrated on reducing or refining the set of Nash equilibria in some games. In this paper, we survey some equilibrium concepts based on perturbations of strategies that refine the set of Nash equilibria. We discuss the pros and cons of each concept and its relationship to the others by the use of numerous examples and intuition. It is hoped that this survey will enable the economist to consider the relevance of a particular equilibrium concept to a given economic model of interest. Journal of Economic Literature Classification Number: C72.

Equilibria in Non‐cooperative Games Ii: Deviations Based Refinements of Nash Equilibrium

“…Refinements of Nash equilibrium based on deliberate deviations are not entirely divorced from the perturbations based refinements discussed in Sadanand and Sadanand ( 1994). The important distinction, however, is that the deviations in this paper are thought to be deliberate manipulations by players while all the perturbations based concepts (except stability) view deviations as 'mistakes'.…”

“…The important condition is that these beliefs must be reasonable in the sense to be defined below. 'This additional condition on consistent beliefs (see Sadanand and Sadanand, 1994) results in a refinement of sequential equilibrium. It also refines the set of Cho-Kreps equilibria.…”

“…In this paper, we assume that the reader has knowledge of the definitions and notation developed in the first part of this survey (Sadanand and Sadanand, 1994).' 11.…”

“…In this sense, the player is being quite pessimistic. This pessimism provides some further restrictions on consistent assessments (see Sadanand and Sadanand, 1994) that refines the set of sequential equilibria.5…”

Ideal Reactive Equilibrium

“…We will call such an information set, or single decision point, where a player can make an incredible threat, pivotal. Now, if we alter the payoffs for 1 A good literature survey on refinements can be found in Govindan and Wilson [5] or Sadanand and Sadanand [6,7]. It is well understood that this is not a pure dichotomy.…”