Competitive Equilibrium in Generalized Games: A New Interpretation

The purpose of this paper is to provide an alternative version of a generalized game, slightly different from the one provided in the seminal paper of Arrow and Debreu (1954). In this revised framework, we introduce the concept of a competitive equilibrium and show how it can be applied to a slightly modified prisoners’ dilemma and the traditional model of general equilibrium theory. We obtain a ‘folk theorem’ for some generalized games which are like repeated non-cooperative games. A significant result that we obtain is that a strategy profile is a competitive equilibrium if and only if it is a second period maximizer of every Bergson–Samuelson social welfare function. We prove existence results for the case where all the strategy sets are subsets of Euclidean spaces and for the case where all the strategy sets are non-empty and finite. The Arrow–Debreu economy is introduced in our setting as an illustration of a finite abstract economy where the preferences of the agents are independent of the strategy profile chosen in the initial period. Finally, we suggest a refinement of competitive equilibrium called an optimal competitive equilibrium and study its relationship with competitive equilibrium through some examples.