The Existence of Equilibrium in Discontinuous Economic Games, II: Applications

Abstract

In part I of this study we established two existence theorems for mixed-strategy equilibrium in games with discontinuous payoff functions (see Theorems 4(4*) and 5(5*) in Dasgupta and Maskin (1986); hereafter D-M (1986)). In this second part we use the second of these two theorems to prove the existence of mixed-strategy equilibrium in some wellknown discontinuous economic games that fail to have pure-strategy equilibria. The models we analyse are the Bertrand-Edgeworth example of price setting duopolists with capacity constraints (see Section 2.2); price competition among firms producing differentiated products (Hotelling (1929) and d'Aspremont, Gabszewicz and Thisse (1979); see Section 2.3); spatial competition (Eaton and Lipsey (1975) and Shaked (1975); see Section 3); and models of market dependent information (Rothschild and Stiglitz (1976) and Wilson (1977); Section 4). The paper concludes (Section 5) with a classification of these models.