Nash equilibria, variational inequalities, and dynamical systems (original) (raw)

Nash equilibrium is the central notion of rational behavior in noncooperative game theory.1 Our purpose here is to discuss various conditions under which a strategic form game possesses at least one Nash equilibrium. Strategic settings arising in economics are often naturally modeled as games with infinite strategy spaces. For example, models of price and spatial competi" tion (Bertrand (1883), Hotelling (1929)), quantity competition (Cournot (1838)), auctions (Milgrom and Weber (1982)), patent races (Fudenberg et.