equilibrium is unique, it is increasing on τ (see Lippman, Mamer and McCardle
(1987), Milgrom and Roberts (1990), Milgrom and Shannon (1992))^∖ This is
analogous to our Propositions 4 and 6 (but in our case individual strategies
are not always increasing on τ, see example 6). Notice that the distinction
between idiosyncratic and generalized shocks does not play any role in
Supermodular games. At the best of my knowledge there are no results in the
Supermodular games literature on the effect of entry (Propositions 1-3) below)
or the effect of a change in τ on payoffs (Proposition 5 and example 6).
The rest of the paper goes as follows. The next Section explains the
basic model and the main assumptions. Section 3 studies the effect of an
increase in the number of players and Section 4 focuses on shifts of the
marginal payoff curve. Finally Section 5 gathers our final comments.
(1) Other properties of Supermodular games are that 1) the existence of a Nash
equilibrium does not require quasi-concavity of the payoff functions, and 2)
under certain circumstances, if there are several Nash equilibria, they can be
Pareto-ranked. Applications of Supermodular games include Bayesian games and
oligopolistic competition (see Vives (1990)), stability and learning (see
Lippman, Mamer and McCardle (1987), Milgrom and Roberts (1990) and Krishna
(1993)) and coordination problems in a macroeconomic framework (see Silvestre
(1993) for a survey of this literature). For general surveys on Supermodular
games see Fudenberg and Tirole (1991) and Vives (1993).