IV.- THE EFFECTS OF SHOCKS
In this Section we will study the effect of an exogenous shift in the
payoff function on the relevant variables. We will assume that the payoff
function of player i can be written as U = U (x , x, t) where t is a one
i i i i i
dimensional parameter which is possibly different for different players (in
the Cournot model t may represent either the factors behind the demand side
i
or the cost side or as in Farrell and Shapiro (1990) the quantity of capital
own by firm i). In this Section, in order to simplify the proofs we will
assume that Nash Equilibria are interior. Then, the first order condition
reads T (x , x, t) = O. Finally the values of the strategies and payoffs in a
i i i
Nash Equilibrium will be denoted by xf, x*, and Uf.
Assumption 4
) is strictly increasing in t..
This assumption allows us to interpret increases in t. as shifts to the
right of the marginal payoff curve, i.e. t can be regarded as a measure of
i
the impact of a shock on the marginal payoff of player i.
We will distinguish two types of shocks: idiosyncratic and generalized.
In the first we will study the impact on the market of a variation in a single
t (i.e. an increase in the price of the factors or the taxes payed by player
i
i). In the second we consider a simultaneous variation in all t, i = l,...,n.
i
This corresponds, for instance, to a shift in the common demand function or
the price of a factor used by all players in the industry. In this case,
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