Introduction

This chapter contains two examples of static, symmetric, positive-sum games with two strategic players and a play by nature: (1) a microeconomic game between duopolists with joint costs facing uncertain demands for differentiated goods and (2) a macroeconomic game between two countries with inflation-bias preferences confronting uncertain demands for money. In both games, each player can choose either of two variables as an instrument. In our terminology, both are linear-reaction-function games because reaction functions are linear in the chosen instruments.

More than a century ago, it was discovered that there are both Cournot (1838) and Bertrand (1883) equilibria for duopoly games with no uncertainty. There are many examples of multiple (Nash) equilibria in linear-reaction-function games with no uncertainty. In the standard differentiated duopoly game with linear demands and independent, quadratic costs, there are four equilibria if each duopolist can choose either price or quantity as an instrument. That is, there are as many equilibria as there are possible pairs of instrument choices. Likewise, in two-player macroeconomic games with quadratic utilities and linear economies there are as many equilibria as there are possible pairs of instrument choices.

The explanation of the existence of multiple equilibria in linear-reaction-function games with no uncertainty is the same as the explanation of a familiar result. Poole (1970) and Weitzman (1974) show that with no uncertainty a single controller is indifferent among instruments. Likewise, with no uncertainty if one player chooses his instrument and sets a value for it, the other is indifferent among instruments.