Trejos-Wright with a 2-unit bound: existence and stability of monetary steady states

We investigate in details a Trejos-Wright random matching model of money with a consumer take-it-or-leave-it offer and the individual money holding set {0,1,2}. First we show generic existence of three kinds of steady states: (1) pure-strategy full-support steady states, (2) mixed-strategy full-support steady states, and (3) non-full-support steady states, and then we show relations between them. Finally we provide stability analyses. It is shown that (1) and (2) are locally stable, (1) being also determinate. (3) is shown to be unstable.