If dollarization is a credible commitment to maintain a fixed exchange rate, then it is an irreversible decision. This paper explicitly models the unique feature -- irreversibility -- of a dollarization policy. In addition, it is the first paper to recognize that if a dollarization is a potential exchange rate regime choice, then the equilibrium is a mixed strategy equilibrium. The case of Argentina's possible dollarization is considered. I compute Nash equilibria and the transition probabilities that a country will move from a currency board regime to dollarizing, or floating, in one year, or two years, out to seven years. I model shocks to the exchange rate as a jump-diffusion process. The jumps represent large "asymmetric" shocks to the exchange rate -- such as Brazil's 1999 devaluation. The probability of dollarization is inversely related to the jump probability.
