Technical Note - Analysis of Scrip Systems: On an Open Question in Johnson et al. (2014).

In a recent paper, Johnson et al. (2014) [Johnson K, Levi DS, Sun P (2014) Analyzing scrip systems. Oper. Res. 62(3):524–534.]use an infinitely repeated game with discounting, among a set of homogeneous players, to model a scrip system. In each period, a randomly chosen player requests service; all the other players have a choice of whether or not to volunteer to provide service. Among the players who volunteer, the service provider is chosen using the minimum-scrip rule: a player with the minimum number of scrips is chosen as the service provider. The authors study the always-trade strategy for a player, that is, the strategy of a player always willing to provide service, regardless of the distribution of scrips among the players. A key result of their work is that, under the minimum-scrip rule, for any number of players and for every discount factor close enough to one, there exists a Nash equilibrium in which each player plays the always-trade strategy. This result, however, is established under an ass...