Bertrand delegation games with implementability in weakly undominated SPNE

In this paper we investigate a delegation game in which the underling situation is represented by a standard Bertrand price competition. In contrast to Fershtman, Judd, and Kalai ([1987], hereafter FJK), we employ a weakly undominated SPNE as the equilibrium concept based on Shino [2012] and keep the notion of the implementability unchanged. We first point out that optimal price setting behaviors derived by the assumption of mutually rational players in FJK are hard to justify from a standard game theory view in that they are assumed to play a weakly dominated strategy even when each of them has the weakly dominant strategy. Next, it is shown that there exists a compensation scheme fully implementing the most collusive outcome in which firms jointly set the monopoly price and equally share the profit.