On the selection of leader in Stackelberg games with parameter uncertainty

In leader-follower Stackelberg games, the leader determines and announces its strategy first by anticipating the follower’s reaction function, and the follower determines its strategy as a best response to the leader’s strategy. Thus, there is a perceived advantage in assuming the role of leader in a Stackelberg game. When the roles of the players are not determined a priori, both players must mutually agree on the selection of the leader. Such an agreement is possible only if the players realise that they are both better off with the agreed selection of leader as compared to when the other player is selected as leader. In games with parameter uncertainty, the availability of this option depends on the parameter space over which the game is defined. In this paper, we describe the partitioning of the parameter space to characterise when a Stackelberg solution based on an agreed leader selection exists and when it does not. The resulting partition can then be used to determine the probability of occurrence of all possible games where agreement can and cannot be reached. We illustrate the results using two examples.