Bernhard von Stengel, Department of Mathematics, LSE
speaks on " Leadership Games".

From his email: "I decided to focus on the "easy" and introductory results rather than the technical challenging ones.  I will also give a very swift introduction to game theory and to Nash equilibrium, since not everyone will know that, I assume.

A "Leadership Game" is obtained from a game in strategic form by letting on player become the "leader", who can COMMIT to a strategy, against which the other player or players (called "followers") react.  The classic example is the Stackelberg game, which is the leadership game obtained from the Cournot duopoly game of quantity competition, the oldest formally defined "game".

First, we present a simple result on "follower payoffs in symmetric duopoly games", where we give a general and very short proof of the following property of a leadership game for a symmetric duopoly game, for example of price or quantity competition.  Under certain standard assumptions, the follower's payoff is either HIGHER than the leader's, or LOWER than even in the simultaneous game. A possible interpretation is that "endogenous" timing is difficult since the players either want to move both second or both first.  Apart from the surprising result, the setup introduces key concepts of game theory and its modelling assumptions using only simple mathematics, and a very basic economic model.

Secondly, we study leadership games for the mixed extension of a finite game, where the leader commits to a mixed, that is, RANDOMIZED STRATEGY. In a generic two-player game, the leader payoff is unique and at least as large as any Nash payoff in the original simultaneous game. In non-generic two-player games, which are completely analyzed, the leader payoffs may form an interval, which as a set of payoffs is never worse than the Nash payoffs for the player who has the commitment power. In other words, the power to commit never hurts, even when best responses are not unique.

The two papers are available online:
paper 1
paper 2