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: