Power, Conflicts, and Subordination

Power, defined as the ability to longer sustain a mutually damaging
situation, is shown in the present paper to have an important explanatory
ability, both with regards to the outcome of the game and to the way this
outcome is reached. In our model, inspired from the Theory of Moves of
Brams (1994), two agents, each choosing among two actions at their respective
decision nodes, play a sequential game on an infinite time horizon.
Their preferecences for the different states of the game, both intermediate
and final and their time preferences enable us to determine the respective
power of the players, which in turn sheds light on the equilibrium path
which, from our viewpoint, deserves as much importance as the final outcome
does. We show that the player who is most able to incur losses -the
power wielder- imposes on his opponent the strategy he should adopt, the
latter having the choice but to comply or be punished. These equilibrium
strategies are proved to be subgame perfect and unique. When the power
differential between players is mutually recognized, the dominant agent
can in most situations even decide on the identity of the first mover. The
stronger player reaps therefore all the potential benefits in this negotiation
process that could in a way be interpreted as a bargaining game. To make
the link with a widely analyzed real world conflict situation, we apply our
model to the Cuban Missile Crisis.