Summary : Game theory basics

12 janvier, 2015 | Commentaires fermés sur Summary : Game theory basics

Game theory is a key tool for decision making analysis in international relations. I suggest the summary of the chap. 2 The two person zero sum game with equilibrium points from the classic « Game theory : a non technical introduction » by Morton D. Davis (Dover publication, 1997) to catch the essence of the Game theory concepts.


It considers how one should make decisions, and to a lesser extent, how one does make them if he tries to act rationally. An actor decision is linked to his goals, if he knows the consequences of each of its options, the solution is a logical deduction of the search for maximum gains. This rationality is supporting the normative view of the decision process by the Game theory.

An actor is playing within the environment he tries to manipulate. Reciprocally, the environment influences his choices. It is formalize through a group of actors interacting with each other through a game. Each actor follow the rational decision process. There is equality between each actor, they are in the same position within the environment. Each actor knows the rules of the game with the same intelligence. It is a game of perfect information because each one knows exactly what is going on at the same time for all the duration of the game.


Each actor picks a decision. It defines a strategy, as a result of this joint choice. The result is a reward or a punishment for each actor, the payoff.

It is represented with a matrix :


To simulate the interaction between the actors, you pick a row (A1 or A2) as the actor A’s choice, an a column (B1 or B2) as the actor B’s choice at the same time. As a consequence, each one has the same level of knowledge of the situation, neither knows when choosing what the other has picked. The number  is the amount that actor A gain, if it is positive, or lose if it is negative. It is the relative gain of the game, it is the value of the game. It is a zero sum game because what an actor gain is what the other lose.

An equilibrium situation is a stable outcome of the game associated with a strategy which maximize the gains of each actor. It is considered stable because if an actor unilaterlly picks another choice to increase its gain, he changes the strategy and it will decrease the gain of the other actor.

The strategy outcome is an equilibrium if neither actor gains by changing strategy unilaterally. Such an equilibrium situation is easy to find.

Since B would choose the minimum value of any row, A should choose the maximum value of these values. This value is called the maximin and it is the very least that A can be sure of getting. B should choose the column that minimizes these maxima. That outcome is called the minimax.

The payoff associated with an equilibrium point is the smallest in its row and the largest in its column. For the preceding payoff matrix, 0 is the equilibrium value of the game.

Another technic is to eliminate dominated strategies. A strategy dominates if an actor’s payoff with another choice is always at least as much as that of other actor choice and at least some of the time actually better than B’choice. The only undominated strategy is the equilibrium one.