Penned by – Shivani Kotak and Dhvani Kaneria
Have you ever had this urge to know about your opponent’s strategy in a game?
Firstly, let us understand what Game Theory is, so, Game Theory is the branch of mathematics concerned with the analysis of strategies for dealing with competitive situations where the consequence of a participant’s choice of action depends crucially on the actions of other participants?
Now, to put it easily, let’s understand it using an example.
Let’s say, two people are arrested for a particular crime, and the police are uncertain which person committed the crime, and which person was assisting the crime. Each is given a choice: to remain silent or to tell the truth. The possible outcomes are as follows:
- Both remain silent → they are both soon released.
- One of them betrays the other → the betrayer goes free and the other is imprisoned.
- Both betray each other → they both are held for a shorter time.
Now, the best option for any prisoner who wanted the least of imprisonment is to betray the other one.
Try as many combinations, you will get a shorter sentence when you betray, comparatively.
In some two-person, two-strategy games, there are combinations of strategies for the players that are in a certain sense “stable”. This will be true when neither player, by departing from its strategy, can do better. Two such strategies are together known as a “Nash equilibrium”. Nash equilibria do not necessarily lead to the best outcomes for one, or even both, players.
After learning the fundamentals of game theory, we attempt to understand it better by utilizing the historical example of the Cuban missile crisis. In that case, the “players” being studied were the United States and the Soviet Union. The Cuban missile crisis was the product of a Soviet attempt in 1962 to nuclear−armed ballistic missiles in Cuba, just 90 miles from the U.S. shore. These missiles were efficient enough to hit a large portion of the United States.
The US now sought the quick removal of Soviet missiles, and authorities in the US assessed two options to accomplish this goal:
- A Naval Blockade over Cuba(B)
- A “Surgical” Air Strike over Cuba(A)
The alternatives thought by Soviet authorities were:
- Withdrawal of their missiles(W)
- Maintenance of their missiles(M)
|Soviet Victory, U.S. Defeat|
|States (U.S.)||Airstrike(A)||U.S. Victory, Soviet Defeat|
4=best; 3=next best; 2=next worst; 1= the worst
Nash equilibria in bold
Both sides had more proposals than the two possibilities presented, and various modifications on each. The Soviets, for example, sought the withdrawal of American missiles from Turkey in exchange for the withdrawal of their missiles from Cuba, a demand that the US publicly ignored.
Let us examine these policies and outcomes in better detail:
- BW: The U.S. blockades Cuba and the Soviet Union withdraws its missiles. This approach is unstable since both players have a reason to switch to more aggressive tactics.
- AW: If the U.S. were to change its strategy to the airstrike, the play would move to (4,2).
- BM: If the Soviets were to change its strategy to maintenance, the play would move to (2,4).
- AM: If the players are facing the mutually worst-case scenario of (1,1), that is, nuclear war, both would want to avoid it, rendering the strategies connected with it unstable.
This classic game theory structure gives us no knowledge about which outcome would be chosen because the table of payoffs is symmetric for the two players. This is a common difficulty in interpreting the results of a game-theoretic analysis, where more than one equilibrium position can arise.
Nevertheless, most observers of this crisis believe that the two superpowers were on a collision course. They also agree that neither side was inclined to choose an irreversible technique.
 and 
Although the United States “won” in one way by convincing the Soviets to withdraw their missiles, Premier Nikita Khrushchev of the Soviet Union secured a promise from President Kennedy not to attack Cuba, implying that the end outcome was a type of compromise. This case could be better portrayed by sequential bargaining – a structured form of bargaining between two participants, in which the participants take turns in making offers.
This blog was only able to sketch the fundamental notions of game theory to analyze some of their philosophical dilemmas and challenges. To clearly understand game theory, however, formal treatment is required. Game theory is a considerably more complex topic; here are some resources to help you grasp it better: